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FULL PROPOSAL TO DEVELOP A

PhD IN MATHEMATICS EDUCATION AT THE

UNIVERSITY OF MASSACHUSETTS DARTMOUTH

For Off-Campus Review Last Revision: January 15th 2009

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TABLE OF CONTENTS

LIST OF TABLES.................................................................................................................... iii LIST OF FIGURES ....................................................................................................................v 1. PROPOSAL DEVELOPMENT ..............................................................................................1

1.A Introduction, Background, and Process for Developing the Program..............................1 2. PURPOSE AND GOALS........................................................................................................3

2.A Program Link with Campus Mission Priorities...............................................................3 2.B Program Purpose............................................................................................................3 2.C Learning Objectives: Knowledge and Skills to be Acquired by Program Graduates........6 2.D Strategies for Assessing Graduates’ Skills and Ongoing Program Quality and Effectiveness...........................................................................................................................8 2.E Measures or Benchmarks to Determine the Accomplishment of Program Goals.............9

3. NEED FOR THE PROGRAM ..............................................................................................11 3.A,B Evidence of Student Demand and Current Career Opportunities...............................11 3.C Relationship to Other Existing Programs......................................................................13 3.D Survey Findings on Quality and Needs of Proposed Program.......................................15

Survey Response Set A: Summary of Respondents interested in program..........................15 Survey Response Set B: Summary of Respondents who are Professionals in Mathematics Education (e.g. Professors) ................................................................................................17

4. CURRICULUM....................................................................................................................19 4.A Complete Description of the Curriculum......................................................................19 4.B Academic Integrity and Subject Area Coverage ...........................................................20 4.C Course Categories and Sequencing ..............................................................................20

Year 1 ...............................................................................................................................23 Year 2, semester one .........................................................................................................23 Year 2, semester two .........................................................................................................24 Year 3 ...............................................................................................................................26 Year 4 ...............................................................................................................................27

4.D Course Descriptions.....................................................................................................28 4.E Credits to Complete Program and Other Graduation Requirements ..............................36 4.F Certification, Licensure, and Specialized Accreditation................................................36 4.G Independent Work and Internships...............................................................................36 4.H External Advisory Committee......................................................................................37

5. FACULTY............................................................................................................................38 5.A Current Faculty and additional positions allocated to the program................................38 5.B Other Instructional Resources ......................................................................................39

6. STUDENTS..........................................................................................................................40 6.A Estimated Enrollment First Year and at Full Implementation .......................................40 6.B Students to be served ...................................................................................................41 6.C Admission criteria........................................................................................................41 6.D Expected Time to Graduation and Projected Degree Completion Rates.......................44 6.E Transferability of Credit and Articulation Agreements ................................................44

7. ADMINISTRATION AND OPERATION............................................................................47 8. RESOURCES .......................................................................................................................49

8.A Projected Student Enrollments and Necessary Faculty .................................................49 8.B Graduate Assistantships: Teaching/Research Assistantships.........................................49

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8.C Infrastructure: Equipment, Facilities and Library .........................................................51 8.D Field and Clinical Resources........................................................................................53 8.E Revenue/Cost Model....................................................................................................53

9. EXTERNAL REVIEW .........................................................................................................57 9.A, B Report of the External Review Team, Institutional Responses .................................57

10. REFERENCES ...................................................................................................................59 APPENDIX A: LETTER OF INTENT .....................................................................................61 APPENDIX B: SURVEY DATA..............................................................................................65

Survey Set A: Prospective students .......................................................................................65 Survey Set B: Peer-Evaluation ..............................................................................................72

APPENDIX C: LETTERS OF SUPPORT/EVALUATION ......................................................77 APPENDIX D: EXTERNAL ADVISORY BOARD OF KAPUT CENTER .............................89 APPENDIX E: FACULTY CURRICULUM VITA ..................................................................95 APPENDIX F: REPORTS OF EXTERNAL EVALUATORS, INSTITUTIONAL RESPONSES...............................................................................................................................................135

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LIST OF TABLES Table 1. Enrollment Projections ................................................................................................40 Table 2: Faculty Responsibilities...............................................................................................49 Table 3: Revenue from Program up to Steady State (AY 2009-AY2012) ..................................53 Table 4: 4-Year Budget of the Proposed Mathematics Education PhD Program .......................54 Table 5. Comparison of Income and Expenses: Years 1-4 .........................................................55

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LIST OF FIGURES

Figure 1. Program of study........................................................................................................22 Figure 2. Ethnicity of respondents.............................................................................................65 Figure 3. Present occupation of respondents..............................................................................65 Figure 4. Type of career respondents aim to pursue...................................................................66 Figure 5. Interest in pursuing a doctoral program in math education..........................................66 Figure 6. Interest in pursuing doctoral program in math education at UMass Dartmouth. ..........67 Figure 7. Ranking of features of proposed program...................................................................68 Figure 8. Rating of factors in choosing a doctoral program........................................................69 Figure 9. Importance of a research assistantship........................................................................70 Figure 10. Importance of a teaching assistantship......................................................................70 Figure 11. Respondents’ opinion of how innovative the program is based on its features ..........71 Figure 12. Respondents’ opinion of working on research projects through the Kaput Center. ....71 Figure 13. Age of respondents...................................................................................................72 Figure 14. Present occupation of respondents. ...........................................................................72 Figure 15. Ranking of features of proposed program.................................................................73 Figure 16. Residents’ opinion of how innovative program is based on its features.....................74 Figure 17. Respondents’ opinion of working on research projects through the Kaput Center. ....74 Figure 18. Extent to which respondents would recommend a doctoral program in math education

at UMass Dartmouth. ........................................................................................................75

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1. PROPOSAL DEVELOPMENT

1.A Introduction, Background, and Process for Developing the Program

The PhD in Mathematics Education at UMass Dartmouth is the result of many years of

research and development originally pioneered by Professor James Kaput. Many research

programs that are now sustained investigations were inspired by his work. The James J Kaput

Center for Research and Innovation in Mathematics Education (hereafter called the Kaput

Center), established at UMass Dartmouth in February 2007 has become a core resource for the

formulation of a PhD program.

The goals and mission of the proposed PhD program are synergistic with the operation of this

Center: to foster the spirit of innovation. It is this essence that we wish our doctoral students to

be part of and learn from in their educational experience at UMass Dartmouth.

Over the last 10 years, UMass Dartmouth has focused on building faculty strength in

Mathematics Education as a core research area and to provide the basis for a signature doctoral

program capable of advancing the mathematics education as a field of inquiry and addressing the

acute shortage of highly qualified mathematics education researchers in our higher education

institutions and relevant knowledge-based industries. This proposal is the result of deep thought

by the core faculty and consultation with many constituencies such as teachers and teacher

educators throughout Massachusetts, faculty and staff from the Kaput Center, its Research

Advisory Board, as well as several universities and major research institutes here in the United

States and abroad. A needs survey of educators and students was conducted to assess the demand

and quality of our proposed program. We also include testimonials from faculty of major

research institutions and universities asked to critically evaluate our program proposal.

In December 2004, under the leadership of Chancellor Professor James Kaput, the

Mathematics Education Faculty submitted to Chancellor Jean MacCormack a Letter of Intent to

Submit a Preliminary Proposal for a Ph. D. Program in Mathematics Education (Appendix A)

describing their initial plans for an innovative Ph. D. program. Approval to proceed with a

formal preliminary proposal was granted by the administration in April 2005. The proposal of

this program was originally to be coupled with the proposal of a new Mathematics Education

Research Center. The Kaput Center for Research and Innovation in Mathematics Education was

created first in February 2007 with the support of Chancellor MacCormack and approval by

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UMass President Jack Wilson. We now propose the creation of a PhD program that is to be

coupled with the work done at the Kaput Center as originally envisioned.

In December 2007 a PhD Planning Committee was established (Drs. Hegedus, Blanton,

Moreno). Shortly after that, Provost Anthony Garro and Associate Vice Chancellor Richard

Panofsky granted administrative approval to develop a full proposal. The proposal was reviewed

and approved by the Curriculum Committee of the newly established School for Education,

Public Policy, and Civic Engagement, the University Curriculum Committee and Faculty Senate.

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2. PURPOSE AND GOALS

2.A Program Link with Campus Mission Priorities

The goals and purposes of the PhD in Mathematics Education are firmly in line with the

mission of the University: “The University of Massachusetts Dartmouth distinguishes itself as a

vibrant public university actively engaged in personalized teaching and innovative research, and

acting as an intellectual catalyst for regional and global economic, social, and cultural

development.” It advances the university’s mission by creating an environment to conduct

research through collaboration with industry, research and academic institutions, and

practitioners of innovative mathematics education research at the national and international level;

and it will use best teaching practices in educating its students.

The Vision Statement for UMass Dartmouth includes an aspiration: “UMass Dartmouth

aspires to create additional Masters and Doctoral programs, with commensurate support, in

addition to enhanced technological capabilities for the delivery of our educational and outreach

programs.” In its doctoral emphasis, research basis that brings substantial support, and

innovative interest in pedagogy and instructional methodology, the proposed doctoral program in

mathematics education contributes substantively to accomplishing this vision. Furthermore, the

educational approach of the proposed program is founded in the high principles envisioned in the

opening paragraph of the university’s Vision Statement: “Within a climate that is inclusive,

open, and diverse, UMass Dartmouth will be the university of choice for students seeking high

quality liberal arts and science programs as well as professional academic programs that build a

foundation for civic responsibility, individual skills, and professional success.” Finally, the

proposed program supports the campus strategic plan’s call for a substantial change in emphasis

towards graduate and doctoral education and their accompanying campus basis in research and

creative activity.

2.B Program Purpose The PhD in Mathematics Education aims to build on the success and potential of existing

research programs at UMass Dartmouth, particularly those situated in the Kaput Center, and to

contribute to the campus’s mission to “develop graduate programs in areas of importance for our

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region” and “support sub-disciplinary graduate programs where departments already have

strength … and when there is a demand for graduates.”

During the program of study, students will complete a Masters of Science in Mathematics

Education as preparation for advanced doctoral work and the dissertation. Students will apply

and be accepted only into the doctoral program and not for a separate master’s degree.

The primary aim of the proposed doctoral program is to produce stewards of the discipline,

as defined by The Carnegie Foundation for the Advancement of Teaching in its Initiative on the

Doctorate: “to educate and prepare those to whom we can entrust the vigor, quality, and integrity

of the field.” Moreover, its explicit interdisciplinary approach, that has deep connections

nationally and internally and reflects cutting-edge technological innovations in program delivery,

is intended to address specific challenges identified by the Carnegie Initiative (Walker, Golde,

Jones et al., 2008). These challenges involve new technologies in “altering and accelerating the

way new knowledge is shared and developed” (p. 2), a vision of a global marketplace for

scholarship, and recognition that “much of the most important, path-breaking intellectual work

going on today occurs in the borderlands between fields, blurring boundaries and challenging

traditional disciplinary definitions” (p. 2). Our program pays particular attention to how

curricular and research components can be integrated systematically to connect students’

learning to faculty scholarship and thereby provide authentic learning experiences that produce

graduates with strong research skills. We are guided by a metaphor of apprenticeship as a

“theory of learning and a set of practices that are widely relevant” (p. 91); the activity of

apprenticing encompasses and strengthens all curricular and research components of the doctoral

program.

Our program and the Kaput Center share common goals and approaches. Much more than a

collection of projects, the Center is an intellectual community that fosters “intellectual risk

taking, creativity, and entrepreneurship” (see Walker et al., 2008, p.11) and, in the spirit of the

Carnegie Initiative’s formation of scholars, offers incubation through which a doctoral program

can provide “real partnerships between faculty and students, habits of respect for and interest in

one another’s work, and the lively exchange of ideas in which new knowledge is formed and

transformed” (p. 11). The cutting-edge funded research of the Math Ed faculty within the Center

provides a core strength for the proposed program and establishes its uniqueness in comparison

with other doctoral programs in the Commonwealth of Massachusetts and many other

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institutions, as do the Kaput Center’s affiliations with academic institutions and non-academic

partners (e.g., Technical Education Research Centers (TERC), the Educational Development

Center (EDC), and SRI International).

Massachusetts is a highly appropriate location in which to start an innovative mathematics

education doctoral program. The Commonwealth of Massachusetts enjoys one of the greatest

concentrations of research, development and expertise in mathematics and science education in

the nation and attracts a significant concentration of federal research and development (R&D)

money in these fields. Historically, much of this funding has come to three independent R&D

organizations in the Boston area—The Concord Consortium, the Educational Development

Center (EDC), and TERC—and our faculty have significant professional relationships with each

of these as well as other organizations. Within the University of Massachusetts system, it is

UMass Dartmouth that has had the strongest links with these R&D institutions, largely through

the sustained work of the mathematics education faculty building upon the pioneering work of

James Kaput. Massachusetts’ citizens benefit greatly from its unparalleled R&D leadership in the

medical sector. Our program will help build the bridges between the region’s robust R&D

accomplishments to actual, practical benefits in the education of our citizens.

The interests of the Math Ed faculty and of the 80+ member Research Advisory Board of the

Kaput Center cover grades K-20 and a wide range of contemporary issues in mathematics

education: Algebraic thinking grades K-20, improving mathematics teaching through district-

wide collaboration, integrating new technological innovations (e.g., wireless connectivity and

haptic devices) in K-12 mathematics classrooms and its impact on participation and motivation,

developing proof-based reasoning from elementary through undergraduate classrooms, evolution

of symbol use and symbolic thinking in mathematics, theories of mathematical learning and

teaching from multi-disciplinary perspectives, and efficacy studies and diffusion of innovation.

A majority of these interests are being explored through projects funded by the National Science

Foundation and the US Department of Education (approx. $5.5m funded projects in progress

with additional research proposals in preparation or under review to federal and private agencies,

including several Foundations (e.g., Kauffman, MacArthur, Toyota). This level of research

funding (to be distinguished from professional development and service-oriented funding) would

be unusual at a Research-I university and is unprecedented at a regional university of our type.

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This level of consistent funding will accelerate in the presence of a PhD program and the

resulting increase in the size of our research community.

Mathematics education is crucial for our nation and globally. As a field of research, it

developed in the latter half of the 20th century out of a disconnect that had become apparent

between the discourse of teaching and student learning. In the need to reformulate what is taught,

as well as how and why it is taught, mathematics education plays an important role in our

society. It is transforming the field of curricular design and development and applying new

learning tools. Now that the chasm between teaching and learning mathematics has emerged as a

formal area of study, universities have offered graduate programs to develop the new field and

produce its future teachers and scholars. There has been a new recognition of the multi-versal

and dynamical nature of knowledge production.

The University needs to embrace the future with scientific education as the sustaining

foundation of what has been called the century of information and knowledge. Globally and

nationally, we have the critical ability to transfuse scientific and technological developments into

our educational realities. Heretofore lacking in technology-rich environments and teachers

trained in effective pedagogies, today’s school culture requires the gradual but deep re-

orientation of its practices to gain access to powerful ideas of mathematics and to new habits of

mind including exploring, modelling, handling of information, and the ability to systematize. It is

possible to cultivate powerful ideas that generate different levels of mathematical thinking both

at the level of the classroom and at the level of the global educational system, to create an open

system responsive to the multidimensional influences of its social and cultural environment.

A doctoral program in Mathematics Education at UMass Dartmouth would offer innovative

answers to these educational needs by providing future mathematics educators with the

educational infrastructure and advanced research training to become researchers and leaders in

the field of mathematics education.

2.C Learning Objectives: Knowledge and Skills to be Acquired by Program Graduates

The program is designed to attract and educate students of diverse backgrounds for

employment in a variety of educational institutions as well as scientific institutions, industries

and federal agencies. It focuses on interdisciplinary perspectives within mathematics education

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research. Our graduates will be highly competitive in today’s marketplace for educational

scholars within a wide range of actual employment classifications. Furthermore, our PhD

candidates will enjoy multiple opportunities for enhancing traditional scholarly training through

participation in such practical academic endeavors as publishing and organizing lectures and

colloquia.

The doctoral program will provide students with the knowledge and skills to

(a) re-construct, appropriate, and develop mathematical knowledge;

(b) explore different approaches that emerge from the study of the research literature in the

field of mathematics education and related disciplines; and

(c) write original research that represents their own contribution to knowledge.

Graduates of the program should be able to produce original research in the field with deep

social and cultural commitments. The PhD program is designed to build the intellectual skills

that our graduates will need to utilize new and future technologies and communication

infrastructures and to develop them into knowledge environments. Our graduates should be able

to use critical thinking to deal with the adaptation, adoption, and transformation of knowledge

and information from other cultures and earlier times. They will formulate and design solutions

to complex educational problems.

The PhD in Mathematics Education is also designed to create a focused track of study over 4

years to build skills in the following critical areas:

(a) the nature of scientific inquiry in mathematics education and related disciplines including

the cognitive sciences and the learning sciences,

(b) appropriate methods of research design regarding data collection and analysis,

particularly focused on contemporary qualitative and quantitative methods (e.g. HLM,

discourse analysis, micro-analytical video analysis)

(c) the production of new researchable questions especially on the boundaries of particular

disciplines (e.g. learning sciences), and

(d) the ability to design and conduct a research study with unique findings to advance the

field of mathematics education.

This experience will involve a continual and iterative research process beginning in the first year

of study that culminates in a PhD dissertation at the end of 4 years. The program involves a high

degree of required courses supplemented by specific electives.

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The program of study that students will complete consists of 72 credits that include 18 credits

of introductory coursework to develop students’ knowledge of research tools, methodologies and

theories in mathematics education research, 18 credits of preparatory coursework to refine and

focus students’ understanding of the research process and theory building, and 36 hours of

advanced doctoral coursework including dissertation research.

2.D Strategies for Assessing Graduates’ Skills and Ongoing Program Quality and Effectiveness

We will employ three main strategies over the first 5 years of the program to ensure effective

program delivery and to refine its efficiency. These strategies are:

(1) Student E-portfolios,

(2) Faculty Evaluation and Assessment Procedures, and

(3) Internal and External Advisory Councils.

Each strategy will contribute to our effective operation of the program to accomplish a

prescribed set of learning outcomes and program objectives.

Student E-Portfolios: Students will construct e-portfolios of their learning experiences across

the course of the program via an on-line proprietary database developed by Kaput Center faculty

and staff (incorporating PhP/MySQL and a Mac XServe configuration) to allow PodCasts and

workflows from multi-media sources. Students will upload assessments of individual courses and

end-of-year program evaluations and apply them to a set of expected learning outcomes outlined

by the core program faculty. Students will also upload extramural activities such as papers or

presentations that they have developed with or without the support of faculty, as well as other

artifacts that they count as evidence of their learning. The resulting reflections and artifacts will

be assessed by faculty and other evaluators.

Faculty Evaluation and Assessment Procedures: The Faculty will create course and end-of-

year learning outcomes and objectives, which will be used to establish a survey instrument for

students and external evaluators to use as an evaluation to measure of achievement of program

outcomes. Students will react to these criteria in their e-portfolios, while faculty, administrators

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and evaluators will be able to export these as reports from the e-portfolio portal. Faculty will also

use assessment procedures for each of the major milestones of the program, such as a

preliminary qualifying examination at the end of Year 2, a dissertation proposal defense

(examined by the program committee at the end of Year 3), and a final defense of the dissertation

(end of Year 4).

Internal and External Advisory Councils: Annually, faculty reviewing the students’ e-

portfolios and their performance at progression milestones will summarize results for review by

the Dean of the School of Education, Public Policy, and Civic Engagement, who will report them

to central administrators such as the Associate Provost for Graduate Studies and the Provost;

sample student e-portfolios may be provided. Focus groups of PhD candidates will provide

feedback. An Executive Advisory Council (which will include members of the Kaput Center

Advisory Board) will receive summary reports on a bi-annual basis to assess whether the

program is meeting its expected goals and may also view sample student e-portfolios. These

three core strategies supplement other methods in use, such as traditional peer-evaluation, end-

of-year Examination Board meetings (where all relevant teaching faculty meet to assess student

achievement and assess grades), and the five-year cycle of AQAD external review procedures.

Results from student surveys of future employment will be added to their portfolios after

graduation as we continue to track whether our students enter into the career trajectories we

propose here.

2.E Measures or Benchmarks to Determine the Accomplishment of Program Goals

Measures or benchmarks designed to determine accomplishment of program goals were

identified around 5 key areas: Faculty; Students; Research; Program of Study; and Resources.

Indicators for each of these areas include the following: Faculty

Faculty members meet the requirement of the institution for graduate education with all faculty members holding the earned doctorate.

Faculty members conceptualize and implement productive programs of research and scholarship.

Faculty members design and deliver high quality instruction synergistically linked to current research as well as their own particular research programs.

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Faculty members create an environment in which mentoring, socialization of students, and the existence of a community of scholars is evident.

Students

Students are selected from a pool of highly qualified applicants in accordance with admission criteria consistent with those of the institution.

Students actively develop research skills and knowledge of the field to prepare them as “stewards of the discipline.”

Students develop an expertise of scholarship through participation in authentic learning experiences.

Research and Scholarship

Research is an explicit component of the mission of the institution and a core feature of the program design.

Strong research programs, developed over a number of years and now facilitated through the Kaput Center, exist to support the goals of the program.

Faculty will maintain a level of scholarly productivity commensurate with the needs of the program.

Program of Study

The program of study reflects the interdisciplinary nature of mathematics education, drawing on multiple fields of knowledge to strengthen scholarship.

Core content is provided through an approach that integrates curriculum and research activity.

Student scholarship is developed through progressive research experiences based on collaborations with faculty at the host institution as well as partner institutions.

Resources

Faculty resources are available to initiate the program, and faculty resources will be added to maintain the program and accomplish its goals.

Technical and support services are available and accessible to faculty and students. Library and database resources are sufficient to support the program. Space and equipment (e.g., computers; seminar rooms; study and social areas) are

sufficient.

Faculty will collect data on these indicators and implement assessments for annual review and

improvement.

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3. NEED FOR THE PROGRAM

3.A,B Evidence of Student Demand and Current Career Opportunities

The need for doctoral programs in mathematics education is well documented. In the last

several decades, a convergence of research—embodied in international perspectives on

mathematics education (see Wirszup & Streit, 1987, 1989, 1993), the rise of cognitive science

and social, situated learning perspectives over behaviorism (e.g., Gardner, 1985; Greeno,

1989)—and a growing consensus for reform in teaching and learning K-16 mathematics—as

outlined in documents such as the Curriculum and Evaluation Standards (NCTM, 1989) and the

Principles and Standards for School Mathematics (NCTM, 2000)—has led to the emergence of

mathematics education as a field of inquiry in its own right for which faculty are hired. In a

recent study by Reys (2006) 90% of institutions reported hiring at least one mathematics

education faculty person during the last 5 years. However, doctoral degree production in

Mathematics Education has not met demand; a study published in 2001 showed that, at that time,

the number of doctorates awarded has not increased significantly (Reys & Kilpatrick), with

particular implications, for example, for the supply of mathematics education faculty available to

administer doctoral programs (Reys, 2000, 2002). Furthermore, some faculty positions are not

filled; for example, in 2005-2006, over 40% of Institutions of Higher Education (IHEs) were

unsuccessful in hiring mathematics education faculty (Reys, 2006). In brief, there is, still, an

inadequate national infrastructure of doctoral programs (Reys, Teuscher, Nevels, & Glasgow,

2007).

The need for doctoral education identified at a national level is consistent with findings from

our own needs assessments regarding a doctoral program in mathematics education. Informally,

the Math Ed faculty receive requests or inquiries about a potential PhD program on average once

a month since its “intent to propose a Math Ed PhD” was posted on its group’s website.

Formally, we have conducted a needs analysis surveying over 400 people in schools,

universities, and research institutions locally (in MA and RI) as well as nationally and

internationally. In particular, the survey assessed need from potential students as well as quality

in the proposed program by advisors, school administrators, senior researchers and university

faculty. (See 3.D for details of this assessment.) This need for Mathematics Education in IHEs is

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coupled with a growing demand for highly-qualified educational researchers in institutions and

industry who have a deep knowledge of mathematics, educational theory, and methodology and

can participate in innovative research programs.

A doctoral program at UMass Dartmouth will address an urgent national problem by

preparing graduates for a variety of essential careers in a variety of scientific institutions,

industries, and federal agencies, as well as the education sector. Moreover, because the proposed

program focuses on interdisciplinary perspectives in mathematics education research (rather than

administration-oriented programs such as educational leadership in school systems), we expect

our graduates to be highly competitive in today’s marketplace for educational scholars in the

field of mathematics education.

We anticipate that many students will come from the ranks of teaching practitioners (e.g., at

elementary, secondary, or 2-4 year college levels) as well as education-related fields (e.g.,

curriculum design, research centers). As they proceed through our program, many will advance

to different careers or career levels, while others will return with a new expertise and

productivity to an existing career. The primary career trajectories that our program specifically

focuses on supporting are:

1. Entering Higher Education and in particular the Professoriate (including 2-4 year

colleges)

2. Research Scientists in Research Institutions/Think-Tank Centers

These two career trajectories are similar in nature and preparation but can differ in the types

of job responsibilities (e.g. teaching). Our proposal describes the type of preparation that is

necessary for researchers and professors in today’s society and how we can successfully provide

such an educational experience. We also present evaluations of the innovative nature of the

program and the best practices that we are proposing to meet the needs of students on these

particular career trajectories. These include letters of support, surveys, and an external review

team’s evaluation.

In addition, we believe that students on the program could successfully graduate into other

more applied research careers, which include but are not limited to:

1. Advanced agency or industry settings focused on improving educational attainment; and

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2. Research and Development in the design and implementation (grades K-20) of advanced

learning technologies and associated resources.

3.C Relationship to Other Existing Programs Competition: There are few, if any, programs across the United States that have the

integration with industry research and development partners that we propose, and few, if any,

that bring the ideas of distributed, technological environments and apprenticeships to their

doctoral training programs in the ways we propose. Thus, we feel that in terms of quality and

quantity our proposed doctorate will be nationally significant.

Uniqueness: Our primary aim is to produce stewards of the discipline of mathematics

education: well-educated and trained researchers and scholars who can develop our subject in

breadth and depth to meet the mathematics education needs of the coming century. The proposed

doctoral program:

1. Is intended to be less oriented towards serving schools, districts and practice directly (an

orientation already served by existing EdD programs in the UMass system) and strongly

oriented towards careers in research, scholarship and development, and

2. Will deliberately and systematically draw intellectual resources from across departments,

colleges, campuses, and even university boundaries, to form faculty teams that embody a

range of competencies and interests rarely, if ever, available within any given university

unit.

3. Will indirectly bring improvements to schools and to society by expanding the theoretical

and practical bases for mathematics education.

As we will show in the section on curriculum, we offer a unique process for embedding

research projects within the curriculum; in addition, we will offer our students sustained

interaction with international scholars and research projects in the Kaput Center; these elements,

too, create a difference between our proposed program and those offered in other places.

We list here 5 potential competitors in the UMass system or the Massachusetts Higher

Education system and an explanatory note on differences from our proposed programs:

1. EdD in Mathematics and Science Education, Department of Teacher Education and

Curriculum Studies, School of Education, UMass Amherst

(http://www.umass.edu/education/academics.html). The Mathematics, Science and Learning

Technologies doctoral program provides a practical approach enabling students to use new

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research findings to improve the learning and teaching of mathematics and science from pre-

school to higher education.

2. EdD in Mathematics and Science Education, Graduate School of Education, University of

Massachusetts Lowell (http://www.uml.edu/gse/Programs_of_Study/Doctorate.html). Their

doctoral program focuses on evaluation and the development of concepts in mathematics and

science.

3. PhD in Mathematics, Science, Technology, and Engineering Education, Department of

Education, Tufts University (http://ase.tufts.edu/education/programs/research/MSTE.asp).

The doctoral program at Tufts is a broad, interdisciplinary program that admits no more than

5 full-time students per year focusing on theory and research on learning and development,

cognitive science, and the socio-cultural foundations of education. It is closest to our

program in design and intentions.

4 EdD in Curriculum and Teaching, Boston University

(http://www.bu.edu/sed/programssecondarymathematics.htm). Their program focuses on

preparation of students for leadership positions in school systems or postsecondary positions

in junior, community, or technical colleges, and in teacher training colleges and universities.

5. PhD in Educational Studies, Lesley University

(http://www.lesley.edu/offcampus/term/nphdsoe_edstudies.html). Their doctoral program is in

Educational Studies and not specifically in Mathematics Education Research.

A significant difference of our proposed program from many of these programs is that ours

will fundamentally focus on research in mathematics education. Unlike other programs, our

proposed program does not focus on broader areas such as Teacher Education or Policy

Education with math education as a sub-focus. While there are similarities to Tufts’ program, we

also have long-standing collaborations with Tufts (e.g., through research projects and our faculty

serving on graduate committees there) that do not necessarily place us in direct competition with

them. These programs also have different requirements (such as advanced mathematics courses)

that shape the potential focus of their programs and their pool of graduate students and

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differentiate it from ours. The kernel of our program is to focus on cutting-edge research theory

and methods in mathematics education research.

3.D Survey Findings on Quality and Needs of Proposed Program Over 400 people were contacted by email to complete a survey compiled by researchers in

the Kaput Center at UMass Dartmouth, approved by the UMass Dartmouth Internal Review

Board in February 2008. In this original cohort, 31% were local K-12 teachers, 17% were

members of the Kaput Center Advisory Board, and 52% were Heads of Math, Math Ed, and Ed

Departments at Universities & Colleges in Massachusetts and Rhode Island. Respondents belong

to just one of these groups.

Sixty people responded (65% of respondents are potential students, while 35% presently

advise or teach in a PhD program elsewhere). Responses by potential students are categorized

under Survey Response Set A. Responses of those in the profession comprise a peer-assessment

of the quality and attractiveness of the program; these are categorized under Survey Response

Set B. Representations of these datasets can be found in Appendix B. A preliminary copy of the

program with associated curriculum was available to all respondents on a website.

Overall, results show an anticipated demand for the proposed program by people from

various backgrounds. There is a majority of demand from the K-12 Education sector (some of

whom would seek to change careers). Moreover, the program is deemed innovative, with many

leaders in the field of mathematics education responding that the program and its particular

emphasis on the development of research scholarship would be significant and would attend to a

genuine need to increase numbers of researchers and professors in mathematics education.

Survey Response Set A: Summary of Respondents interested in program

We present a summary of the responses with relevant findings that supports the

establishment of the proposed program and in particular, possible expectations of incoming

students.

Demographics: The majority of the responses (51%) were between 26-41, and were presently

teachers (73%), graduate students (9%) or other professionals (9%). 36% were male and 64%

female. Such figures reflect the initial sample pool (i.e. largely teachers).

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Interests: The survey illustrated that respondents are interested in a wide variety of careers

that are aligned with our proposed career trajectories. Whilst a majority are interested in pursuing

teaching (it was not clear whether some meant K-12 or 2-4 year colleges, although through

personal communication we know of several potential students who would want to enter the

latter), many also wished to pursue careers in the professoriate (30%), administration, or another

field. 61% were interested in pursuing a doctorate in mathematics education (n=24), and of those

88% wished to pursue such a program here at UMass Dartmouth, equating to 21 people and our

potential initial application pool.

Assessment of Opportunities: We outlined a list of 6 main features that described the program

and asked respondents to rank their importance. In summary, a focus on fundamental issues and

cutting-edge research (particularly digital technologies and new curricular perspectives) and

authentic learning experiences (e.g. internships) were deemed most important and grant-writing

least important. We believe that it is part of the enculturation of a new researcher to understand

the demands and needs (such as external funding) that will become apparent as they complete the

program rather than before entering the program. So such responses are interpretable.

Beliefs: Respondents were asked how important a teaching assistantship and/or a research

assistantship was to them. These questions were not asked exclusively. Responses were similar

to both questions. 65% thought a teaching assistantship was important (with 31% responding it

was “Very Important”), and 72% thought a research assistantship was important (with 31%

responding it was “Very Important”). A covariance analysis illustrated that while respondents

who thought research assistantships and teaching assistantships were important (or very

important) were very similar, those who thought each type of assistantship was “Very Important”

were fairly distinct. In summary, about a third of our respondents deemed a teaching

assistantship necessary and equally a third thought a research assistantship was necessary. This is

reflected in our projected costs for the program, but please note that this survey was conducted

with no information about the eligibility or application procedure for these types of assistantships

and so should be treated as an attitudinal response more so than a needs response.

In summary, almost everyone responding (90%) in this survey set believed the program was

innovative and important (93%) that students would be working on research projects through the

Kaput Center.

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Survey Response Set B: Summary of Respondents who are Professionals in Mathematics Education (e.g. Professors)

Demographics: The majority of the respondents were 50+ (65%) with 62% Male and 38%

Female. 78% were professors or researchers in higher education or research institutions, with the

remainder being administrators or professionals in related fields. The majority of respondents

were from (R-1) Research Universities or major Research Institutions.

Important Features of the Program: Respondents were in total agreement that the program

had many important features but most noteworthy was that the program was a focused 4-year

program focused in developing research skills through authentic learning experiences. And

although grant writing and applied skills such as speaking in peer-reviewed venues were still

deemed important they were viewed as the least important feature of the program.

Evaluation: 94% of the respondents evaluated the program innovative based upon six

features used in assessing its importance (see appendix B for the full list). All respondents

believed that it was critical that the program worked closely with the Kaput Center (65% Very

Important; 35% Important) because of its innovative research programs investigating

foundational issues in mathematics education.

Peer-Recommendation: Finally, 94% of all respondents would recommend (59% “Highly

Recommend”) students or colleagues to pursue the proposed doctoral program in mathematics

education. Please note that many of the respondents would already have Masters students

working with them at their institutions.

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4. CURRICULUM

4.A Complete Description of the Curriculum The PhD in Mathematics Education falls into three distinct phases:

1. Introduction to mathematics education research,

2. Preparation Phase for advancement to advanced doctoral status, and

3. Production Phase of advanced courses and final dissertation.

At an appropriate level, all courses feature authentic learning experiences in research

institutions and projects, and an interactive thinking/writing process to develop cutting-edge

research and discovery as part of the student’s experience. Research scholarship thus pervades

the curriculum, uniting theory and practice. Technology is also embedded throughout: wherever

possible, courses will be blended with a variety of delivery methods, including on-line video

seminars, iTunesU/Podcasting, and active use of Blogs and Wikis, as part of the regular mode of

sharing and learning content and expressing evolving ideas in and around coursework. A central

Blog/Wiki will be available for students to interact and share their ongoing work outside of

classes.

Systematic use of electronic learning support technologies will form the basis for cumulative

evaluation of students’ learning and program success, as explained in Section 2.D of our

proposal on program evaluation. Thus, while it falls into distinct phases, with its supporting

technological infrastructure, research associates, and resources from the Kaput Center, the

program will offer a single coherent experience for students, bringing their learning in courses

and interaction outside courses into the development of a community of scholars who work

together to develop their own skills and become innovative and creative thinkers.

Because of the program’s central focus on the development of research scholarship, specific

attention will be given to the development of research ethics, including appropriate

acknowledgement of sources, proper protocols for conducting research on human subjects, the

process of institutional IRB approval, and institutional certification for conducting research (i.e.,

CITI certification). While research ethics will be addressed specifically in a Year 1 course (MAE

654), it will also be threaded implicitly throughout the program as students participate in

authentic learning experiences and, through this, are mentored in the practice of ethical policies

for conducting research.

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4.B Academic Integrity and Subject Area Coverage

Academic integrity of the program will be maintained through the administration of a strong,

connected program of coursework and research experiences that reflect the demands of the field

of mathematics education. In particular, the program has been designed to include relevant,

focused coursework that addresses foundational issues in mathematics education. Additionally, a

focus on the development of research skills and practices is threaded throughout this coursework

to support students’ transition from practice of research skills with supervision to independent

mastery of research scholarship. This is also evidenced in the design of the Introductory and

Preparatory phases of the program (Years 1 and 2) that culminate in the qualifying exam. In

particular, students will be mentored through Years 1 and 2 in the practices of research and will

demonstrate their skills in successful completion of the qualifying exam. Years 3 and 4 are

designed to support increasing autonomy in students’ ability to design and implement a research

study, culminating in the dissertation.

The instructional faculty are leaders in the field of mathematics education, and through their

established research programs and international connections with researchers through the Kaput

Center, we present a program that not only addresses contemporary issues but relevant research

paradigms and methodologies to address major and complex questions in the field today.

4.C Course Categories and Sequencing Figure 1 offers a schematic outline of how the program is designed for a full-time student to

complete the program in 4 years. While the specific sequencing of coursework may vary across

semesters within a particular year, the proposed coursework for a particular year is intended to be

invariant. For each element, we describe the individual components and rationale. In summary,

students will complete 72 credits that include:

18 credits of introductory coursework to develop students’ knowledge of research tools,

methodologies and theories,

18 credits of preparatory coursework to refine and focus students’ understanding of the

research process, and

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36 hours of doctoral work – 12 hours of doctoral coursework and 24 hours of dissertation

research advising to support and guide the production of the final dissertation.

The program is designed primarily to be a four-year program for full-time students. We have

incorporated specific elements, such as the formation of an identified cohort, intensive advising

of students as learning partners, the use of e-portfolios, and other community-emphasizing

features, specifically to encourage students to progress in a regular manner and make that

achievable. Part-time students or ABDs starting full-time jobs in their fourth year would be

permitted to complete their requirements up to but in no more than six years. Requests for

extensions will be considered on a case-by-case basis in line with the rules and regulations for

graduate study at the University of Massachusetts Dartmouth.

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Year Fall Semester Spring Semester 1 (Introduction) Introduction to Qualitative Methods

(MAE650) – 3 cr. Introduction to Quantitative Methods (MAE651) – 3 cr. Introduction to Mathematics Education Research (MAE652) – 3 cr.

Theories of Mathematical Learning (MAE653) – 3 cr. Research Seminar – Capstone Course (MAE654) – 3 cr. Developing Research Skills Pt.1 (MAE655) – 3cr.

Total 9 credits 9 credits 3 Topics in Mathematics Education Research (MAE660-679) – 9 cr.

Research Seminar – Capstone Course (MAE681) – 3 cr. Developing Research Skills Pt.2 (MAE682) – 3 cr. Qualifying Exams

2 (Preparation)

Authentic Learning - Internship (MAE680) – 3 cr.

Total 9 credits (average) 9 credits (average)

3 (Production) 2 Advanced Doctoral Courses from MAE750-769 – 6 cr. Dissertation Research (MAE 772) – 3 cr. Select Dissertation Committee Chair

2 Advanced Doctoral Courses from MAE750-769 – 6 cr. Dissertation Research (MAE 773) – 3 cr. Dissertation Proposal Defense (end-of-year)

Total 9 credits 9 credits 4 (Production) Dissertation Research (MAE774) – 9 cr.

Dissertation Research (MAE775) – 9 cr. Final Oral Defense (end-of-year)

Total 9 credits 9 credits Grand Total 36 credits 36 credits

Figure 1. Program of study

Year 1 will require core courses to be successfully completed; there is no variation in the

offerings. Year 2 would allow some choice of topics within the courses outlined below. Upon

completing the 36 credits in Years 1 and 2, students are eligible to take the qualifying exams to

enter the advanced doctoral program. (Note that students will receive an MS in Mathematics

Education upon successful completion of the qualifying examination and coursework for Years 1

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and 2.) Successful completion of coursework requires that the student have a cumulative GPA

not less than 3.0.

Students who enter with a bachelor’s degree will complete the entire sequence. “Advanced

Standing” can be given to applicants who enter with an advanced degree in an appropriate

background (e.g., MS/MA in Mathematics Education, Mathematics, a related science, or an

MAT with mathematics specialization); Advanced Standing permits the waiver of up to 24

credits within first and second year courses. A decision to offer Advanced Standing is made

along with other admissions decisions; thus, in the admissions approval process for each

individual applicant, it will be evaluated by the Math Ed Program Director/Graduate Committee,

the School Dean, and the Associate Provost for Graduate Studies. Amounts of advanced standing

awarded and the specific courses waived will reflect the level and curriculum coverage of the

previous.

Following the successful completion of the qualifying exams for the Preparation phase, the

candidates will start their advanced doctoral coursework and dissertation. Qualifying

examinations that are not passed initially may be repeated once.

The following courses will be required or offered in Years 1-4.

Year 1 6 core requirements

MAE650 – Introduction to Qualitative Methods

MAE651 – Introduction to Quantitative Methods

MAE652 – Introduction to Mathematics Education Research

MAE653 – Theories of Mathematical Learning

MAE654 – Research Seminar.

MAE655 – Developing Research Skills Part 1.

Year 2, semester one Students will be offered three topics courses from the following list as they are developed. (NB.

Courses offered will be subject to student demand and needs)

MAE660 – Foundational Issues in Mathematics Education

MAE661 – Research on Mathematics Teacher Education Part 1

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MAE663 – Developing & Implementing Mathematics Curriculum

MAE664 – Research on Technology in Mathematics Education

MAE665 – Design Principles for Technology in Mathematics Education

MAE666 – Frameworks for Research Analysis

MAE667 – Research in Elementary Grade Mathematics

MAE668 – Research in Middle & High School Mathematics

MAE669 – Research in Undergraduate Mathematics Education

MAE670 – Developing Theory

MAE679 – Topics in Mathematics Education

We are also developing core mathematical courses that address a K-20 approach to the following

mathematics topics:

(1) Algebraic thinking,

(2) Mathematics of Change and Variation

(3) Mathematical Proof

(4) Geometric reasoning

(5) Discrete Structures

(6) Number Theory

(7) Mathematical Problem Solving

Our focus in these courses is on the development of smart mathematical knowledge that, more

importantly, develops students’ understanding of the use and application of this knowledge in

mathematics education. Students admitted conditionally based on a deficiency in their

mathematical preparation will be required to take up to 12 credit hours in addition to existing

program course requirement to meet these deficiencies.

There will never be more than 20 electives shown in the graduate catalogue at one time.

Year 2, semester two MAE680 – Authentic Learning (Internship).

MAE681 – Research Seminar.

MAE682 – Developing Research Skills Part 2.

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Advising is important, and students interrelate closely with faculty at all levels of study.

Students will choose faculty in the first 2 years to advise them on their research experiences that

culminate in the qualifying exam. More than one faculty member can thus serve an introductory

student, and the faculty member(s) may be different than the student’s Dissertation Advisor

selected for the Production phase for Years 3-4. In addition, every student will be assigned a

Graduate Program Advisor from the STEM department (who will mentor and assist in

scheduling courses and monitoring sound progress overall). We expect that work in the first two

years will develop a student’s potential to conduct research and develop the skills necessary to

complete their final dissertation. This is assessed in the qualifying exams. At the Production

stage in Years 3-4, students need to choose one faculty member as Dissertation Advisor for the

remainder of the program (who teaches Dissertation Research MAE77X to that student).

There will be some flexibility in when students can conduct their internship (MAE 680) vs. a

topics course. The internship could be done in the Fall or Spring, or for some who it might be

possible to conduct this experience during the summer (particularly for those students who want

to travel out-of-State or be part of an International Exchange project). Internships will be

flexible scheduled on a case-by-case basis with the representative course (MAE 680) being

offered all year round.

As part of their coursework (specifically, MAE 655, 682 and, depending on the student’s

focus, MAE 680), students will be expected to design and complete a pilot study during Years 1

and 2. This requirement will necessarily relate closely to content and skills addressed in

coursework in Years 1 and 2. This is likely to be part of a research project conducted at the

Kaput Center or through one of its associates, or students may start their own research project in

local schools or undergraduate classrooms. The study should reflect the student’s synthesis of

knowledge gleaned from coursework during the Introductory and Preparatory phases, concerning

the nature and process of research, the use of appropriate methodologies, the application of

relevant theories of learning, and the development of scholarly writing skills. It will culminate in

the qualifying exam.

Students who have no K-16 teaching experience will be advised to complete a teaching

internship prior to qualifying for the Advanced Doctoral Phase of the program.

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Any identified deficiencies regarding admission requirements or in students’ teaching

experience will be met prior to entering the advanced doctoral phase of the program (Production

Phase).

Qualifying Exams

The qualifying exam at the end of Year 2 will include:

1. submission of an 8000-word paper, based on the student’s pilot study completed

during Years 1 and 2, to the Graduate Committee for evaluation along the lines of

the skill sets developed in the student’s coursework;

2. submission of a proposal to present research to a national or international

conference based upon the student’s pilot study completed in Years 1 and 2;

3. presentation of the student’s pilot study in the Kaput Center; and

4. an [oral, written, or both] examination based on coursework completed in Years 1

and 2.

The qualifying exam should demonstrate the skill set that the student has developed through

the Introductory and Preparatory phases of the doctoral program.

Following successful completion of this part of the program, the Master of Science degree

will be awarded as a credential along the way toward the doctorate. Note that students will apply

and be accepted only into the doctoral program not for a separate master’s degree, which as

described in this document, is an integral part of the doctoral training. The master’s degree

awarded after 36 credits may also serve as a point of termination should the student elect to leave

the program.

Year 3 During the Production Phase, students will continue their doctoral training through advanced

course work. In addition, they will conduct Dissertation Research with a faculty member. During

Year 3, dissertation research is expected to focus on conducting a full literature review, framing

the main issues and guiding points of the study, and collecting research data. It is expected that

the student will also complete the preliminary writing phase of the dissertation in preparation for

the proposal defense at the end of Year 3. It is expected that the student will keep the selected

faculty advisor through the completion of the PhD Dissertation during Years 3 & 4. During the

third year, the student will have an identified Dissertation defense committee and chair (assumed

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to be their main faculty advisor), and complete the defense of the Dissertation proposal at the end

of Year 3 when they will have completed all coursework.

During Year 3, students will complete 4 advanced doctoral courses from the following list:

MAE750 – Analyzing Participation and Engagement in Mathematics Classrooms

MAE751 – Contemporary Issues in Elementary Grade Classrooms

MAE752 – Research on Proof and Reasoning in Mathematics

MAE753 – Applied Research on Technology in Mathematics Education

MAE754 – Semiotics and Symbolic Cognition

MAE755 – Principles of Creativity & Innovation in Mathematics Education

MAE756 – Advanced Theoretical Development

MAE769 – Advanced Topics in Mathematics Education

There will never be more than 10 advanced doctoral courses offered in the graduate catalogue

at one time.

Dissertation Research

MAE772 & 773 – Dissertation Research

While many students’ dissertation research will be supervised by a member of the core

Mathematics Education faculty, faculty from other departments or institutions can co-supervise

dissertations alongside a member of the core Math Ed faculty (if approved by the Program

Director in consultation with the Graduate Committee and the Dean of the School). The use of an

adjunct supervisor can provide an authentic learning experience that converges lines of research

and coursework to enrich the project and experience of the student.

Students’ Dissertations will build on their work completed in the preliminary years, relying

on research skills developed particularly in courses MAE655/682 (Developing Research Skills

Parts 1&2).

Year 4 Students will be expected to work primarily on their final Dissertation, through registration in

MAE774 and MAE775. These two courses permit a student to receive 18 credits of instruction to

assist in the completion of his or her research study and the writing of the final Dissertation.

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The final oral defense examination will be completed at the end of Year 4 on submission of

the final Dissertation. Successful completion of the Dissertation, including the oral defense, final

approval by the student’s doctoral committee, and approval for library submission as well as

successful completion of all course work will serve as the exit criteria for the doctorate.

4.D Course Descriptions All courses are 3 credits each unless otherwise stated

Introductory & Preparatory Courses MAE650 – Introduction to Qualitative Methods

Language and social inquiry; issues related to the ideas of knowing, explaining, understanding,

confirming, etc.; evaluative and effective elements in inquiry; empirical testability of

propositions; quantitative and qualitative procedures of data collection and analysis; study of

example cases.

MAE651 – Introduction to Quantitative Methods

Integrates research design, data analysis, data interpretation, and APA format report writing

across the two dominant paradigms in contemporary psychology. The course includes the use of

the SPSS statistical software for univariate parametric and some non-parametric models. The

course contains a strong experiential component to prepare students for thesis writing.

MAE652 – Introduction to Mathematics Education Research

This course will introduce PhD students to fundamental problems pertaining to mathematics

education that have been instrumental to constitute and define it as a research field. Students will

be introduced to important ideas in the field and why these ideas are significant in defining the

activity of research in mathematics education. The study of how these theoretical and pragmatic

problems have been approached by a community of researchers will help students understand, in

broad terms, the nature of research in the field and, at the same time, offer a panorama of new

areas of inquiry that are presently being transformed into research programs.

MAE653 – Theories of Mathematical Learning

29

This course will examine contemporary theories of learning psychologies and their applications

to research in mathematics education. The course is intended to help students understand ways of

knowing and how this drives research. Particular attention will be given to enabling students to

situate their research in relevant theoretical frameworks and understand the implications of

theoretical frameworks on research design.

MAE654 – Research Seminar

This is a capstone course designed to synthesize critical research processes, theories of learning,

and current research themes in mathematics education to which students are introduced in their

first year. From this synthesis, students are expected to select and refine a researchable topic for

their pilot study to be conducted during the Introductory and Preparatory phases of the doctoral

program (Years 1 and 2). The course will also give explicit attention to ethics in research,

including appropriate forms of acknowledgment in the use of existing research and proper

protocols and procedures for conducting research on human subjects.

MAE655 – Developing Research Skills Part 1

This course will focus on building the skill set necessary to conduct research for the dissertation,

most likely focused on background fundamental issues in mathematics education research. It will

build exploration, analysis and writing skills. Students will learn the skills to give shape to their

thinking. In particular, during this course, students will be expected to identify a problem for

which they will conduct a pilot study during the Introductory and Preparatory phases of the

program.

MAE660 – Foundational Issues in Mathematics Education

Students will be introduced to the fundamental problems and issues in mathematics education

research, historical perspectives, present research perspectives and future trajectories of research

including interdisciplinary perspectives on potential solutions and cutting-edge approaches. The

course will expect students to understand and analyze the present status of the field of

mathematics education and viable approaches to addressing foundational issues.


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This course will introduce students to research on pre-service and in-service teacher learning and

teacher education. It will critically examine the research base concerning contemporary learning

theories and their application to teacher learning. It will also study current effective forms of

teacher professional development and pre-service education and the research supporting these

approaches. Students will critique competitive grants funding research on teacher learning and

professional development as a way to learn about current trends and to develop grant-writing

skills.


This course extends the concepts studied in MAE661 through applied research in an authentic

teacher learning setting. To initiate this, students will write a mock grant proposal to conduct

original research with teachers. The proposal should reflect clear connections to the research

base studied in MAE661 as well as the research skills being developed during Years 1 and 2. It

will be refined through critique by student review panels prior to implementation of the study.

After implementation of the study, students will analyze their findings, prepare a written analysis

for peer review, and present their findings to the class.

MAE663 – Developing & Implementing Mathematics Curriculum

This course focuses on analyzing grades K-16 curriculum, intentions for students’ learning

outcomes, associated pedagogical styles and integration. Students will examine existing reform

and basal curricula texts, and the development of new activities and activity structures that

replace or transform existing texts based upon present mathematics education theory and new

technologies. Students will also be introduced to issues behind curricula reform and integration

focusing on fidelity of implementation.

MAE664 – Research on Technology in Mathematics Education

This course aims to explore important areas of mathematics through the use of innovative digital

technologies. We will examine how certain technologies can be used to transform the

introduction of a mathematical topic in such ways that the learner can represent, understand and

develop symbolic reasoning in a conceptual and more applicable way. Here we explore the use

of dynamic, interactive mathematics including simulations and affordable visualization tools and

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analyze related research literature on their impact on teaching and learning.

MAE665 – Design Principles for Technology in Mathematics Education

This course focuses on the design principles of 21st Century digital technologies and their

particular role in transforming communication and representation in mathematics classrooms.

Students will analyze and critique the specific designs and functionality of a suite of technologies

with particular focus on their impact on pedagogy, classroom discourse, conceptual

development, assessment and new forms of mathematical expression. When possible, leading

software designers will be included in the course as guest speakers.

MAE666 – Frameworks for Research Analysis

This course focuses on the development of a specific set of research tools relevant to the study of

mathematical reasoning in a variety of contexts, including the analysis of mathematical

discourse, gesture, flow of interaction, and learning outcomes such as pre-post tests of content.

Attention will be spent connecting research methods to theoretical frameworks and practical

outcomes of analysis. Students will be expected to produce a specific analysis of some classroom

data.

MAE667 – Research in Elementary Grade Mathematics

This course examines current research on issues of teaching and learning elementary grades

mathematics. It will focus on central research questions and findings in the field, research

designs framing this work, and relevant theories of learning and their application in the research

base. While particular focus will be given to early algebraic thinking, the course will overview

significant areas of research and their connections to current educational reforms. In addition,

students will be expected to conduct a research project on children’s mathematical thinking in a

specific area of research (e.g., early algebra, fractional thinking). The design, implementation,

and analysis of the study should reflect the student’s understanding of core components of

research being developed in Years 1 and 2.

MAE668 – Research in Middle & High School Mathematics

This course examines current research on issues of teaching and learning middle and high school

32



base. While particular focus will be given to middle and high school algebra, geometry, and data

analysis, the course will overview significant areas of research and their connections to current

educational reforms. In addition, students will be expected to conduct a research project on

children’s mathematical thinking in a specific area of research (e.g., proportional reasoning). The

design, implementation, and analysis of the study should reflect the student’s understanding of

core components of research being developed in Years 1 and 2.

MAE669 – Research in Undergraduate Mathematics Education

This course examines current research on issues of teaching and learning undergraduate



base. While particular focus will be given to advanced mathematical thinking, the course will

overview significant areas of research and their connections to current educational reforms. In

addition, participants in the course will be expected to conduct a research project on

undergraduate student’s mathematical thinking in a specific area of research. The design,

implementation, and analysis of the study should reflect the student’s understanding of core

components of research being developed in Years 1 and 2.

MAE670 – Developing Theory

This course will enable students to understand a theory as an artifact to generate interpretations

of research problems and their data. It intends to develop the skills necessary to delineate

answers to carefully chosen aspects of research questions, from alternative theoretical views with

respect to the one originally used to investigate the problem in question. The course will offer

students the opportunity to display their actual understanding of the main streams of the

discipline as well as some basic methods and techniques conducive to research.

MAE679 – Topics in Mathematics Education

33

This course allows for individual and/or group study under supervision of a mathematics

education faculty member in an area of mathematics education research that is not otherwise part

of graduate course offerings.

MAE680 – Authentic Learning (Internship).

This course will be conducted at a local research institution (e.g., TERC), the Kaput Center, or at

a national or international institution (e.g., SRI International, CINVESTAV, Mexico). Students

will be mentored by an Adjunct Research Associate at the host institute to develop their research

skills through activities such as data collection and analysis and to enhance their awareness of

the complexities of educational research. Host institutions will provide a “mentor” who is an

Adjunct Research Associate of the Kaput Center. The operation of the Kaput Center assures this

would be a suitable mentor to apprentice a student in the field of research. It is expected that,

while the course would be the administrative responsibility of a Math Ed faculty member, the

mentor at the affiliated institution would be the main instructor. An assigned Math Ed faculty

member, as the instructor of record, will monitor the progress of the student through consultation

with the mentor. The time spent by a student at the mentoring institute will be negotiated based

on the geographical location (e.g., 2 weeks of concentrated experience at an out-of-state location,

vs. a 1-day per week visit at an MA institution). It is expected that the Adjunct Research

Associate will benefit from having an additional research assistant for the time period (see

Letters of Support, Appendix C).

MAE681 – Research Seminar

This is a second capstone course aimed at preparing a student for their qualifying exams by

synthesizing the lessons learned by the authentic learning experience and focusing research

questions in preparation for their advanced coursework. In addition, the course will focus on

formal writing both for grant applications, scholarly articles and the dissertation.

MAE682 – Developing Research Skills Part 2

This course aims to synthesize prior coursework/research experience, focusing on methods and

research questions, in preparation for students’ main research project in Year 3. It also focuses

on the development of skills to defend one’s work and preparation for the written component of

34

the student’s qualifying exams. Students will develop essential experience/skills in designing

research, reading research critically, writing scholarly work, and developing proposals for

research funding. Students will give oral presentations on their research topics and plan of study

for peer review.

MAE750 – Analyzing Participation and Engagement in Mathematics Classrooms

In this course, students will observe real-life examples of complex classroom interactions. They

will learn to document and analyze these interactions from a number of theoretical perspectives,

including gesture and linguistic anthropology. Micro-analytic video analysis will be used for

tracking interaction cycles and participation frameworks in classrooms and understanding how

mathematical ideas are communicated and flow in classrooms. Topics include: discourse

analysis; non-verbal communicative acts such as gesture and deixis; participation frameworks;

and linguistic anthropology.

MAE751 – Contemporary Issues in Elementary Grade Classrooms

Students will study recent advances in the teaching and learning of mathematics to elementary

and middle school students. Areas to be covered will typically include: development of

children’s mathematical reasoning in K-8; current research in the development of children’s

algebraic thinking; recent research on ratio, proportion and fractions learning; student and

teacher understanding of geometry and measurement; technology use in elementary

mathematics; teacher professional development; and school implementation and effecting policy.

MAE752 – Research on Proof and Reasoning in Mathematics

This course will critically examine the research base on proof and reasoning across grades K-16.

It will explore epistemological issues of the nature of proof and the role and meaning of proof as

it evolves across grades K-16 and as it has emerged historically. To support the ongoing

development of critical reading and scholarly writing skills, the student will write a synthesis of

the research base focusing on a specific aspect of proof and reasoning and will present their

synthesis orally.

MAE753 – Applied Research on Technology in Mathematics Education

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Students will examine recent and cutting-edge development in digital technologies relevant or

applicable to the teaching and learning of mathematics. Students will be able to describe a broad

range of digital technologies and the theories of mathematical learning underpinning their use,

design and implementation. We will also focus on how the particular affordances of such

technology aid mathematics education, overcome barriers such as normative teaching beliefs,

social barriers, and diversity, and develop theories of democratizing access for all students.

MAE754 – Semiotics and Symbolic Cognition

This course focuses on the study of theories of the use and evolution of sign systems with

particular reference to new and emerging symbolic systems across grades K-16 mathematics.

Students will analyze popular and modern theories of semiotics and semiosis, and methods of

semiotics to understand the use of signs and representational infrastructures in mathematics

education with particular emphasis on reference, deixis, and interaction.

MAE755 – Principles of Creativity & Innovation in Mathematics Education

This course will consist of mini-projects focused on proof-of-concept development of

educational initiatives in mathematics education, implementation and analysis. Concepts of

design, fidelity, diffusion of innovation theory, dissemination strategies for scaling educational

solutions, principles of commercialization and technology transfer will be addressed in the

context of 21st Century adoption strategies and policy.

MAE756 – Advanced Theoretical Development

This course will examine specific, newly established literature as well as ongoing work in the

particular field of students’ dissertation research projects. The purpose of the course is to enable

students to gain deep conceptual control inside a particular area of research that will transform

their knowledge and allow them to display versatility and creativity in their own projects, going

beyond adopting and adapting approaches developed by other researchers.

MAE769 – Advanced Topics in Mathematics Education

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This course entails individual and/or group study under supervision of a mathematics education

faculty member in an advanced area of mathematics education research that is not otherwise part

of graduate course offerings.

MAE772-MAE773 – Dissertation Research (3 credits per course)

This course sequence focuses on conducting a full literature review, framing the main issues and

guiding points of the student’s dissertation research, and collecting appropriate research data. It

is expected that the student will also complete the preliminary writing phase of the dissertation in

preparation for the proposal defense at the end of Year 3. The preliminary writing phase

(essentially, the first several chapters of the dissertation) will focus on theoretical perspectives,

relevant research framing the study, and preliminary data analysis from the student’s fieldwork.

MAE774-775 – Dissertation Research (9 credits per course)

This course sequence builds on MAE772-773 to complete analysis and writing for the final

Dissertation.

4.E Credits to Complete Program and Other Graduation Requirements Successful completion of the program of study will be to achieve a GPA of 3.0 or higher,

pass the qualifying exam, defend a Dissertation proposal to the satisfaction of the defense

committee, and defend a final Dissertation to the satisfaction of the examining committee.

4.F Certification, Licensure, and Specialized Accreditation Not applicable.

4.G Independent Work and Internships Students will be mentored by an Adjunct Research Associate at the host institute to develop

their research skills through activities such as data collection and analysis and in enhancing their

awareness of the complexities of educational research. Host institutions will provide a “mentor”

who is an Adjunct Research Associate of the Kaput Center. The operation of the Kaput Center

assures this would be a suitable mentor to apprentice a student in the field of research. It is

37

expected that, while the course would be the administrative responsibility of a Math Ed faculty

member, the mentor at the affiliated institution would be the main instructor. An assigned Math

Ed faculty member, as the instructor of record, will monitor the progress of the student through

consultation with the mentor. The time spent by a student at the mentoring institute will be

negotiated based on the geographical location (e.g., several weeks of concentrated experience at

an out-of-state location, vs. a 1-day per week visit at an MA institution). It is expected that the

Adjunct Research Associate will benefit from having an additional research assistant for the time

period (see Letters of Support).

4.H External Advisory Committee A final report of the external evaluation team will be added to this package upon completion.

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5. FACULTY

5.A Current Faculty and additional positions allocated to the program

At steady state there will be a core of five full-time Math Ed faculty members to fulfill the

research, teaching, advising and thesis supervision obligations. This core faculty group will also

count with several members of the Advisory Board and Adjunct Research Associates of the

Kaput Center some of whom will be available to teach in the program as part-time lecturers (on-

line or on-site) as needed. A full complement of the Kaput Center’s Advisors and Associates list

can be found in Appendix D and on-line at http://www.kaputcenter.umassd.edu/associates/.

In the first year of operations (AY09-10) the Math Ed Faculty of the STEM Department in

the School of Education, Public Policy, and Civic Engagement will increase from 3 to 4

members. A search for this position is already in process. A fifth member will be added in the

third or fourth year, based on anticipated enrollments. These two positions have been designated

for faculty with a doctorate in mathematics education or a related field and who have an

established program of research optimally with grant funding in mathematics education research.

In addition, as its research and service roles expand, the Kaput Center will continue to see

increased hiring and, through that, increased opportunities for PhD program faculty and student

research assistantships.

The research experience of the present Math Ed faculty crosses many disciplines, including

teacher education, design and implementation of innovative technologies, the evolution and use

of sign and symbol systems in mathematics (semiotics), discourse analysis, micro-analytic video

analysis, early childhood learning, and curriculum design and development across the grades.

The faculty also brings many years of experience in teaching PreK-20.

Stephen Hegedus is a Full Professor and Director of the Kaput Center for Research and

Innovation in Mathematics Education. He is currently the principal investigator of several funded

projects and is a leader in designing and commercializing innovative applications of technology

in mathematics education. He currently has several NSF and US Department of Education

funded projects on participation in wireless connected mathematics classrooms and scaling up

technological innovation totaling $4.5m. He has co-supervised 6 PhD students at Oxford

University, and presently 1 student with Roberta Schorr at Rutgers University. He has also

39

supervised at UMass Dartmouth 6 Masters dissertations in mathematics education (MAT

program) with local teachers and is presently supervising 2 more projects.

Maria Blanton is an Associate Professor, with strong research interests in early algebra and

proof and reasoning. In particular, she is at the forefront of research in children’s early algebraic

thinking and has led (with the late James Kaput) federally funded research projects resulting in

numerous publications of articles, invited book chapters, and books. She currently is the

principal investigator of a $600,000 grant National Science Foundation (NSF) grant to research

proof and reasoning in K-16 mathematics and is co-leading the organization of an international

group of scholars in framing avenues for advancing research in this area and in producing

scholarly publications that reflect this.

Luis Moreno-Armella is a Full Professor, and is an active member of the National System of

Researchers, Mexico, (level III, highest level) with an appointment for five years beginning

January 2006. He is a member of the Mexican Academy of Sciences, and was formerly

International Adviser to the National Ministry of Education, Colombia. He has been adviser to 8

PhD students and 20 Master’s students in the last two decades. He is currently the Co-PI with

Hegedus on the US Department of Education funded project on participation in wireless

connected mathematics classrooms totaling $2.5m.

See Appendix E for full resumes of the core faculty.

5.B Other Instructional Resources In addition, the ongoing research projects of the faculty, in conjunction with the Kaput

Center and its research associates, will provide the context for the work of the students, their

fieldwork and production of their dissertation. The Center's strong connections with local school

districts make it possible for students to conduct their fieldwork in formal school settings. The

Center's rich database of classroom video in diverse settings from elementary schools to

undergraduate classrooms, from teacher pre-service courses to in-service research and

professional development, combined with multiple datasets from various projects, also offers

students the ability to conduct their fieldwork within this data corpus. Adjunct faculty from other

departments and universities and local research institutions (e.g., TERC) will assist in the

delivery of the “Authentic Learning” course, as well as co-supervise final dissertations with the

core faculty (please see letters of support in Appendix C).

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6. STUDENTS

6.A Estimated Enrollment First Year and at Full Implementation In national terms, most higher education institutions produce fewer than one doctorate in

mathematics education per year. Only the five largest programs consistently have produced

several graduates annually, with the top two—University of Georgia, and Teacher’s College,

Columbia—graduating approximately 7-8 mathematics education doctorates annually. The

University of Georgia is a particularly interesting case because it has a long-term record of

graduating significant numbers of mathematics education doctorates, and the majority of those

are of a high quality. In 2003-2004, the Mathematics Education Department at the University of

Georgia, with 13 academic faculty, had 53 PhD students and 71 Master’s students, for an average

4 PhD students and 5.5 Master’s students per faculty member. Thus, figures of 25 PhD students

per student cohort (every 4 years) for the current proposal at UMass Dartmouth are reasonable

(i.e. an average of 5 students per faculty member).

Enrollment decisions are based on the assumption that the proposed PhD at UMass

Dartmouth will expedite student progression through closer supervision and accelerated course

work. Faculty will provide students with intense supervision and research socialization

throughout their program of study. Students will likewise begin dissertation related activities in

Year 2 (Fall) of the program. This will serve as preparation for their qualifying exams (at the

end of year 2) and projected formal work on their dissertation in years 3 and 4.

Academic Year (Year of PhD Program Running)

Yr of Entry AY2008 (0) AY2009 (1) AY2010 (2) AY2011 (3) AY2012 (4)

Year 1 9 9 9 9

Year 2 7 7 7

Year 3 5 5

Year 4 5

TOTAL 0 9 16 21 26

Graduation 5

Table 1. Enrollment Projections

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Table 1 displays our projected student intake with attrition rates of approximately 25% per

year in the first two years of each student cohort. Such attrition rates are aligned with national

averages (see a recent report from the Council of Graduate Schools – www.phdcompletion.org),

but show a lower than average attrition because of the cohort-based design, highly-structured

curriculum, and methods of continual assessment. In summary, we expect a steady-state cohort

of 26 students.

6.B Students to be served We anticipate admitting annually an average of 9 new students for the first 4 years (i.e., first

cycle of the program). We will assess expectations for increasing program enrollment

periodically during this period. At steady state (i.e. in the fourth year) the total student body for

the PhD program should level off to approximately 26 students.

While we expect many students to be recent graduates of university programs or to come

from the K-16 teaching sector (including two and four year colleges), a significant group will be

overseas students and/or come from research centers and R&D institutions. Some will come with

a bachelor's degree, while others with an appropriate masters degree may be candidates for

advanced standing.

Expected future career trajectories for our graduates are focused on meeting the economic

and societal needs that we face in education today and include the Professoriate, Government

Agencies, Research Institutions (Private and Public), and Industry (e.g., software/curriculum

design).

6.C Admission criteria Students will be admitted to the PhD program based on an analysis of a comprehensive set of

measures used to determine their readiness for doctoral studies. As noted in the Curriculum

section, students will be admitted into the Ph.D. program, not separately for a master’s degree

that will be awarded as a credential along the way to the doctorate. Admission will be

determined by the Graduate Coordinator in consultation with the Graduate Committee, to

produce recommendations that will then be reviewed by the Dean of the School and the

Associate Provost for Graduate Studies, who confers official admission of all graduate students

to UMass Dartmouth. Prospective students will meet the following criteria for admittance into

the program:

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Master’s degree (or equivalent) with a minimum GPA of 3.0 (or equivalent) from an

accredited program in a field appropriate as preparatory work for doctoral studies in

mathematics education. Students will be required to submit transcripts from all post-

secondary institutions so that a determination can be made regarding the nature of

preparatory course work and the student’s successful completion of it. Students who

do not meet this requirement may be admitted conditionally, with the expectation that

appropriate measures will be taken to address the requirements. Decisions will be

made on a case-by-case basis.

Acceptable scores on the Graduate Record Examination.

Statement of interest and intent indicating research and teaching potential. Applicants

should include with this any evidence of such potential (e.g., curriculum vitae,

descriptions of research projects on which the student participated and his/her

contribution to the project, published or submitted articles, or artifacts of conference

presentations).

Three letters of recommendation from people who have worked closely with the

applicant in an academic or professional setting concerning the applicant's abilities

and performance relevant to research and teaching potential.

Based on the inputs above and individual communications as needed, the program is looking

for evidence of ability and motivation to succeed in a mathematics education research program

and potential then to contribute to the field. As a field of research, mathematics education draws

on an eclectic blend of disciplines. Because of the rich interdisciplinary nature of the field, the

proposed program is intentionally designed to be inclusive of applicants with many backgrounds.

It is also important to stress the design of the program is tightly focused by a cohort model.

Students will be expected to follow a well-defined program (as outlined in section 4) that focuses

their study each year for preparation and production of the dissertation via specific courses and

electives. The cohort model aims to strengthen coherence of the overall program of study. So, on

admission, students will need to show evidence that they understand the expectation of the

program and how this approach will strengthen their research skills over time.

Indeed, we expect this diversity to enrich not only the overall experience of all doctoral

students in the program, but the potential contribution students can make to the research aims of

both the program and Kaput Center. As such, our entrance criteria are not based on the

43

completion of a bachelor’s degree in mathematics, but in a field of study that is appropriate as

preparatory work for doctoral studies in mathematics education.

Mathematics education is defined by scholars who bring varied points of essential expertise -

from fields as diverse as mathematics, the cognitive sciences and linguistics - to their work. As

the Carnegie Initiative on the Doctorate notes, "much of the most important, path-breaking

intellectual work going on today occurs in the borderlands between fields, blurring boundaries

and challenging traditional disciplinary definitions" (Walker et al., 2008, p. 2). It is important

that doctoral programs in mathematics education, entrusted with producing scholars of

tomorrow, both reflect and draw from this diversity of thinking. As such, the doctoral program

proposed here will be enhanced - not limited - by students who bring to the program differing

backgrounds of academic preparation from either the technical or social sciences.

To achieve this, the quality of the program will require a flexible perspective on admission

criteria that involves case-by-case assessment of applicants' academic preparation in fields that

serve mathematics education. We expect that some students will have strong backgrounds in

mathematics and other technical sciences, while others will have strong preparation in

educational theory and the social sciences. As a general requirement, candidates for our program

will have had mathematical experiences in their professional and scholarly life. For example, we

expect that students will have strong backgrounds (as evidenced by a bachelors degree) in

mathematics, science, engineering, computer science, psychology, cognitive science, technology,

or mathematics education. Alternatively, we expect candidates to be competent in a professional

activity; for example, having more than 3 years as a teacher at any level in mathematics or a

related area, being a professional provider of teacher professional development in mathematics,

or being a major developer of educational software or curriculum, or professional development

guides in mathematics. We expect that students in our program will be competent in the level of

mathematics at the grade level within which they are expecting to conduct their educational

research as well as the deep connections that this area of knowledge has with other places in the

K-20 curriculum. All, however, will contribute synergistically to a program that educates future

scholars in the varied research domains that comprise mathematics education. Students will be

expected to meet any program deficiencies before qualifying for the Production Phase

(Advanced Doctoral Phase).

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Any perceived deficiencies in the applicant’s previous course work that can be addressed by

additional pre-requisite preparation will be determined by the Graduate Coordinator in

consultation with the Graduate Committee and stated along with the official notification of

admission. Additionally, the Graduate Coordinator, in consultation with the Graduate

Committee, will determine if graduate credits obtained at other accredited institutions are

acceptable for transfer into the program, subject to the criteria and limitations of the campus'

graduate regulations. Because of the highly focused and connected nature of the program, we do

not anticipate that granting transfer credit will be standard practice. Also, students with an earned

masters will be considered for Advanced Standing.

6.D Expected Time to Graduation and Projected Degree Completion Rates Students whose cumulative GPA drops below 3.0 (on a four-point scale) after 15 or more

semester hours of earned credit or who are making insufficient progress, are subject to

consideration of dismissal. The program will monitor students' progression, and will impose

whenever appropriate a “probation period” offering a semester or a year to recover their

cumulative GPA score to 3.0 or higher. If they do not succeed during this time, students will be

dismissed from the graduate program. Individuals who have been dismissed may be allowed to

re-enter the program at a later time if they reapply for admission and show new evidence of

academic credibility.

It is expected that full-time students will complete the PhD in mathematics education in four

years. Although this is an ambitious target, many innovative curriculum features have been

devised to achieve this goal (students with less experience, e.g., only a bachelor’s degree, might

conceivably extend their final year of dissertation work). We expect that most students would

complete all the requirements for the degree in four years. Part-time students or ABDs starting

full-time jobs in their fourth year would be permitted to complete their requirements using no

more than six years. Requests for extensions will be considered on a case-by-case basis.

6.E Transferability of Credit and Articulation Agreements Consistent with other PhD programs, students’ transcripts will be evaluated, and up to 6 post-

master’s graduate credits from other universities may be accepted in transfer toward the PhD

45

degree. Courses will be subject to approval for transfer by the Graduate Coordinator in

consultation with the Graduate Committee. Only courses for which students earned a grade of B

or better will be considered for transfer. Transfer credit from research project experiences will be

assessed on a per-case basis.

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7. ADMINISTRATION AND OPERATION

The PhD program in Mathematics Education will be administered with existing faculty and

infrastructure in the STEM Department of the School of Education, Public Policy, and Civic

Engagement, in consultation with affiliated faculty in other departments, and within the existing

administrative structure of graduate studies at UMass Dartmouth. The Graduate Program

Committee, chaired by the Graduate Program Director, will provide direction and oversight for

the management of the PhD program, including admissions criteria and individual admission

actions, curriculum development, program planning, operating policies and procedures, and

program evaluation/quality control. All proposed guidelines and policies would comply with the

general operating policies for academic programs on the UMass Dartmouth campus. The faculty

recommends admission of students, while the procedures for application and completion of files

are managed centrally by the Office for Graduate Studies on campus.

The Graduate Program Committee will review proposed program changes and make specific

recommendations with respect to all aspects of the program. Student advising will be handled by

faculty advisors in the STEM Department, under the guidance of the Graduate Committee and

Graduate Program Director. The program director will work closely with the Kaput Center

Director on issues of resource allocation and stipends for graduate students generated by the

Kaput Center or related grants through the Center.

As regular members of the UMass Dartmouth faculty, the Math Ed faculty are subject to the

institution's policies and procedures as regards union contracts, workload assignments,

progression and evaluation, curriculum change, university service, and many other matters. The

program will be subject to the regular processes for evaluation, such as the five-year periodic

review called AQAD, student evaluations of teaching, and an annual assessment cycle.

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8. RESOURCES

8.A Projected Student Enrollments and Necessary Faculty Table 2 below lists the numbers of courses required each year and the numbers of

dissertations being advised. At steady state 8 courses per semester will be taught with 10 students

having advanced to the dissertation-preparation stage and requiring advanced advising and

supervision.

Plans call for 5 full-time faculty to cover instructional and research advising needs for these

students, based on a teaching-load allocation for research-active faculty in doctoral programs that

has become the standard at UMass Dartmouth, of a 2/2 teaching load (two courses per semester)

and including responsibility for supervision of students preparing dissertations (supervising three

doctoral students at a time).

AY2008 (0) AY2009 (1) AY2010 (2) AY2011 (3) AY2012 (4) AY2013 (5)

Total # of PhD

Courses

0 6 12 16 16 16

Expected # of

dissertations in

progress

10 10+

Graduation 5 5

Table 2: Faculty Responsibilities

The two new faculty members to be hired will be supported by an existing vacant line in the

STEM Department originally allocated for mathematics education and through enrollment-

produced income as well as research grant expansion. Specifically, faculty assigned full time to

the PhD will be as follows: Four in the first year and five after the third or fourth year.

8.B Graduate Assistantships: Teaching/Research Assistantships At program “steady state” it is expected that two-thirds of the students in the program, or 17

approximately, will benefit from a graduate assistantship support. The others will be self-

supporting or supported by their employer or home-country government. Of the 17

assistantships, approximately 7 will be supported in their second/third through fourth year on

research assistantships from faculty grants through the Kaput Center or in the form of industry-

50

sponsored projects. Another 10 students at “steady-state” will be supported as graduate teaching

assistants. In the first year there will be 4 teaching assistantships (TAs) available, increasing by 2

every year until reaching the goal of 10 teaching assistantships by the fourth year (at steady-

state). Depending on qualifications, all will teach either undergraduate introductory courses,

graduate courses for teachers seeking licensure or in the MAT program particularly those in

Mathematics Education. The numbers of teaching assistantships vis a vis research assistantships

will differ per year and at each stage of the cohort but we expect to support the same proportion

of students each year to reflect needs presented in our survey analysis as well as to reflect the

importance of supporting students who will be committed to the program on a full time basis. It

is expected that a significant portion of the teaching assistantships will be geared to attract

talented new students, support the front-end of the student cohort, and to develop teaching skills

for those interested in pursuing a professoriate career. The research assistantships will be

directed to support students in year 2 onwards of the cohort when initial attrition has passed and

students begin to focus on a pilot research project.

The teaching and research assistantships will be available on a competitive basis with the

following assessment criteria: (1) Potential for teaching excellence, (2) Potential for Research

Excellence, (3) Hardship needs after (1) and (2) are met.

The teaching assistantships will be initially set at $12,000 annually per award with some

tuition waiver. The research assistantships will be approximately $19,000 per year (including

summers) with a waiver of tuition and academic fees if grant supported. While such awards are

subject to the successful reward of soft funds and hence are non-determinable, our resource

model incorporates them as a very likely program goal. In addition, once the PhD program has

been established, it will be possible to apply for funds for pre-doctoral programs from private

and federal sources (e.g., US Ed and NSF) in a competitive fashion, in addition to specific R&D

projects in the Kaput Center. Furthermore, the Center will be actively soliciting funds from

private and industrial sources to support these assistantships. This will be a more long-term

funding source and we will expect such donations to occur through ongoing partnerships and

collaborations with UMass Dartmouth and industry through the practical research and

commercial efforts of the Kaput Center.

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8.C Infrastructure: Equipment, Facilities and Library In the first three years, program facilities will be located in the Kaput Center at the Fairhaven

campus. The center presently occupies 3,500 square feet for faculty, research project staff, and

desk space for 4 graduate students. There is also a Resource room with space for graduate

students to work. The Resource room includes most mainstream basal curriculum texts for K-12

and undergraduate programs. SmartBoard technology, video conferencing, telephone

conferencing facilities and TV/DVD/Video equipment are also available in this space. It is

expected that students will share desk space on a needs basis.

No additional space, or relocation expenses would be incurred in the first cycle of the

program, but as the student cohort increases and/or research projects of the Center evolve in size

more space may be needed.

Classroom space at the Fairhaven Campus is shared by the Kaput Center and the Center for

University, School and Community Partnerships. There are three classrooms available, as well as

high-tech resource rooms within the Kaput Center where data analysis, data processing and

seminars are and will continue to be conducted.

In the start-up years of the program, students will be able to use equipment at the Kaput

Center. The Center is a high-fidelity research facility with a high-tech physical infrastructure

largely funded by research grants from external agencies, and start-up funds from UMass

Dartmouth. These include:

• High-speed connectivity to the Internet and a secure pipeline to Campus e-resources via

hardware VPN (as if we were on campus)

• Gigabit connectivity within the Center and secure 802.11a/b/g/n wireless connectivity

• Video-Conferencing/audio casting equipment incorporating the UMass Wimba service

• Blog and podcasting via an XServe Mac OS 10.5 Leopard Server

• DVI/VGA video projection with podium facilities

• Ceiling mounted projectors + HD/DVI Document Cameras (video recording available)

• 66-inch rear projection SmartBoard with connection to the Internet & Public Wiki

• 20-computer Apple Wireless Learning Lab with Apple and Windows OS and a suite of

mathematical and mathematics educational software (e.g., Mathematica, Maple, Matlab,

SPSS, Sketchpad, Cabri, MS Office, Adobe, Macromedia, etc)

• HDTV + HD equipment for high quality broadcasting and presentation

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• HD cameras/DV cameras

• High speed digital video processing machines with large screen displays (Mac)

• Part-ownership of the SAN Campus backbone system (safe and reliable back up of server

side resources including web and database administration)

• Public and Private Wiki sites and other digital software to manage projects and e-

portfolios

• On-line secure databases and data-mining facilities including quantitative and qualitative

software (e.g., SPSS, HLM6, nVivo)

In addition, the Kaput Center has a terabyte server of multi-media data from several projects

and teaching experiments that are digitally available under a secure network at the Center,

allowing users to create workflows from digital cameras, either directly or after recording an

event, straight to a Podcast or Blog, completely automating the video process and publishing

procedure. This will be especially useful for students wishing to record classrooms or events at

the Center.

The University Library provides services and resources in support of all academic programs,

research, and intellectual pursuits of the university community. Faculty and students have the

ability to search online databases. Faculty can use and borrow materials from any of the

nineteen academic and research libraries which make-up the Boston Library Consortium (BLC.)

In addition, The Kaput Center also has a library and a resource room that supplements the

holdings of the main campus library. It includes many Math Ed journals and periodicals dating

back 20 years and a wide selection of K-16 mathematics curricula. Among the Center’s library

holdings are over a thousand books covering areas of Mathematics Education,

Anthropology/Evolutionary Theory, Cognitive Psychology/Science, Representation theory,

Computer Science and Design, Learning Sciences, Linguistics and Discourse Analysis,

Complexity Theory, Mathematics, Philosophy, Socio-Cultural Studies, and Quantitative and

Qualitative Methodology (over $20K worth of major Handbooks in this category alone). The

Center will continue to add cutting edge, contemporary, and cross-disciplinary literature that is

not always available on the main University Campus.

As these resources are demanded by the teaching faculty and doctoral students of the new

program, the Library in conjunction with the PhD program faculty will assess what else needs to

53

acquired or subscribed to. A modest library annual allocation of $5,000 per year has been set up

for this purpose.

8.D Field and Clinical Resources All field resources will be obtained from the Kaput Center and related research projects. The

main resource the Kaput Center has in this regard is its international advisory board of over 80

scholars with whom we can connect our PhD students with, either through present projects or

Center associations. The Center has several Adjunct Research Associates who can offer

internships for future projects or in other ways assist in the future education of our students. In

addition, many students will have existing associations relevant to the field of mathematics

education and will often use schools in the region and their professional locations as sites for

field observations and research investigations.

8.E Revenue/Cost Model Based on the current tuition/fee structure at UMass Dartmouth, tuition/fees will be sufficient to

support the program. This is based on admitting 9 students each year. Table 3 outlines income

from tuition for the first four years of the program, anticipating attrition by 2 students in the

second year and 2 more by the third year in each cohort. Generated tuition and fees are based

upon a 7:3 ratio of in-state to out-of-state students at steady state. Anticipated revenue amounts

to approximately $408,992 per year at steady state.

AY2009(1) AY2010(2) AY2011(3) AY2012(4) GENERATED TUITION AND FEES Mass $50,733 $89,580 $115,334 $142,553 Non-Mass $27,695 $57,053 $88,147 $121,055 State Appropriation $50,325 $89,467 $117,425 $145,384 GRAND TOTAL to campus $128,753 $236,100 $320,906 $408,992

Student STATUS 9 16 21 26 # In State 7 12 15 18 # Out-of State 2 4 6 8

Table 3: Revenue from Program up to Steady State (AY 2009-AY2012)

A 3% increase in fees and tuition has been included per year. Best estimates for State Appropriation used.

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The main source of costs will be the 5 full time faculty members necessary to cover the core

instructional and research advising needs for these students. Of these, only the fifth line (to be

hired in the third year) represents a new allocation of resources. This is reflective of the long

term planning that was started back in 2005 when Chancellor MacCormack and then Provost

Esposito approved the initiative to start strengthening the faculty resources in Mathematics

Education at UMass Dartmouth (see Appendix A). Current investments in the 4 faculty positions

(one vacant and under a search) amount to $254,853. Additional costs include general

administrative costs, library/resource room acquisitions, marketing and graduate assistantships.

Budget Categories

Year 1 AY2009

Year 2 AY2010

Year 3 AY2011

Year 4 AY2012

Personnel • Additional Faculty to current 4 positions

o 1 new position in year 3 • ½ Administrative Assistant I

• Graduate Teaching Assistantships (net) (tuition & fee waivers)

24,148

16,500 16,560

80,000 10,529

18,337

General Administrative Costs

2,500

Instructional Materials and Library Acquisitions Materials (includes Kaput Resource Center)

5,000

Facilities and Equipment Start up Faculty @ $2,500/each

2,500

-- (2,500)

2,500

-- (2,500)

Field and Clinical Resources -- -- -- -- Marketing/Promotional material 3,500

TOTAL NEW PROGRAM EXPENSES 37,648 33,060 93,029 18,337 CUMULATIVE TOTAL 37,648 68,208 161,237 177,074

Table 4: 4-Year Budget of the Proposed Mathematics Education PhD Program

New expenses are illustrated in Table 4. These are noted in the year it first occurs and recurs

thereafter unless otherwise stated. The bottom line of new costs incurred to provide the program

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is given in the cumulative total per year. The recurring cost after steady state will be TA waivers

at $69,575 (increasing with changes in fees) thereafter per 4-year student cohort (as described in

the Personnel row in table 4).

As illustrated in Table 5 tuition/fee income will amply cover new planned expenses of the

proposed PhD Program.

Year New Income New Expenses

Year 01 Year 02 Year 03 Year 04

Tuition/fees

$128,753 $107,347 $84,806 $88,086

$37,648 $33,060 $93,029 $18,337

Subtotal $408,992 $177,074 Table 5. Comparison of Income and Expenses: Years 1-4

In addition to the projected revenue shown in Table 3, faculty grants (funded research) are

anticipated to provide research assistants (RA’s) support to approximately 7 PhD students at

steady state in year 4.

In sum, existing strengths in faculty, adjunct research expertise, physical location, library

resources, equipment, and revenues from grants and industry partnerships as well as campus

resources, all provide a solid basis to implement this program is in cost-effective manner.

Strategies have been identified to expand these resources as enrollments grow to our anticipated

steady-state level.

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9. EXTERNAL REVIEW

9.A, B Report of the External Review Team, Institutional Responses All final reports will be attached as appendix F.

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10. REFERENCES

Gardner, H. (1985). The mind's new science: A history of the cognitive revolution. New

York: Basic Books.

Greeno, J. (1989). Situations, mental models, and generative knowledge. In D. Klahr &

K. Kotovsky (Eds.), Complex information processing: The impact of Herbert Simon. Hillsdale,

NJ: Lawrence Erlbaum.

National Council of Teachers of Mathematics. (1998). The nature and role of algebra in

the K–14 curriculum. Washington, DC: National Research Council, National Academy Press.

National Council of Teachers of Mathematics. (2000). Principle and standards for school

mathematics. Reston, VA: Author.

Reys, R. E. (2000). Doctorates in Mathematics Education: An acute shortage. Notices of

the American Mathematical Society, 47(10), 1267-1270.

Reys, R. E. (2002). Mathematics education positions in higher education and their

applicants: A many to one correspondence. Notices of the American Mathematical Society,

49(2), 202-207.

Reys, R. E. (2006). A report on jobs for doctorates in mathematics education in

institutions of higher education. Journal for Research in Mathematics Education, 37(4), 262-

269.

Reys, R. E., & Kilpatrick, J. (2001). One field, many paths: US Doctoral programs in

mathematics education. Washington, DC: Conference Board of the Mathematical Sciences.

Reys, R. E., Teuscher, D., Nevels, N., & Glasgow, B. (2007). Doctoral programs in

mathematics education in the United States: 2007 progress report. Paper presented at the 2007

Doctoral Programs in Mathematics Education: Progress in the Past Decade Conference, Kansas

City, Kansas.

Walker, G. E., Golde, C. M., Jones, L., Bueschel, A. C., & Hutchings, P. (2008). The

formation of scholars: Rethinking doctoral education for the Twenty-First century. San

Francisco: Jossey-Bass.

Wirszup, I., & Streit, R. (Eds.) (1987). Developments in school mathematics education

around the world: Volume 1. Reston, VA: National Council of Teachers of Mathematics.

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around the world: Volume 2. Reston, VA: National Council of Teachers of Mathematics.


around the world: Volume 3. Reston, VA: National Council of Teachers of Mathematics

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APPENDIX A: LETTER OF INTENT

MEMORANDUM

To: Chancellor MacCormack From: Mathematics Education Research Group: Chancellor Professor James Kaput, Professor Gary

Davis, Associate Professors Maria Blanton & Stephen Hegedus Re: Letter of Intent to Submit a Preliminary Proposal for a PhD Program in Mathematics

Education Cc: Chair of the Mathematics Department, Dean of the College of Arts and Science, Chair of the

College of Arts and Sciences Curriculum Committee, Chair of the University Curriculum Committee, President of the Faculty Senate, Chair of the CAS Departments, Provost

Date: December 2nd 2004 Dear Chancellor:

The Mathematics Education Research Group, of the Mathematics Department, present to you our letter of intent to proceed with a formal application for an innovative PhD program in Mathematics Education. This program, which will be housed within the Mathematics Department at the University of Massachusetts Dartmouth, draws upon partners from outside the academic sector with whom we have had long and productive relationships. The explicit primary aim of the proposed doctoral program is to produce stewards of the discipline, as defined by The Carnegie Foundation for the Advancement of Teaching in its Initiative on the Doctorate: “to educate and prepare those to whom we can entrust the vigor, quality, and integrity of the field.”

The proposed doctoral program optimally builds on and enhances current research and development strengths, and, most importantly, applies those strengths to answer the acute educational needs of our region. It addresses and serves the state and the nation, which are suffering from an extreme and worsening shortage of doctoral level human resources. The program will bring high visibility to our campus’ scholarly achievement and a competitive advantage to our ongoing national-scope R&D and regional professional and school development efforts.

We aim to couple our proposal for an innovative PhD program, with a Center for the Study of Foundational Issues in Mathematics Education– to be submitted separately – that will bring high quality researchers and faculty to our campus. This Center will include as affiliates our non-academic partners, TERC, the Concord Consortium, and, others, e.g. SRI International, with whom we have active research partnerships and contracts.

The interests of our present four core faculty, and affiliated faculty, Professor David Rock (Education), cover grades K-20 and a wide range of contemporary issues in mathematics education: • Algebraic thinking grades K-20. • Dynamical systems and complexity,

secondary though undergraduate. • Improving mathematics teaching grades 4-8

through district-wide collaboration • Integrating new technological

innovations (e.g. calculators and wireless networks) in middle and high school mathematics classrooms

• Developing proof-based reasoning from elementary through undergraduate classrooms.

• Fundamental issues of symbol use and symbolic thinking in mathematics.

• Impact of memory research on learning and teaching mathematics.

• Theories of mathematical learning and teaching from multi-disciplinary perspectives.

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• Development of flexible thinking in mathematics.

• Three-dimensional geometry

A majority of these projects are funded by the NSF or State Federal funds totaling ($3m) independently, and with collaborators ($8m), with additional research proposals under review (presently $1.5m) and in preparation. This level of research funding (to be distinguished from professional development and service oriented funding) would be unusual at a Research I university and is unprecedented at a regional university of our type. This level of consistent funding would accelerate in the presence of a PhD program and the resulting increase in the size of our research community.

Need and Justification: The United States currently has an acute shortage of doctoral students in mathematics education, well documented and analyzed in the reports “One Field, Many Paths:U.S. Doctoral Programs in Mathematics Education”, Reys & Kilpatrick, 2001, Conference Board of the Mathematical Sciences, and “Principles to Guide the Design and Implementation of Doctoral Programs in Mathematics Education”, Association of Mathematics Teacher Educators, 2002. This shortage needs to be addressed with strong innovative doctoral programs because mathematics education needs new and vital stewards of its discipline. Our subject has developed enormous breadth and depth over the past 30 years, as witnessed by the numerous journals, national and international conferences, and research dollars allocated to projects in this field. In order for this vitality to continue, young committed, talented people need to be attracted into doctoral programs that provide them with high level education, training and mentoring.

Massachusetts is a highly appropriate area in which to start an innovative mathematics education doctoral program. In the Commonwealth of Massachusetts resides one of the greatest concentrations of research, development and expertise in the nation in mathematics and science education that also attracts a significant concentration of Federal R&D money in these fields. Historically, much of this funding has come to three independent research and development organizations in the Boston area - The Concord Consortium, the Educational Development Center (EDC), and TERC. While the citizenry of Massachusetts benefit greatly from its unparalleled R&D leadership in the medical sector, there is as yet no parallel in the educational sector - where, it may be argued, the needs are even more pressing and the opportunities as great. Within the University of Massachusetts system, it is the University of Massachusetts Dartmouth that has had the strongest links with these research and development institutions, largely through the sustained and deep pioneering work of mathematics education faculty under the intellectual leadership of Jim Kaput.

Significance: How significant will our proposed doctoral program be? There are two aspects to significance – quantity and quality. In national terms, most institutions produce less than one doctorate in mathematics education each year. Only the five largest programs consistently produced several graduates annually, with the top two – University of Georgia, and Teacher’s College, Columbia - graduating approximately 7-8 mathematics education doctorates per year. The University of Georgia is a particularly interesting case because it has a long-term record of graduating significant numbers of mathematics education doctorates, and the majority of those are of a high quality. In 2003-2004 the Mathematics Education Department at the University of Georgia, with 13 academic faculty, had 53 PhD students and 71 Masters students, for an average 4 PhD students and 5.5 Masters students per faculty member. Thus, figures of 25-30 doctoral students for a current faculty of 5-6 (Blanton, Davis, Hegedus, Kaput, new appointment pending, and David Rock) at the University of Massachusetts Dartmouth are not unreasonable. The quality of doctoral programs varies enormously across the nation. We are aware of no programs that have the integration with industry research and development partners that we propose, and few, if any, that bring the idea of distributed, technological working, and apprenticeships to their doctoral training programs. Thus, we feel that in terms of quality and quantity our proposed doctorate will be nationally significant.

Purpose: The purpose of the Program is to educate talented students from a national and international pool based in state-of-the-art educational experiences that prepare them to meet the challenges of research and development for Mathematics Education in the coming century. Graduates will possess deeply

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integrated understanding of subject matter, learning and cognition in that subject matter, and a practical sense of the means and contexts for learning, particularly involving new technologies.

What is Unique About this Program? (1) Our explicit primary aim is to produce stewards of the discipline of mathematics education: well-educated and trained researchers and scholars who can develop our subject in breadth and depth to meet the mathematics education needs of the coming century. The proposed doctoral program is intended to be less oriented towards serving schools, districts and practice directly (an orientation already served by existing Ed.D. programs) and strongly oriented towards careers in research, scholarship and development, (2) The program will deliberately and systematically draw intellectual resources from across departments, colleges, campuses, and even university boundaries, to form faculty teams that embody a range of competencies and interests rarely, if ever, available within any given university unit, (3) The program will systematically engage students in the new forms of distributed intellectual practice, frequently electronically mediated, that we judge will play a major role in, if not dominate, intellectual work in the 21st century, and hence serve as a model of graduate education for the future.

Uniqueness: We believe that such statement makes us unique from our sister campuses, and we will continue to elaborate how we can actually extend the intellectual horizons of our State-wide University through such a proposal, and potential interaction on multiple fronts. We will also aim to maximize the effectiveness of our work with the establishment of a Center for Mathematics Education Research focusing on Foundational Issues in Mathematics Education, to support our proposed doctoral program, both intellectually and fiscally.

Goals: To provide an intellectual service to the local and broader community on research issues that will impact multiple audiences in education, interdisciplinary theory, curriculum and software design, and innovation in related fields. We aim to educate, train and mentor stewards of the discipline - talented people who will become leaders in mathematics education research (Professors of the future), private institution researchers with an impact on national need in Mathematics Education, leaders of educational software initiatives, curriculum writers and designers in industry and government.

Academic Program: The model will be a 3-tier system. The first will be a pre-qualifying core, equivalent to a Masters program, resulting in that degree when appropriate. This will be a 30 credit preliminary, involving courses from Psychology (on research methods), English (on grant and proposal writing) and Mathematics (building on present MTH5*** courses for the MAT program). More detailed descriptions are on our website at http://merg.umassd.edu/programs/phd/)

A second tier will involve: • Internships with our local research institutes (to be detailed in our preliminary) • Advanced mathematics courses with a focus on advanced theories in mathematics education • Seminars with partners via on-line media • Local and distributed seminars

The third tier will consist of a substantial final dissertation, with the committee chair coming from the core mathematics education faculty at the University.

We already have a technological infrastructure in place to provide on-line interactive courses via 1-1 video-streaming, with computers in our mathematics laboratory in Group 1-Room 218, as well as a dedicated high-speed, high-capacity server. Our program aims to fully integrate the technological resources we have in the Mathematics department, the peripheral materials from our research projects, and intellectual links with superior resources via our research and development partners. The majority of such external work is facilitated by a high-speed server that we have funded through internal and external grants. We aim to continue to seek funds to provide continuing effective and efficient technological support to our program.

Costs: We are aiming for an initial cohort of around 6 students. The projected figures will be in our main proposal but we are aiming for around 6 students initially, rising to 9, then 12, in an initial 3-year plan. We will aim to cost out the program in our preliminary proposal based upon faculty time, perceived specialist need and start-up costs.

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We will be requesting minimal start-up costs, in so far as part of our contractual obligations will be utilized in the delivery of the proposed doctoral level courses. We are presently searching for a new junior member of faculty who will provide extra resources. Our complement will be: 1 Full professor (Gary Davis), 2 Associate Professors (Maria Blanton & Stephen Hegedus), 1 Assistant Professor (new appointment, pending), 1 Emeritus Chancellor Professor (Jim Kaput) and many affiliated professors (including David Rock). These figures are in line with national doctoral programs in mathematics education: the national median number of faculty serving mathematics education doctoral programs is 6, with a range from 2 through 13 faculty.

This is our presentation of our intent to propose a PhD in Mathematics Education, Yours Sincerely, Mathematics Education Research Group

Maria Blanton Gary Davis Stephen Hegedus Jim Kaput

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APPENDIX B: SURVEY DATA

Survey Set A: Prospective students Demographics Age of Respondents: 18-25 (9 %), 26-34 (37%), 35-41 (16%), 42-49 (22%), 50+ (16%) Gender: Male (36%), Female (64%)

Figure 2. Ethnicity of respondents

Figure 3. Present occupation of respondents

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Interests What type of career are you aiming to pursue?

Figure 4. Type of career respondents aim to pursue

How interested are you in pursuing a doctoral program in mathematics education?

Figure 5. Interest in pursuing a doctoral program in math education

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How interested are you in pursuing a doctoral degree in mathematics education at UMass Dartmouth?

Figure 6. Interest in pursuing doctoral program in math education at UMass Dartmouth. Assessment of Opportunities Please rank how important you find each of the main features of the proposed program: #1: Authentic learning experiences including internships at research institutions or Center working on a major project or program of work #2: A focused 4-year program designed to develop skills in conducting research in mathematics education #3: Doctoral coursework that includes interdisciplinary perspectives of mathematics education #4: Focus on fundamental issues and cutting edge research in K-16 education, such as the design and implementation of digital technologies in classrooms and the design and integration of new curricular perspectives in K-16 classrooms #5: Training in methodologies specific to mathematics education vs. broader methods #6: Development of applied research skills such as grant writing and writing and speaking in peer-reviewed venues

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Figure 7. Ranking of features of proposed program.

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Rank the following list concerning which factors are most important in your decision on choosing a doctoral program:

- Location - Nature of Program - Tuition Waiver - Opportunity for Teaching Assistantship - Opportunity for Research Assistantship - Faculty and Faculty Research

Figure 8. Rating of factors in choosing a doctoral program.

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Beliefs/Needs How important is a research assistantship to you?

Figure 9. Importance of a research assistantship How important is a teaching assistantship to you?

Figure 10. Importance of a teaching assistantship.

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How innovative do you believe the program is based upon these features?

Figure 11. Respondents’ opinion of how innovative the program is based on its features The PhD program will be closely related to the work of the Kaput Center, a research center focusing on investigation of foundational issues. How important do you find this?

Figure 12. Respondents’ opinion of working on research projects through the Kaput Center.

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Survey Set B: Peer-Evaluation Demographics Gender: Male (62%), Female (38%) Ethnicity: American Indian/Alaska Native (0%), Asian/Pacific Islander (3%), Black, not Hispanic (0%), Hispanic (3%), White (91%), Other (3%)

Figure 13. Age of respondents. Which of the following best describes your present occupation?

Figure 14. Present occupation of respondents.

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Importance Please rank how important you find each of the main features of the proposed program. #1: Authentic learning experiences including internships at research institutions or Center working on a major project or program of work #2: A focused 4-year program designed to develop skills in conducting research in mathematics education #3: Doctoral coursework that includes interdisciplinary perspectives of mathematics education #4: Focus on fundamental issues and cutting edge research in K-16 education, such as the design and implementation of digital technologies in classrooms and the design and integration of new curricular perspectives in K-16 classrooms #5: Training in methodologies specific to mathematics education vs broader methods #6: Development of applied research skills such as grant writing and writing and speaking in peer-reviewed venues

Figure 15. Ranking of features of proposed program

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Evaluation How innovative do you believe the program is based upon these features?

Figure 16. Residents’ opinion of how innovative program is based on its features. The PhD program will be closely related to the work of the Kaput Center, a research center focusing on investigation of foundational issues. How important is this?

Figure 17. Respondents’ opinion of working on research projects through the Kaput Center.

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Peer-Recommendation To what extent would you recommend a student or colleague to pursue a doctoral program in mathematics education at UMass Dartmouth?

Figure 18. Extent to which respondents would recommend a doctoral program in math education at UMass Dartmouth.

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APPENDIX C: LETTERS OF SUPPORT/EVALUATION Professor Celia Hoyles OBE, University of London, UK Dr Jeremy Roschelle, Director, SRI International, CA Professor Tommy Dreyfus, Tel-Aviv University, Israel Professor Roberta Schorr, Rutgers, NJ Professor Lyn English, Queensland University of Technology, Australia Professor Richard Lesh, Dean, Indiana University, IN Professor Jim Middleton, Provost, Arizona State University, AZ Dr Teresa Rojano, Cinvestav, Mexico

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APPENDIX D: EXTERNAL ADVISORY BOARD OF KAPUT CENTER

Name Affiliation Field of Expertise Nancy Ares

University of Rochester, USA Social Cognition, Culture & Race

Ferdinando Arzarello Universitá di Torino, ITALY

Nicolas Balacheff

Laboratoire Leibniz, FRANCE Teaching and Learning of Mathematical Proof

Yaneer Bar-Yam

New England Complex Systems Institute, USA

Complexity Theory, Complex Systems

Hyman Bass

Michigan State University, USA

Mathematician’s Use of Symbols, Elementary Mathematical Thinking

Corey Brady Learning Soft Inc., USA Discourse, Networks, Technology Design and Use, Activity Theory

David Carraher

TERC, USA Early Algebra

Jere Confrey

North Carolina State University, USA

Simulations, Policy, Assessment

Al Cuoco Educational Development Center, USA

Assessment Design, Lesson Study

Ubiratan D’Ambrosio BRASIL Ethnomathematics, International Collaborations

Sarah Davis

National Institute of Education, SINGAPORE

Connected Classrooms, Affect, Agents, Anonymity

Chris Dede Harvard University Human Capabilities for Knowledge Creation, Sharing, and Mastery that Emerging Technologies Enables

Tommy Dreyfus Tel Aviv Univeristy, ISRAEL Mathematical Thinking, Pedagogy

Raymond Duval FRANCE Linguistics, Mathematical Register

Ted Eisenberg Ben Gurion Univeristy, ISRAEL

Learning Theory

Lyn English

Queensland Univeristy of Technology, AUSTRALIA

Learning Sciences, Mathematical Thinking

William Finzer KCP Technologies, USA Megan Franke

University of California, Los Angeles, USA

Teacher Learning, Professional Development, Elementary Mathematics

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Paul Goldenberg

Educational Development Center, USA

On-line Networks

Gerald Goldin

Rutgers University, USA Affect, Cognition, Representation Theory

Charles Goodwin

University of California, Los Angeles, USA

Linguistics, Gesture

Angappa (Guna) Gunasekaran

University of Massachusetts Dartmouth, USA

Human Management

Rogers Hall

Vanderbilt University, USA Cognition, Culture

Eric Hamilton

United States Air Force Academy, USA

Innovation, International Collaborations, Networks

Guershon Harel

Univ. of California at San Diego, USA

Advanced Mathematical Thinking, Proof, Teaching & Learning of Linear Algebra

Celia Hoyles

University of London, UK Technology, Geometry, Undergraduate Education

Nicholas Jackiw

KCP Technologies, USA Technology Design & Use for Early Learners, Futurism

Barbara Jaworski

Loughborough University, UK Undergraduate Education, Teacher Development

Keith Jones

University of Southampton, UK

Knowledge Acquisition, Knowledge Usage, Mathematics in Education, Learning Technology

David Kirshner

Louisiana State University, USA

Situated Cognition

Cliff Konold

University of Massachusetts Amherst, USA

Study of How Children/Adults Reason About Probability, Statistics & Data Analysis, Designing Curricula, Tools & Programs to Foster Statistical Understanding

Colette Laborde

Equipe IAM, FRANCE Instrumental Genesis, Dynamic Geometry

Jean-Marie Laborde Cabrilog, FRANCE Dynamic Geometry Richard Lesh

University of Indiana, USA Modeling, Foundational Research

Marcia Linn

University of California at Berkeley, USA

Technology & Innovation

Chee-Kit Looi

National Institute of Education, SINGAPORE

Learning Sciences

Joanna Mamona-Downs

University of Patras, GREECE

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Maria Allesandra Mariotti

Universita di Siena, ITALY Dynamic Geometry

Fred Martin

University of Massachusetts Lowell, USA

Robotics, Computer Science

John Mason

Open University, UK Mathematical Thinking & Learning, Problem-Posing

James Middleton

Arizona State University, USA Methodology

Nicholas G. Mousoulides

Elena Nardi

University of East Anglia, UK Advanced Mathematical Thinking, Undergraduate Mathematics Practice

Ricardo Nemirovsky

San Diego State University, USA

Dynamic Mathematics, Video Analysis

Richard Noss

London Knowledge Lab, UK Technology, Representation Theory

Michael Otte Bielefeld University, GERMANY

Scientific Discovery, Semiotics, Analysis

William Penuel

SRI International, USA Discourse Analysis, Dialogic Inquiry, Evaluation

Demetra Pitta-Pantazi

University of Cyprus, Cyprus

Norma Presmeg

Illinois State University, USA Semiotics

Luis Radford Laurentian University, CANADA

Kinesthetics, Semiotics

Steve Rasmussen KCP Technologies, USA Technology & Curriculum Innovation

Teresa Rojano

ILCE, MEXICO International Collaboration

Jeremy Roschelle

SRI International, USA

Susan Jo Russell TERC, USA Early Algebra, Proof in the Early Grades

Nora Sabelli

SRI International, USA Math & Science Education Innovation, International Colloboration

Adalira Sáenz-Ludlow

Univ. of North Carolina at Charlotte, USA

Semiotics, Proof, Dynamic Geometry

Deborah Schifter

Educational Development Center, USA

Mathematics Education, Applied Mathematics

Analucia Schliemann Tufts University, USA Algebraic Reasoning, Algebra

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Notation in Elementary Schools, Mathematics Education, Cognitive Development

Alan Schoenfeld

Univ. of California at Berkeley, USA

Theories of Mathematical Thinking, Policy, Pre-Service

Roberta Schorr

Rutgers University, USA Teacher Growth, Affect

Judah Schwartz Tufts University Alternative Modes of Assessment and Science Education for Middle-School and Elementary School Teachers

Falk Seeger Bielefeld University, GERMANY

Psychological Questions for Representation, Theory for Learning Based on Cultural-Historical Psychology

Annie Selden New Mexico State University, USA

Undergraduate Mathematics

John Selden New Mexico State University, USA

Advanced Mathematical Thinking

Anna Sfard

David Shaffer

University of Wisconsin Madison, USA

Semiosis, Evolution Theory

Nathalie Sinclair

Simon Fraser University, CANADA

Technology, Aesthetics, Motivation

Finbarr (Barry) Sloane Arizona State University, USA Psychometrics, Research Design

Judith Sowder

San Diego State University (Professor Emerita)

Mathematics Education, Number Sense, Professional Development

Bharath Sriraman

University of Montana, USA Generalization, Abstract Reasoning

Walter Stroup

University of Texas at Austin, USA

Classroom Connectivity, Agency, Social Theory

Despina Stylianou

City College of New York, USA

Proof & Reasoning

David Tall

University of Warwick, UK Theories of Learning, Advanced Mathematical Thinking

Deborah Tatar

Virginia Tech, USA Cognitive Science, Data Analysis

Pat Thompson

Arizona State University, USA Algebra, Multiplicative Reasoning, Statistical and

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Probabilistic Reasoning Dina Tirosh Tel Aviv University, ISRAEL Theories of Learning Pessia Tsamir

Tel Aviv University, ISRAEL Mathematics Education

Phil Vahey

SRI International , USA Technology & Curriculum Innovation

Shlomo Vinner

Ben Gurion University of the Negev, ISRAEL

Mathematics Education

Keith Weber Rutgers University, USA Advanced Mathematical Thinking, Justification

Michal Yerushalmy

University of Haifa, ISRAEL Mathematics Teaching & Learning, Technology in Education, Design of Learning Environments

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APPENDIX E: FACULTY CURRICULUM VITA

Resumes of:

Professor Blanton

Professor Hegedus

Professor Moreno-Armella

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Maria L. Blanton The James J. Kaput Center for Research and Innovation in Math Education

Associate Professor of Mathematics Education Department of Mathematics

University of Massachusetts Dartmouth 285 Old Westport Road No. Dartmouth, MA 02747-2300 E-mail: [email protected] Phone: (508) 999-9171 Academic Degrees: Ph.D., Mathematics Education, (Minor, Mathematics), North Carolina State University, 1998 M. A., Mathematics, University of North Carolina - Wilmington, 1991 B. A., Mathematics, Secondary Certification, University of North Carolina - Wilmington, 1989 Professional Appointments: Assistant Professor, Dept of Mathematics, University of Massachusetts Dartmouth, 1998-2003 Associate Professor, Dept of Mathematics, University of Massachusetts Dartmouth, 2003-present Scholarship and Professional Activities (1998 - present): Selected Professional Activities Senior Executive Research Associate, Initiating Faculty Member, The James J. Kaput Center for Research and Innovation in Mathematics and Science Education, University of Massachusetts Dartmouth. Editorial Panel, Journal for Research in Mathematics Education. I was appointed by the National Council for Teachers of Mathematics as a member of the editorial panel for May 2008-May 2011. JRME is a highly competitive and highly regarded journal that is viewed internationally as one of the top journals in the field (only approximately 10% of international submissions are accepted for publication). Advisory Board Member for the NSF project “Toward a Scalable Model of Mathematics Professional Development: A Field Study of Preparing Facilitators to Implement the Problem-Solving Cycle." (PIs – Hilda Borko, Stanford University; Karen Koellner, University of Colorado, Boulder) 2008-2011. Advisory Board Member for the NSF project “Developing Conceptual and Procedural Knowledge: The Roles of Self- and Instructional Explanations”. (PI – Bethany Rittle-Johnson, Vanderbilt University) 2008-2011. Presenter, Chancellor’s Colloquium Series, UMass Dartmouth (with Stephen Hegedus), Re-thinking K-12 Mathematics for the 21st Century: Challenges, Innovations and New Directions. December, 2007 Expert Consultant, Teachscape, San Francisco, CA. Hired as a consultant to provide a videotaped interview for inclusion in online graduate course on Algebra in the Elementary Grades. Co-Organizer & Co-Chair (with D. Stylianou, CCNY-CUNY and K. Weber, Rutgers) of the International Invitational Conference on Research Paradigms in the Teaching and Learning of Proof, Providence, RI, 2007. Invited Participant and Group Leader, 2006 for the Mathematical Association of America/National Science Foundation Conference Algebra: Gateway to a Technological Future. I served as the small group leader for the early algebra subgroup. The committee’s task was to define funding priorities in algebra research for NSF. The conference was attended by about 30-40 invited participants. Invitation reflects a recognition of leadership in an area of research (i.e., early algebra). Advisory Board Member for the privately-funded project “Measure Up”, University of Hawaii, 2005

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Co-Organizer & Co-Chair (with D. Stylianou, CCNY-CUNY) of the International Invitational Conference on Teaching and Learning Proof Across the Grades, Providence, RI, 2004. Elected to National Office (Recording Secretary) for the NCTM/AERA Special Interest Group in Mathematics Education 2005-2007. Proposal Review Panelist, National Science Foundation REC Division (Feb. 2004; May 2004; May 2005) Participant, the National Science Foundation Principal Investigators Project Meeting, Washington, DC, 2004, 2005, 2006. Research Associate, The National Center for the Improvement of Student Learning and Achievement in Mathematics and Science, University of Wisconsin, Madison (OERI-funded) http://www.wcer.wisc.edu/ncisla/ (1998-2003). Research Associate, The Early Algebra Research Group, http://www3.umassd.edu/classes/EAR601GS/ Membership in Professional Organizations: International Group for the Psychology of Mathematics Education (PME) Psychology of Mathematics Education-North America (PME-NA) American Educational Research Association (AERA) National Council of Teachers of Mathematics (NCTM) Mathematical Association of America (through 2001) Association of Mathematics Teacher Educators (through 2005) Co-Chair and Organizer, Teaching and Learning Proof Across the Grades: Removing Uncertainty. A Working Symposium at the National Council of Teachers of Mathematics Research Pre-Session, Salt Lake City, UT (2008). (with D. Stylianou, P. Herbst, K. Weber, E. Knuth, and C. Rasmussen). Organizer, Exploring Frameworks for Capturing Students’ Mathematical Identities in Diverse Classroom Settings. (with D. Stylianou, S. Hegedus, A. Ingram-Goble, M. Gresalfi, W. Penuel and C. Brady) (2008). A Research Symposium organized by Blanton for the 2008 American Educational Research Association Annual Conference, New York, NY. Invited Discussant (2005) for Symposium "Can Patterning Support Early Algebra Learning (organized by Joan Moss, OISE/University of Toronto), Annual Meeting of the National Council of Teachers of Mathematics, Anaheim, CA. Co-chair, Early Algebra Working Group, PME 2003 (Honolulu, Hawaii), 2004 (Bergen, Norway); PME-NA 2002 (Athens, Georgia) Co-chair, Mathematical Proof Working Group, PME-NA 2004 (Toronto, Canada). Co-chair, Algebra in the Early Grades Pre-Conference to PME/PME-NA, Honolulu, Hawaii (2003) Co-Chair and Organizer, When Is Teacher Change Generative And Self-Sustaining?: Exploring Effective Design Issues In Four Professional Development Programs. Research symposium at the Annual Meeting of the American Educational Research Association, New Orleans, LA (2002). Early Algebra Research Conference Invited Participant: October 2001 (UMD); May 2002 (TERC, Cambridge, MA) Sabbatical host (2002) for Dr. Manuela David, Universidade Federalde Minas Gerais, Brazil

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Consultant, video case reviewer, Teachscape Project (a nationally-funded project) (2001). Invited Panelist (2000), Algebra Working Group (PME-NA), Tuscon, Arizona. Program Committee Member, 20th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education, Raleigh, NC. (1998) Research Grant Activity: Research Grants Awarded Principal Investigator, Invigorating The Early Undergraduate Mathematics Experience: Understanding Linkages Between Social And Cognitive Aspects Of Students’ Transition To Mathematical Proof ($580,350, 2003-2008). Awarded by the National Science Foundation, Research on Learning and Education (ROLE) Division (D. Stylianou - Co-Principal Investigator). Co-Principal Investigator, Generalizing to Extend Arithmetic to Algebraic Reasoning. ($750,000, 1999-2003). Awarded by the U.S. Department of Education, Office of Educational Research and Improvement. (James J. Kaput - Principal Investigator) Project Director, Research Experience for Undergraduates ($14,000, 2005). Awarded by the National Science Foundation in conjunction with ongoing NSF ROLE project to support undergraduate opportunities for participating in research. Recipient, UMass Dartmouth Travel Grants to support research presentations. Fall 2004, Spring 2005, Fall 2005; Spring 2006; Fall 2006; Spring 2007; Fall 2007; Spring 2008 - $4000. Project Director, Building a Mathematics Faculty Community of Practice, $1000. Awarded by the UMass Dartmouth Provost's Office (2004). Grant Proposals Under Revision Blanton, M (Principal Investigator), with co-Principal Investigator E. Knuth, University of Wisconsin Madison. $3.5 million. Developing Algebra-Ready Students for Middle School: Exploring the Impact of Early Algebra. A proposal to the National Science Foundation Discovery Research K-12 Program. (Revised submission scheduled for January 2009). Grant Proposals Submitted (not funded) Co-Principal Investigator. (with S. Hegedus, Principal Investigator). James J Kaput Center for Research and Innovation in Mathematics Education Center grant proposal submitted to Institute of Educational Sciences, US Department of Education. $10 million. (submitted November 2007, unfunded). Principal Investigator. Algebrafying an Elementary School District: Understanding Change in Teachers' Professional Practice and Its Impact on Student Learning and Achievement. ($592,000 for 5-year project). Submitted to the National Science Foundation, EARLY CAREER, 2002. Co-Principal Investigator, Integrating Physical Activity and SimCalc Simulations to Build Math of Change Concepts in Elementary Grades, ($1.1 million for 3-year project). Submitted to the National Science Foundation, Research on Learning and Education (ROLE) Division, 2002. (James J. Kaput, Principal Investigator; Maria Blanton Stephen Hegedus, Despina Stylianou, Co-Principal Investigators). Research in Progress: Blanton, M., Dougherty, B., Schifter, D., Levi, L., & Crites, T. (to appear) Essential Understandings for Algebra: Grades 3-5. Invited as lead writer for NCTM series publication. Book in preparation.

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Stylianou, D., Blanton, M., & Chae, N. Undergraduate students’ proof schemes and problem solving strategies: A closer look for relationships. Manuscript in preparation. Blanton, M., & Stylianou, D. Linking transactive reasoning in whole-class discourse to undergraduate students’ learning of proof: What difference do our words make? Manuscript in preparation. Blanton, M., & Stylianou, D. Changing participation and identity through instructional scaffolding that promotes transactive discussion. Manuscript in preparation. Manuscripts Under Review/To Appear: Blanton, M., & Kaput, J. (to appear) Building mathematical generality into curriculum and instruction. Invited chapter to appear in invited monograph, The Development of Algebraic Thinking: Cognitive, Curricular, and Instructional Perspectives. To be published in the Advances in Mathematics Education Monograph Series. New York: Springer. Blanton, M. Early Algebra. (to appear). Invited paper to be published in the proceedings of the CSMC 2nd International Curriculum Conference: Future Curricular Trends in School Algebra and Geometry, University of Chicago, Info Age Publishing. Stylianou, D. A., & Blanton, M. “Undergraduate Students’ Understanding Of Proof: Relationships Between Proof Conceptions, Beliefs, And Classroom Experiences With Learning Proof”. Manuscript submitted to Journal for Research in Mathematics Education. Blanton, M. & Stylianou, D. “Interpreting a Community of Practice Perspective in Discipline-Specific University Faculty Professional Development”. Manuscript submitted to Innovations in Higher Education. Books Published: Stylianou, D., Blanton, M., & Knuth, E. (Eds). (December, 2008) Teaching and Learning Proof Across the Grades: A K-16 Perspective. Mahwah, NJ: Taylor & Francis Group. Blanton, M. (Spring, 2008) Algebra and the Elementary Classroom: Transforming Thinking, Transforming Practice. Invited book. Portsmouth, NH: Heinemann Publishers. Kaput, J., Carraher, D. & Blanton, M., Eds. (2008) Algebra in the Early Grades Mahwah, NJ: Lawrence Erlbaum Associates/Taylor & Francis Group. Invited Book Chapters and Journal Articles (Refereed): Blanton, M., & Kaput, J. (2008). Building district capacity for teacher development in algebraic reasoning. In J. Kaput, D. Carraher, & M. Blanton (Eds.), Algebra in the Early Grades. Mahwah, NJ: Lawrence Erlbaum Associates/Taylor & Francis Group. Blanton, M., Stylianou, D., & David, M. (2008). The nature of scaffolding in whole-class discourse on mathematical proof. In D. Stylianou, M. Blanton & E. Knuth (Eds). Teaching and learning proof across the grades: A K-16 perspective. Mahwah, NJ: Taylor & Francis Group. Kaput, J., Blanton, M., & Moreno, L. (2008). Algebra from a symbolization point of view. In J. Kaput, D. Carraher, & M. Blanton (Eds.), Algebra in the Early Grades. Mahwah, NJ: Erlbaum. Blanton, M. (to appear). Elementary children can do algebra and even enjoy it. In B. Dougherty & L. Lee (Eds.), Mathematics Education Research Series. InfoAge Publishing. Blanton, M., & Kaput, J. (2005). Helping elementary teachers build mathematical generality into curriculum and instruction. Invited article in Special Edition on Algebraic Thinking, Zentralblatt für Didaktik der Mathematik (International Reviews on Mathematical Education). Edited by Jinfa Cai and Eric Knuth. Vol. 37 (1), 34-42.

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Kaput, J., & Blanton, M. (2005) Algebrafying the elementary mathematics experience in a teacher-centered, systemic way. In T. Romberg, T. Carpenter, & F. Dremock (Eds.) Understanding Mathematics and Science Matters (pp. 99-125). Mahwah, NJ: Lawrence Erlbaum Associates. Blanton, M., & Kaput, J. (2004). Design principles for instructional contexts that support students’ transition from arithmetic to algebraic reasoning: Elements of task and culture. In R. Nemirovsky, B. Warren, A. Rosebery, & J. Solomon (Eds.), Everyday matters in science and mathematics (pp. 211-234). Mahwah, NJ: Lawrence Erlbaum. Articles in Refereed Journals: Soares, J., Blanton, M., Kaput, J. (2005). Thinking algebraically across the elementary school curriculum, Teaching Children Mathematics 12(5), 228-235. Blanton, M., & Kaput, J. (2005). Characterizing a classroom practice that promotes algebraic reasoning. Journal for Research in Mathematics Education 36(5), 412-446. Blanton, M., Westbrook, S., & Carter, G. (2005). Using Valsiner’s zone theory to interpret teaching practices in mathematics and science classrooms. Journal of Mathematics Teacher Education 8(1), 5-33. Blanton, M., & Kaput, J. (2003). Developing elementary teachers' algebra eyes and ears. Teaching Children Mathematics, 10(2), 70-77. Blanton, M. (2002). Using an undergraduate geometry course to challenge pre-service teachers' notions of discourse. Journal of Mathematics Teacher Education, 5, 117-152. Blanton, M., Berenson, S, & Norwood, K. (2001). Exploring a pedagogy for the educative supervision of prospective mathematics teachers. Journal of Mathematics Teacher Education, 4(3), 177-204. Blanton, M., Berenson, S., & Norwood, K. (2001). Using classroom discourse to understand a prospective mathematics teacher’s developing practice, Teaching and Teacher Education: An International Journal of Research Studies, 17(2), 227-242. Blanton, M., Hollar, J. C., & Coulombe, W. N. (1996). College calculus students’ graphical constructions of a population growth model, The Mathematics Educator, 7(1), 15-25. Blanton, M., & Sadek, I. S. (1994). Optimal active pointwise control of thin plates via state-control parametrization. Int. J. of Systems Science, 25, (pp. 2001-2014). Blanton, M., & Sadek, I. S. (1992). Optimal active pointwise control of vibrating thin plates. J. Franklin Inst., 329(3), (pp. 801-815). Blanton, M. (1991). Teaching reading in the math classroom. The Clearing House, 64(3), (pp. 162-164). Research Reports/Monographs: Carpenter, T., Blanton, M., Cobb, P., Franke, M., Kaput, J., & McClain, K. (2004). Scaling Up Innovative Practices in Mathematics and Science. Research Report of the National Center for Improving Student Learning and Achievement in Mathematics and Science. Proceedings Editor: S. Berenson, K. Dawkins, M. Blanton, W. Coulombe, J. Kolb, K. Norwood, & L. Stiff (Eds.), (1998), Proceedings of the Twentieth Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education, Raleigh, North Carolina. Invited Plenary Address/Presentations:

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Blanton, M. (2008). Early Algebra. Invited presentation at the CSMC 2nd International Curriculum Conference: Future Curricular Trends in School Algebra and Geometry, University of Chicago. Blanton, M. (2006). Democratization of Mathematics Education: Early Algebra as a Particular of the General. Invited Plenary Address remembering the life and work of James Kaput, Annual Meeting of the Research for Undergraduates in Mathematics Education 2006 National Conference, Rutgers University, New Brunswick, NJ. Refereed Proceedings With Research Presentation: Stylianou, D., Chae, N. & Blanton, M. (2006). Students’ proof schemes: A closer look at what characterizes students’ proof conceptions. In Proceedings of the 2006 Meeting of PME-NA, Yucatan, Mexico. Blanton, M., Stylianou, D., & Theustad, N. (2005) Undergraduate students’ proof conceptions, beliefs about proof and classroom experiences with learning proof, In Proceedings of the 2005 Meeting of PME-NA, Blacksburg, VA. Stylianou, D., & Blanton, M. (2005). Undergraduate students' proof conceptions. EARLI Conference, Cyprus. Blanton, M., & Stylianou, D. (2004). "A 'Proof Story': Across the Grades: Beginning a Conversation on the Learning of Proof in Grades K-16". In Proceedings of the 2004 Meeting of PME-NA, Toronto, Canada. Blanton, M., & Kaput, J. (2004). Elementary grades students' capacity for functional thinking. In M. Hoines and A. Fuglestad (Eds.), Proceedings of the 2004 Meeting of PME, (Vol. 2, pp. 135-142). Bergen, Norway: Bergen University College. Olive, J., & Blanton, M. (2004). Developing algebraic reasoning in the early grades (K-8): The Early Algebra Working Group. In M. Hoines and A. Fuglestad (Eds.), Proceedings of the 2004 Meeting of PME, (Vol. 1, p. 269). Bergen, Norway: Bergen University College. Blanton, M., Stylianou, D., & David, M. (2003). The nature of instructional scaffolding in undergraduate students' transition to mathematical proof. In N. Pateman, B. Dougherty, & J. Zilliox (Eds.), Proceedings of the 2003 Joint Meeting of PME and PMENA, (vol. 2, pp. 113-120), Honolulu, Hawaii: Center for Research and Development Group, University of Hawaii. Olive, J., Blanton, M., & Kaput, J. (2003). The role of syntax and technology in the development of algebraic reasoning in the early grades (K-8). In N. Pateman, B. Dougherty, & J. Zilliox (Eds.), Proceedings of the 2003 Joint Meeting of PME and PMENA, Honolulu, Hawaii: Center for Research and Development Group, University of Hawaii. Blanton, M., & Stylianou, D. (2002). Exploring sociocultural aspects of undergraduate students’ transition to mathematical proof. In D. Mewborn, et al (Eds.), Proceedings of the Twenty-fourth Annual Meeting for the North American Chapter of the International Group for the Psychology of Mathematics Education, (Vol. 4, pp. 1673-1680). Athens, GA. Olive, J., Blanton, M., & Iszak, A. (2002). Investigating and enhancing the development of algebraic reasoning in the early grades (K-8): The Early Algebra Working Group. In D. Mewborn, et al (Eds.), Proceedings of the Twenty-fourth Annual Meeting for the North American Chapter of the International Group for the Psychology of Mathematics Education,(Vol 1, pp. 119-135). Athens, GA. Stylianou, D. A. & Blanton, M. (2002). Sociocultural factors in undergraduate mathematics: The role of explanation and justification. In Proceedings of the Second International Conference on the Teaching of Mathematics. Crete, Greece. Blanton, M., & Kaput, J. (2002). Design principals for tasks that support algebraic reasoning in elementary classrooms. In A. Cockburn & E. Nardi (Eds.), Proceedings of the Twenty-sixth International Conference for the Psychology of Mathematics Education,(Vol. 2, pp. 105-112), Norwich, England.

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Kaput, J., & Blanton, M. (2001). Algebrafying the elementary experience Part I: Transforming task structures. In Proceedings of the ICMI-Algebra Conference in Melbourne, Australia, December, 2001. Blanton, M., & Kaput, J. (2001). Algebrafying the elementary mathematics experience Part II: Transforming Practice on a District-Wide Scale. In Proceedings of the ICMI-Algebra Conference in Melbourne, Australia, December, 2001. Blanton, M., & Kaput, J. (2001). Student achievement in an elementary classroom that promotes the development of algebraic thinking. In R. Speiser, et al (Eds.), Proceedings of the Twenty-third Annual Meeting for the North American Chapter of the International Group for the Psychology of Mathematics Education, (Vol. 1, pp. 99-108), Snowbird, Utah. Blanton, M., Westbrook, S., & Carter, G. (2001). Using Valsiner’s zone theory to interpret a pre-service mathematics teacher’s zone of proximal development. In M. Heuvel-Panhuizen (Ed.), Proceedings of the Twenty-fifth International Conference for the Psychology of Mathematics Education, (Vol. 2, pp. 177-184), Utrecht, The Netherlands. Blanton, M. & Kaput, J. (October, 2000). Generalizing and progressively formalizing in a third grade mathematics classroom: Conversations about even and odd numbers. In M. Fernández (Ed.) Proceedings of the Twenty-Second Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Columbus, OH, ERIC Clearinghouse, pp.115-119. Blanton, M., & Kaput, J. (July, 2000). Characterizing generative and self-sustaining teacher change in a classroom practice that promotes students’ algebraic thinking. In T. Nakahara & M. Koyama (Eds.), Proceedings of the Twenty-Fourth International Conference for the Psychology of Mathematics Education, (Vol. 1, p. 144), Hiroshima, Japan. Blanton, M. (1999). Using the undergraduate classroom to challenge prospective secondary teachers’ notions of mathematical discourse. In O. Zaslavsky (Ed.) Proceedings of the Twenty-Third Annual Conference of the International Group for the Psychology of Mathematics Education, (Vol. 1, p. 266) Haifa, Israel. Blanton, M., & Westbrook, S. (1998). Examining zones of discourse in prospective mathematics teachers’classrooms. In S. Berenson, K. Dawkins, M. Blanton, W. Coulombe, J. Kolb, K. Norwood, & L. Stiff (Eds.), Proceedings of the Twentieth Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education, (Vol. 1, p. 255), Raleigh, North Carolina. Blanton, M., & Berenson, S. B. (1998). The nature of mathematical discourse in a prospective teacher’s classroom. In S. Berenson, K. Dawkins, M. Blanton, W. Coulombe, J. Kolb, K. Norwood, & L. Stiff (Eds.), Proceedings of the Twentieth Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education, (Vol. 1, p. 250), Raleigh, North Carolina. Blanton, M., & Berenson, S. B. (1997). Mediating pedagogical content knowledge through social interactions: A prospective teacher’s emerging practice. In J. A. Dossey, J. O. Swofford, M. Parmentie, & A. E. Dossey (Eds.), Proceedings of the Nineteenth Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education. Bloomington/Normal, Illinois. Rowell, D., Norwood, K., & Blanton, M. (1997). Children’s representations of multiplication. In J. A. Dossey, J. O. Swofford, M. Parmentie, & A. E. Dossey (Eds.), Proceedings of the Nineteenth Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education. Bloomington/Normal, Illinois. Vidakovic, D., Berenson, S. B., & Blanton, M. (1997). The role of technology in lesson planning: The case of preservice teachers. In J. A. Dossey, J. O. Swofford, M. Parmentie, & A. E. Dossey (Eds.), Proceedings of the Nineteenth Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education. Bloomington/Normal, Illinois.

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Vidakovic, D., Berenson, S. B., & Blanton, M. L. (1997). The role of technology in lesson planning: The case of five preservice teachers. In J. Willis, J. D. Price, S. McNeil, B. Robin, & D. A. Willis (Eds.), Technology and Teacher Education: Proceedings of the Eighth Annual Conference of the Society for Information Technology and Teacher Education. Orlando, Florida. Blanton, M., & Vidakovic, D. (1996). Preservice teachers’ ideas on investigative activities in geometry using microcomputers. In E. Jakubowski (Ed.), Proceedings of the Eighteenth Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education. Panama City, Florida. Berenson, S. B., & Blanton, M. (1996). Preservice teachers ideas’ on teaching the concept of area. In E. Jakubowski (Ed.), Proceedings of the Eighteenth Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education. Panama City, Florida. Blanton, M., & Coulombe, W. N. (1995). College calculus students’ use of verbal and graphical representations to interpret rate of change models. In D. Owens (Ed.), Proceedings of the Seventeenth Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education. Columbus, OH. Refereed Research Presentations (No Proceedings Available): Blanton, M., & Stylianou, D. (2008). The nature of identity in classroom discourse that promotes students’ transactive reasoning. Paper presented at the 2008 American Educational Research Association Annual Conference as part of the symposium Exploring Frameworks for Capturing Students’ Mathematical Identities in Diverse Classroom Settings. Helft, S., Stylianou, D., & Blanton, M. (2008). Understanding the development of aspects of proof construction. Paper presented at the 2008 American Educational Research Association Annual Conference, New York, NY. Blanton, M. (January, 2007). Algebra in the elementary grades: Defining research priorities. Presentation given as part of the symposium "Algebra: Gateway to a Technological Future". Annual Meeting of the Mathematics Association of America, New Orleans, Louisiana. Blanton, M., & Stylianou, D. (Spring, 2007). Interpreting a Community of Practice Perspective in University Mathematics Faculty Development. Paper presented at the National Council of Teachers of Mathematics Research Pre-Session Annual Meeting, Atlanta, GA. Blanton, M., & Stylianou, D., (Spring, 2007). Linking discourse to student learning in undergraduate mathematics instruction. Presented at the National Council of Teachers of Mathematics Research Pre-Session Annual Meeting, Atlanta, GA. Stylianou, D., & Blanton, M. (Spring, 2007). Proof schemes and problem solving of undergraduate mathematics students. Paper presented at the American Educational Research Association Annual Conference, Chicago, Illinois. Blanton, M. & Stylianou, D. (November, 2006) ROLE: Invigorating the Early Undergraduate Mathematics Experience. Presentation at the National Science Foundation Principal Investigator Meeting, Washington, DC. Stylianou, D., & Blanton, M. (2006). Undergraduate students’ proof conceptions. Paper presented at the American Educational Research Association Annual Conference., San Francisco, CA. Stylianou, D., Chae, N. & Blanton, M. (2006). Students’ proof schemes: A closer look at what characterizes students’ proof conceptions. Paper presented at Psychology of Mathematics Education - North America Annual Conference, Yucatan, Mexico.

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Blanton, M., (2006). Organizer and chair of The Discourse of Proof and Argumentation Across the Grades, a symposium examining discourse as a lens on understanding teaching and learning proof. The National Council of Teachers of Mathematics Research Pre-Session, St. Louis, Missouri. Blanton, M. (2006). Instructional Scaffolding in Undergraduate Classroom Discourse on Proof: What difference do our words make and how can we tell? Research paper resented at the symposium The Discourse of Proof and Argumentation Across the Grades, The National Council of Teachers of Mathematics Research Pre-Session, St. Louis, Missouri. Stylianou, D., & Blanton, M. (2006). Undergraduate students' proof conceptions. Research paper presented at the Annual Meeting of the American Educational Research Association, San Francisco, CA. (Stylianou presented this joint work.) Blanton, M., & Sytlianou, D. (December, 2005). ROLE: Invigorating The Early Undergraduate Mathematics Experience - Understanding Linkages Between Social And Cognitive Aspects Of Students’ Transition To Mathematical Proof. Poster presentation at the National Science Foundation's PI Meeting. (Stylianou presented this joint work.) Blanton, M. (October, 2005). Informal presentation on the research findings of the ROLE Proof Project. Presented at the Rutgers University Robert B. Davis Center Invitational Conference on Proof and Reasoning, Brigham Young University, Provo, Utah. Stylianou, D., & Blanton, M. (Summer, 2005). Undergraduate students' proof conceptions. EARLI Conference, Cyprus. (Stylianou presented this joint work.) Blanton, M., & Stylianou, D. (2005). Beyond the Veil of Academic Freedom: Building a Mathematics Faculty Community of Practice. Paper presented as part of the symposium "Inspiring Improvement in Collegiate Classrooms: Professional Development for Mathematics and Science Faculty" at the Annual Meeting of the American Educational Research Association. Montreal, Canada. Blanton, M. (2005). Helping teachers build generality into curriculum and instruction. Paper presented as part of the symposium "Issues of Generalization in Teaching and Learning Across the Grades" at the Annual Meeting of the American Educational Research Association. Montreal, Canada. (Invited Participant). Blanton, M. (2005). Helping teachers build generality into curriculum and instruction. Paper presented as part of the symposium "Issues of Generalization in Teaching and Learning Across the Grades" at the Annual Meeting of the National Council of Teachers of Mathematics, Anaheim, CA. (Invited Participant). Blanton, M. (2005). Using the undergraduate mathematics classroom to challenge pre-service secondary teachers' notions of mathematical discourse. Paper presented as part of the symposium "Classroom Discourse Analysis as a Professional Development Tool" at the Annual Meeting of the Association of Mathematics Teacher Educators, Dallas, Texas. (Invited Participant). Dougherty, B., & Blanton, M., (2005). Early Algebra: A Planning Grant for the Future. Panel discussion held at the Hawaii International Conference on Education, Honolulu, HI. (Invited Participant). (Organizers: B. Dougherty & L. Lee) Blanton, M. (2005). The Professional Development Perspective: Early Algebra Research with Teachers in the US. Presented as part of the Early Algebra Symposium at the Hawaii International Conference on Education, Honolulu, HI. (Invited Participant). (Organizers: B. Dougherty and L. Lee) Blanton, M. (2004). Informal presentation on the research agenda of the ROLE Proof Project. Presented at the Invitational Conference on Proof and Reasoning, Emerald Isle, NC.

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Blanton, M., & Stylianou, D. (2003). Instructional Scaffolding and the Zone of Proximal Development: An Examination of Whole-Class Discourse and Student Learning in Mathematical Proof. Presented at SIGMAA Research in Undergraduate Mathematics Education Conference, Scottsdale, Arizona. Blanton, M. (2003). Understanding teacher development in algebraic reasoning within a district-based community of learners. Paper presented as part of the Early Algebra research symposium (D. Carraher, chair), Annual Meeting of the American Educational Research Association, Chicago, IL. Blanton, M., (2003). Exploring the teacher's role in scaffolding algebraic conversations in the elementary classroom. Paper presented as part of the research symposium, Teacher Development through Examination of Practice (K. Koellner-Clark, chair), Annual Meeting of the National Council of Teachers of Mathematics, San Antonio, TX. Kaput, J., & Blanton, M. (2002) Integrating arithmetic and algebraic reasoning: Design elements of tasks and classroom practice. Paper presented in research symposium Design principles as an impetus for teacher change and student learning (Kay McClain, organizer) at the Annual Meeting of the National Council for Teachers of Mathematics, Las Vegas, Nevada. Blanton, M., & Kaput, J. (April, 2002). Developing Elementary Teachers’ Algebra "Eyes and Ears": Understanding Characteristics of Professional Development that Promote Generative and Self-Sustaining Change in Teacher Practice. Paper presented at the Annual Meeting of the American Educational Research Association, New Orleans, LA. Blanton, M., Carter, G., & Westbrook, S. (2001). Using Valsiner’s zone theory to interpret change in classroom practice: Beyond the zone of proximal development. Paper presented at the Annual Meeting of the American Educational Research Association, Seattle, Washington. Blanton, M. & Kaput, J. (November, 2000). A design principle for instructional contexts that facilitate students’ transition from arithmetic to algebraic reasoning. Research presented at the Case Study Instructional Design Conference for associates of the National Center for Improvement of Student Learning and Achievement, Ashland, MA. Blanton, M. (April, 2000). Using a subject area course to challenge secondary pre-service teachers’ models of teaching: A teacher educator’s experience. Paper presented at the Annual Meeting of the American Educational Research Association, New Orleans, Louisiana. Blanton, M. & Kaput, J. (1999). A case study of algebrafying one elementary teacher’s classroom. Presented at the NCISLA Conference on Teacher Change and Professional Development, University of Wisconsin, Madison, WI. Kaput, J., & Blanton, M. (1999). Enabling elementary teachers to achieve generalization and progressively systematic expression of generality in their math classrooms: The role of authentic mathematical experience. Presented at the NCISLA Conference on Teacher Change and Professional Development, University of Wisconsin, Madison, WI. Blanton, M. (1999). Mathematical Discourse in a Prospective Teacher’s Classroom: The Case of a Developing Practice. Paper presented at the Distinguished Paper Awards Session of the American Educational Research Association, Montreal, Canada. Kaput, J., & Blanton, M. (1999). Algebraic Reasoning in the Context of Elementary Mathematics: Making it Implementable on a Massive Scale. Paper presented at the American Educational Research Association, Montreal, Canada. Blanton, M., & Berenson, S. (1999). Exploring a pedagogy for educative supervision. Paper presented at the American Educational Research Association, Montreal, Canada.

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Westbrook, S., Blanton, M., & Carter, G. (1999). Illusions and discourse in the science classroom: Exploring the phantom zone. Presented at the National Association for Research in Science Teaching (NARST), Boston, MA. Blanton, M. L. (1998). Exploring a sociocultural pedagogy for mathematics teacher education. Presented at the International Conference on Symbolizing and Modeling in Mathematics Education, Universiteit Utrecht, The Netherlands. Blanton, M. L. (1998). Mathematical discourse in a prospective teacher’s classroom: The case of an emerging practice. Presented at the Annual Meeting of the North Carolina Association for Research in Education, Greensboro, N.C. Berenson, S. B., Blanton, M. L., &Vidakovic, D. (1998). Integrating research and practice in teacher education. Presented at the First Annual North Carolina Association of Mathematics Teacher Educators, Greenville, N.C. Blanton, M. L. (1997). The nature of representations in prospective teachers’ planned lessons on area. Presented at the Annual Meeting of the North Carolina Association for Research in Education, Greensboro, N.C. Blanton, M. L., Berenson, S. B., & Runesson, U. (1996). Prospective teachers’ use of representations in planned lessons on area. Paper presented at the Annual Meeting of the Association for Teacher Education in Europe, Glasgow, Scotland. Blanton, M. L., Coulombe, W. C. (1996). College calculus students’ use of verbal and graphical representations to interpret rate of change models. Presented at the Annual Meeting of the North Carolina Association for Research in Education, Chapel Hill, N.C. Blanton, M. L., & Hollar, J. C. (1995). College calculus students’ graphical constructions of rate of change models. Presented at the Annual Meeting of the North Carolina Association for Research in Education, Greensboro, N.C. Blanton, M. L., & Sadek, I. S. (1993). Optimal active pointwise control of thin plates via state-control parametrization. Paper presented at the South Eastern (U. S.) Regional Conference on Differential Equations, Wilmington, NC. Blanton, M. L., & Sadek, I. S. (1992). Optimal active pointwise control of vibrating thin plates. Paper presented at the Society for Industrial and Applied Mathematics International Conference on Optimization, Chicago, Illinois. Additional Professional Development Activities (conferences attended without research or workshop presentations): Doctoral Programs in Mathematics Education National Conference, Kansas City, KS, 2007 National Council of Teachers of Mathematics (2000, 2001, 2004), Association for Mathematics Teacher Educators (2000) EDC Seminars for Reform-Based Curricula (2000). Manuscripts Reviewed for the Following Journals: Journal for Research in Mathematics Education Cognition and Instruction Journal of Mathematics Teacher Education Mathematical Thinking and Learning: An International Journal Journal of Curriculum Studies Educational Studies in Mathematics Research in Collegiate Mathematics Education Journal of Computers in Mathematics and Science Teaching Zentralblatt für Didaktik der Mathematik (International Reviews on Mathematical Education)

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Technical Reports (1998 – present): Blanton, M., & Stylianou, D. (2007). Annual Report to the National Science Foundation for ROLE Grant # REC- 0337703. Blanton, M., & Stylianou, D. (2006). Annual Report to the National Science Foundation for ROLE Grant # REC- 0337703. Blanton, M., & Stylianou, D. (2005). Annual Report to the National Science Foundation for ROLE Grant # REC- 0337703. Blanton, M., & Stylianou, D. (2004). Annual Report to the National Science Foundation for ROLE Grant # REC- 0337703. Kaput, J., & Blanton, M. (2003). UMD Final Report to the OERI National Center for the Improvement of Student Learning and Achievement in Mathematics and Science Kaput, J., & Blanton, M. (2002). UMD Semi-Annual Report to the OERI National Center for the Improvement of Student Learning and Achievement in Mathematics and Science Kaput, J., & Blanton, M. (2002). UMD Final Report to the OERI National Center for the Improvement of Student Learning and Achievement in Mathematics and Science Kaput, J., & Blanton, M. (2001). UMD Semi-Annual Report to the OERI National Center for the Improvement of Student Learning and Achievement in Mathematics and Science Kaput, J., & Blanton, M. (2001). UMD Final Report to the OERI National Center for the Improvement of Student Learning and Achievement in Mathematics and Science Kaput, J., & Blanton, M. (2000). UMD Annual Report to the OERI National Center for the Improvement of Student Learning and Achievement in Mathematics and Science Kaput, J., & Blanton, M. (2000). UMD Semi-Annual Report to the OERI National Center for the Improvement of Student Learning and Achievement in Mathematics and Science Kaput, J., & Blanton, M. (1999). UMD Annual Report to the OERI National Center for the Improvement of Student Learning and Achievement in Mathematics and Science Kaput, J., & Blanton, M. (1999). UMD Semi-Annual Report to the OERI National Center for the Improvement of Student Learning and Achievement in Mathematics and Science Blanton, M. (1999). Redesigning mathematics and mathematics methods for elementary pre-service teachers. Final report submitted to PALMS II Systemic Change Contract Program, Massachusetts Department of Education. Vidakovic, D., Berenson, S., & Blanton, M. (1998). Exploring Geometry with Technology: For Teacher Leaders. Raleigh, NC: Center for Research in Mathematics and Science Education. Teaching Effectiveness and Advising (1998-Present) (see dossier for more details) Teaching Innovation Grants: Project Director, Integrating Algebraic Thinking into Core Elementary School Math Concepts: First Steps in Preparing Students for Middle and Secondary Mathematics ($23,000, 2001). Awarded by the Massachusetts Department of Education.

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Project Director, Redesigning Mathematics and Mathematics Methods for Elementary Pre-service Teachers ($10,000, 1999). Awarded by the Massachusetts Department of Education. Courses Taught at UMD: MAT 591/599 Special Topics: Algebraic Thinking in the Elementary Grades (graduate) MAT 599 Special Topics: Algebraic Thinking in the Middle Grades (graduate) MAT 592 Analyzing Teacher Learning in Professional Development for Elementary School Mathematics (Special Topics – Independent Study) MAT 521 Geometry for Secondary Teachers (graduate) MAT 695 Internship (graduate) MTH 181-182 Discrete Structures I, II MTH 310 Methods for Teaching Mathematics for Secondary Teachers MTH 108 Modern Mathematics for Elementary Teachers MTH 111 Calculus I MTH 121 Women in Mathematics MTH 100 College Algebra Selected Workshops Given: K-8 Professional Development: Co-Director (with James J. Kaput) of district-wide implementation of the Mathematics Literacy Initiative, a professional development project designed to integrate algebraic thinking into elementary classrooms, for Fall River Schools (Academic Year - 1998, 1999, 2000, 2001, 2002, 2003). Featured in "Algebraic skills and strategies for elementary teachers and students" (2003), NCISLA In Brief: K-12 Mathematics and Science Research and Implications (vol. 3, no. 1) and in "Teachers Develop Algebra Eyes and Ears" (Fall, 2000), Wisconsin Center for Educational Research (WCER) Highlights. Teaching Geometry with Technology (2-week summer workshop, N.C. State University 1998) Algebraic Reasoning in the Elementary Grades (UMD, Summer 2002 – 1 week) Blanton, M., Kaput, J., & Soares, J. (2003). Developing Elementary teachers’ algebra eyes and ears. Teacher workshop at the Annual Meeting of the National Council for Teachers of Mathematics, San Antonio, TX. Blanton, M., Kaput, J., & Soares, J. (2003). Developing Elementary teachers’ algebra eyes and ears. Teacher workshop at the Annual Regional Meeting of the National Council for Teachers of Mathematics, Boston, MA. Professional Development for School Administrators: Principals Leadership Academy, Fall River Schools, Spring 2001 (with James Kaput) Middle Grades Students: Expanding Your Horizons Presentation (UMD, 1999, 2000) SWIM Career Presentation for middle grades girls (UMD, 2006) Selected Advising Activities: Graduate Committee External Advisor, Tufts University (Advisor for 2 master’s theses, 2006 & 2008 (ongoing)) MAT Graduate Student Advisor, Mathematics Department, UMD, 1998-Present Undergraduate advisor for freshmen mathematics majors, UMD, 2000-Present

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Advisor for Research Assistants – Over a period of 4 years, I have served as a mentor to 8 undergraduate students who participated as research assistants on my NSF project on proof (cited above). While this mentoring activity focused predominantly on students’ project-related work, it also allowed me to mentor them, informally, as students. Student Advisor: Honors Project Faculty Advisor, “Metacognition and the Development of Proof” for MTH 182 student, Spring 2001; Faculty Advisor, UMD Experiential Learning (2 students); Faculty Advisor, Connections Program - (1 student, 2 semesters) University & Community Service – Selected Activities (see dossier for more details) Executive Board Member, Steering Committee Member – The James J. Kaput Center for Research and Innovation in Mathematics and Science Education, University of Massachusetts Dartmouth. Member of University Committees: Internal Review Board (2007-present) SWAT Team for Strategic Planning, Spring 2007 Masters in Arts and Teaching Committee, UMD (1998-present) SouthCoast Regional Math Partnership (2000-presen) Math Education Research Group, UMD (1998-present) University Task Force for Teacher Certification, UMD Curriculum Committee, Mathematics Department (ongoing) Multidisciplinary Programs Committee, UMD University Task Force for Pre-service Teacher Preparation for the Certification Test, UMD Search Committee Member Vice Chancellor of Student Affairs (2007) Assistant professor position, Mathematics Education (2007) Director of Research Administration, ORA (2006) Senior faculty position, Mathematics Education (2006) Assistant professor position, Mathematics Education (2005) Senior faculty position, Mathematics Education (2004) Chair, Department of Education (2004) Assistant Professor, Department of Education (2003) Chair, Department of Education (2003) IMPACT Project Manager (2001) Director, Center for Teaching and Learning (2000) Mathematics/Mathematics Education (2000) Director, Math and Business Center (2000) Assistant Professor, Applied Mathematics (1999) Assistant Professor, Science Education (1999) Classroom Technology Specialist (1999) UMD representative for American Diploma Project (ADP), a national project designed to facilitate the transition for students from secondary to higher education institutions UMD representative in mathematics education for meetings with UMass Deans to develop avenues for cross-campus collaboration in mathematics and science (2002-2003; 2004). UMass Faculty Advance Conference participant (UMD, 2002) on how to develop and offer graduate programs throughout the UMass system in ways that leverage the various strengths of each campus. Associate, The Center for Teaching and Learning, University of Massachusetts Dartmouth (1998-2002) CTL/AAC Departmental Liaison for the Center for Teaching and Learning

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Project Consultant (1999-2000), Curriculum Library Alignment and Sharing Project (CLASP), Mass Networks Education Partnership, Westport Schools Content Specialist (2000-2001) for the development of standards-based, integrated content and pedagogy curriculum by and for area high school and middle school teachers. Resulting courses to be taught at UMD. Project Consultant for the regional IMPACT Curriculum Implementation Center at UMD to support regional school districts in aligning their math and science curriculum with national and state reforms (2000-2002). Participant in STEMTEC, a state-wide initiative designed to implement reform- based teaching practices in university and K-12 instruction (2000-2001). Project MEET - consulted with Project MEET personnel at UMD to integrate technology into the curriculum of future K-12 teachers. OTHER: Honors, Awards, & Fellowships received during my education: NCARE Distinguished Paper Award, “Mathematical Discourse in a Prospective Teacher’s Classroom: The Case of a Developing Practice”, North Carolina Association for Research in Education, 1998. Outstanding Graduate (1998), Department of Mathematics, University of N. C. Wilmington Outstanding Student Manuscript Award, “College Students’ Graphical Constructions of a Population Growth Model”, College of Education and Psychology, N. C. State University, 1996. Honor Societies: Kappa Delta Pi, Pi Mu Epsilon, Phi Kappa Phi, Phi Eta Sigma, Who’s Who in Science & Engineering Outstanding Teaching Assistant, N. C. State University, 1995 N. C. State University Alumni Fellowship, 1992 B. D. Schwartz Graduate Fellowship, University of N. C. Wilmington, 1990 Fred Toney Scholarship, Mathematics, University of N. C. Wilmington, 1988

Adrian D. Hurst Award, Mathematics, University of N. C. Wilmington, 1988

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Academic Curriculum Vitae for Stephen John Hegedus Last updated September 2008

1. BACKGROUND & EMPLOYMENT

Institution Department of Mathematics University of Massachusetts Dartmouth 285 Old Westport Road N. DARTMOUTH MA 02747. USA. e-mail: [email protected] Tel: +1 (508) 999 8321 Fax: +1 (508) 999 9215 Academic Qualifications & Skills Merchant Taylor's Wolverhampton Grammar School September 1984-July 1991 – Scholarship 1. 9 GCSEs; 1 AO; 4 GCEs University of Southampton September 1991-July 1994, Department of Mathematical Studies: 2. B.Sc. (Hons) Mathematics and Economics September 1994-January 1998, Department of Educational Studies: • PhD in Mathematics Education - under an ESRC Scholarship

A Study of the Metacognitive Behaviour of Mathematics Undergraduates in Solving Problems in the Integral Calculus

Employment History Present – March 2007, Director James J Kaput Center for Research and Innovation in Mathematics Education, University of Massachusetts. Present – September 2008, Professor of Mathematics with tenure, Department of Mathematics, University of Massachusetts Dartmouth, USA. August 2008 – July 2004, Associate Professor of Mathematics with tenure, Department of Mathematics, University of Massachusetts Dartmouth, USA. July 2004 – September 2000, Assistant Professor of Mathematics (2000) Department of Mathematics, University of Massachusetts Dartmouth, USA. July 2000 – September 1998, Research Fellow Faculty of Educational Studies, University of Oxford, UK. July 2000 – January 1999, Lecturer Mathematical Institute, University of Oxford, UK September 2000 – November 1999, Educational Consultant Department for Education and Employment (DfEE), UK Government: Maths Year 2000 January 2000. MathFest Organiser Middle England. Department for Education and Employment (DfEE), UK: Maths Year 2000 December 1999 – January 2000, Educational consultant and assistant for the QAA Subject Review, Mathematical Institute, University of Oxford, UK September 1998 – December 1999, College Mathematics Tutor (GCSE & A-Level)

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Oxford Tutorial College, Oxford, UK. September 1994 – July 1998, Assistant Lecturer Faculties of Mathematical Studies and Engineering, University of Southampton, UK June 1998 – July 1998, Consultant, Adult Education Department, University of Southampton, UK Developer of course structure (including generation of annexes and PPI Forms) for Higher Education Certificate in Teaching for Primary School Assistants. September 1997 – July 1998, Lecturer (P/T) on the Masters in Education (MSc) Course Research & Graduate School of Education, Faculty of Education, University of Southampton, UK April 1998 – July 1998, Lecturer (P/T) on the PGCE Course: Mathematics Programme School of Education, Faculty of Education, University of Southampton, UK September 1994 – July 1995, Secondary Mathematics Teacher (P/T) 3. Barton Peverill College, Southampton, UK. 4. Itchen College, Southampton, UK. July 1993 – August 1998, Mathematics A-Level Tutor Home-School Tutoring, Fareham, Southampton, UK.

2. TEACHING & PROFESSIONAL DUTIES Courses Taught Present Institution: I have taught undergraduate and graduate courses (100-500 level) for majors in mathematics, computer science, engineering, pre-service and in-service education: Fall 2007: MTH531 Geometry for Teachers Spring 2007: MTH310/510 Modern Methods for Mathematics Teaching (secondary school) Fall-Spring 2006-7: MAT699. Graduate Thesis (4 dissertations) Fall 2006: MTH531 Geometry for Teachers (secondary school). Spring 2006: MTH310/510 Modern Methods for Mathematics Teaching (secondary school) Fall 2005: Technology in Mathematics Education (Secondary school + undergraduate/graduate) Spring 2005: MTH310 Modern Methods for Mathematics Teaching (secondary school), MTH421 Complex Analysis Fall 2004: MTH131 PreCalculus (with a focus on dynamic geometry and simulations), MTH540 Mathematical Challenges Spring 2004: MTH310 Modern Methods for Mathematics Teaching (secondary school), MTH530 Technology in Mathematics Education Fall 2003: MTH211 Analytic Geometry and Calculus III, MTH508 Statistics and Data Analysis for Teachers Spring 2003: MTH211 Analytic Geometry and Calculus III, MTH499/MTH591 Technology in Mathematics Education (new course) Fall 2002: MTH211 Analytic Geometry and Calculus III, MTH520 Discrete Mathematics

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Spring 2002: MTH310 Modern Methods for Mathematics Teaching (secondary school), MTH592 Mathematical Challenges (new course) Fall 2001: MTH211 Analytic Geometry and Calculus III, MTH511 Calculus and Analysis for Teachers Spring 2001: MTH101 College Algebra, MTH310 Modern Methods for Mathematics Teaching (secondary school) Fall 2000: MTH101 College Algebra, MTH111 Analytic Geometry and Calculus I Previous Institutions: University of Oxford, UK. September 1998 – July 2000 Topics in Mathematics Education, Abstract Algebra University of Southampton, September 1994 – July 1998 Undergraduate Mathematics: Calculus, Advanced Calculus, Linear Algebra & Geometry, Electronics & Mathematics, Introduction to Mathematical Software Packages Graduate Mathematics Education: Curriculum Issues, The Research Process: The construction of the research text. Graduate Students Completed Masters: Silas Coellner. Analyzing Students’ Van Hiele levels of Geometric Thinking using Sketchpad software. Completed May 2005. Donald Kessler. Word Problems and Metacognitive Thinking of Students in Pre-Calculus. Completed May 2006. Present Masters Students: Catie Marchessault Donald Joseph Julie Sunderland Therese Valente Present Doctoral Students Margie Dunn Co-supervising with Dr Roberta Schorr, Rutgers University Courses/Programs Developed Updated courses for Mathematics portion of the Masters of Arts and Teaching – see http://merg.umassd.edu/programs/graduate.html Designed two new courses for Undergraduate Mathematics Program and Mathematics portion of the Masters of Arts and Teaching: MTH 530 Technology in Mathematics Education See http://merg.umassd.edu/programs/graduate/530/main.html This course received a Chancellor’s award for Innovation in Teaching. MTH 540 Mathematical Challenges See http://merg.umassd.edu/programs/graduate/540/main.html Designed three new courses for a MAT Middle School Track for Mathematics Teachers (created through the MMSP project in Wareham) – courses to be approved. MTH531 Geometry for Teachers Podcast – online video of course at:

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http://merg.umassd.edu/programs/graduate/531/podcast/work/Podcast/Podcast.html Academic Administrative Duties Present Institution: Chair of the College of Arts and Sciences Curriculum Committee, September 2004 – June 2007; member of the Committee since September 2003. Member of the Search and Screen Committee for Faculty Position in Mathematics Education, Department of Mathematics, January 2007 – June 2007. Member of the Search and Screen Committee for Faculty Position in Mathematics Education, Department of Mathematics, January 2006 – June 2006. Chair of the Search and Screen Committee for Faculty Position in Mathematics Education, Department of Mathematics, January 2005 – June 2005. Chair of the General Education Committee, Department of Mathematics, May 2001 – 2004. Committee Member of the Institutional Review Board, October 2003 – May 2005. Member of the Mathematics Department Curriculum Committee, June 2007 – September 2003 Junior Academic Adviser, Department of Mathematics, May 2001 – present Designer and Webmaster of http://merg.umassd.edu, website for the Mathematics Education Research Group, Department of Mathematics, May 2001 – present. Member of the K-16 Regional Mathematics Network, University of Massachusetts Dartmouth, September 2000 – present. Faculty Senator, University of Massachusetts Dartmouth, January 2001 – August 2004. Member of the Search and Screen Committee for Senior Hire in Mathematics Education, Department of Mathematics, January 2004 – May 2006. Founder and Coordinator of Mathematics Department Seminar Series (funded by Center for Teaching and Learning, University of Massachusetts Dartmouth), January 2001 – May 2004. Associate with the Center for Teaching and Leaning for the development of Higher Education professional development resources at University of Massachusetts Dartmouth, September 2000 – May 2004. Member of the Search Committee for Department Secretary, Department of Mathematics, University of Massachusetts Dartmouth, January 2002. Member of the Search Committee for Department Secretary, Department of Mathematics, University of Massachusetts Dartmouth, January 2001. Member of the University Masters of Arts and Teaching (MAT) Taskforce committee, October 2000 – May 2004. Member of the MA State-wide Mathematics Task Force. March 2001. Previous Institutions: Member of the General Staff Committee, Department of Educational Studies, University of Oxford, UK, September 1998 – July 2000.

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Designer and manager of the website for the Centre for Research in Mathematics Education (CMER), University of Oxford, UK (URL: http://users.ox.ac.uk/~heg/cmer/). Correspondent to the Vice-Chancellor, University of Southampton, UK, on the proposal of the submission of Theses & Dissertations in electronic format. Faculty Representative on the Computing Services Committee, University of Southampton, UK, October 1997 – July1998. Student Representative on the Faculty Degrees Committee, University of Southampton, UK, September 1994 – August 1996. Faculty Student Representative on the Library Committee, University of Southampton, UK, October 1995-September 1996. Editorial Duties • Editor of the National Working Group’s website: Advanced Mathematical Thinking (URL:

http://www.soton.ac.uk/~amt). • Editor of Mathematical Thinking and Learning Academic Reviewer • Invited International reviewer for the Mathematics Education Research Journal for Australaisia • Reviewer for the NCTM Journal for Mathematics Teacher Education • Reviewer for Educational Studies in Mathematics • Reviewer for Journal for the Learning Science • Reviewer for Journal for Research in Mathematics Education • Reviewer for International Journal for Mathematical Thinking and Learning • Reviewer for Journal for Mathematical Behavior • International Reviewer for the Israeli Science Foundation • Reviewer for the National Science Foundation • Reviewer for various national and international conferences including the Psychology of Mathematics

Education Membership of Professional Bodies • American Mathematical Society (US) • Association for Supervision and Curriculum Development (US) • British Society for the Research in Learning of Mathematics (UK) • International Group for the Psychology of Mathematics Education • International Society of the Learning Sciences (US) • Mathematics Association of America (US) • Mathematical Association (UK) • National Council of Teachers of Mathematics (US) • Special Interest Group of the Mathematics Association of America on the Research in Undergraduate

Mathematics Education (SIGMAA on RUME) • Association for Supervision and Curriculum Development (US)

3. SCHOLARLY WORK Research Funding Current: PI: Democratizing Access to Core Mathematics Across Grades 9-12, $1,979,295 (additional supplement received of $236,248), with Luis Moreno-Armella. US Department of Education, IES Goal 2 (Development), Type A, #R305B070430. July 1, 2007 – June 30, 2011.

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PI: Representation, Participation and Teaching in Connected Classrooms, $1,499,987. NSF ROLE REC-0337710. February 1, 2004 – January 31, 2009. PI: REU (Research Experience for Undergraduates) was awarded in May 2006 to supplement this work, $27,500. This funds two undergraduate research assistantships and some travel. Co-PI: Working with Teachers and Leveraging Technology to Scale Opportunities to Learn More Complex and Conceptually Difficult Middle School Mathematics" (Scaling Up SimCalc, Phase II), NSF REC-0437861, $927,177 – Subcontract from SRI International, CA. September 1, 2004 – August 31, 2009 (PI: Jeremy Roschelle). Completed Grants PI: Symbolic Cognition in Advanced Mathematics, $99,950, with Gary Davis. NSF ROLE REC-044010. March 2005 – December 2007. PI: Classroom Connectivity: Engaging Students’ Minds, Enabling Teachers’ Practice, $10,000. Faculty Professional Development Award. Office of the President, University of Massachusetts. July 2005 – June 2006. Co-PI: Improving Mathematics Teaching Grades 4-8. $480,000 with C. Mars, Wareham/Carver Public Schools. Title IIB: Massachusetts Mathematics and Science Partnership (MMSP), Department of Education, June, 2004 – August 31, 2006. Co-PI: Understanding Math Classroom Affordances of Networked Hand-Held Devices, $1,500,000. NSF-ROLE REC-0087771. July 1, 2000 – January 31, 2004. Senior Personnel: Scaling Up SimCalc: Professional Development for Integrating Technology to Teach More Complex Mathematics (Phase 1), NSF Grant # REC 0228515, $997,608. Subcontract from SRI. October 1,2002 – September 30, 2004. PI: Chancellor’s Committee on Innovation in Teaching, University of Massachusetts Dartmouth, $2900. August 2003 – July 2004. Senior Personnel: Literacy and Content Required Here: Mandating Content Throughout Middle School Curriculum, Education Department, UMass Dartmouth and Keith Middle School. January – December 2004 (PIs: Condon & Kruger). PI: Technological Infrastructure to support Mathematics Education in the local region, President’s Office, University of Massachusetts, $9000. September 2001 – August 2002. PI: Internal grant to support a Mathematics Seminar Series, Center for Teaching and Learning, $8250. January 2001 – December 2001. Economics & Social Science Research Council (ESRC) Research Scholarship (Doctoral Studies) – 1 of 3 awards in UK, $50,000 (equivalent). October 1995 – September 1998. Research Fellowship. Economics & Social Science Research Council (ESRC), UK. $50,000 (equivalent). September 1998 – September 1999. Refereed Journal Articles Moreno-Armella, L., & Hegedus, S., & Kaput J. (2008). Static to dynamic mathematics: Historical and representational perspectives. Special Issue of Educational Studies in Mathematics: Democratizing Access to Mathematics through Technology—Issues of design and Implementation. Vol 68 (2), 99-111. Hegedus, S., & Penuel, W. (2008). Studying new forms of participation and classroom identity in mathematics classrooms with integrated communication and representational infrastructures. Special Issue of Educational Studies

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in Mathematics: Democratizing Access to Mathematics through Technology—Issues of design and Implementation. Vol 68 (2), 171-184 Lesh, R. & Hegedus, S. (2008) Building on the vision of Jim Kaput (1942-2005). Special Issue of Educational Studies in Mathematics: Democratizing Access to Mathematics through Technology—Issues of design and Implementation. Vol 68 (2), 81-84 Hegedus, S. (2007). Classroom connectivity. Educational Technology, XLVII(3), 21-25. Special Issue on Mobile Computing. Hegedus, S. (2006). Jim Kaput – 1942-2005: A mentor, a colleague, a friend. (2006) For the Learning of Mathematics, 26(1), 26–28. Nardi, E., Jaworski, B., & Hegedus, S. (2005). A spectrum of pedagogical awareness for undergraduate mathematics: From “tricks” to “techniques”. Journal for Research in Mathematics Education, 36(4), 284–316. Under review/revision/preparation: Hegedus, S., & Kaput, J. (resubmitted). Improving Algebraic Thinking Through a Connected SimCalc Classroom. Journal for Research in Mathematics Education. Hegedus, S., (under revision). Reflective aesthetics. For the Learning of Mathematics. Hegedus, S., Moreno-Armella, L., & Roschelle, J. (under review). Mathematical foundations in middle school. For Journal of Research and Mathematics Education. Hegedus, S., (in preparation). New forms of participation and engagement in representationally-rich networked classrooms. To submit to Journal for the Learning Sciences (Spring 2008). Hegedus, S. (in preparation). Impact of new activity structures on algebra learning in connected classrooms. To submit to International Journal of Mathematical Thinking and Learning (Spring 2008). Refereed Books Hegedus, S. (2000). What is Mathematics? Department for Education and Employment (DfEE): MathsYear2000, London. (www.counton.org). Including an on-line searchable mathematics education database. Hegedus, S. (in preparation). Representation and Communication. Proposal submitted to Springer (Work conducted as part of sabbatical leave, Spring 2008). Refereed Book Chapters Hegedus, S., & Moreno-Armella, L. (2008). Analyzing the impact of dynamic representations and classroom connectivity on participation, speech and learning. To appear in L. Radford, G. Schubring, & F. Seeger (Eds.), Semiotics in mathematics education: Epistemology, history, classroom and culture. Rotterdam, The Netherlands: Sense Publishers. Kaput, J., Hegedus, S., & Lesh, R. (2007). Technology becoming infrastructural in mathematics education. In R. Lesh, E. Hamilton & J. Kaput (Eds.), Foundations for the future in mathematics and science (pp. 172-192). Mahwah, NJ: Lawrence Erlbaum Associates. Roschelle, J., Knudsen, J., & Hegedus, S. (in press). From new technological infrastructures to curricular activity systems: Advanced designs for teaching and learning. To appear in I. Jacobsen (Ed.), Advanced designs for technologies of learning: International learning sciences perspectives on innovative pedagogical environments. Refereed Conference Proceedings

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Hegedus, S., & Moreno, L. (2007). Research perspectives of the impact of dynamic mathematics on teaching and learning. Proceedings of the First Central and Eastern European Conference on Computer Algebra and Dynamic Geometry Systems in Mathematics Education, Pecs, Hungary. Available for download at: http://matserv.pmmf.hu/cadgme/index_.php?page=topics. Hegedus, S., Moreno, L., & Dalton, S. (2007). Technology that mediates and participation in mathematical cognition. Proceedings of the 5th Congress of the European Society for Research in Mathematics Education (CERME) Conference, Larnaca, Cyprus. Hegedus, S., & Rodriguez, S. (2006). Role of gesture as a form of participation in networked classrooms. In S. Alatorre, J. L. Cortina, M. Sáiz & A. Méndez (Eds.), Proceedings of the 28th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 168). Mérida, Yucatán, Mexico. Hegedus, S., Dalton, S., Cambridge, L., & Davis, G. (2006). Patterns of participation in networked classrooms. In Novotna, H. Moraova, M. Kratka, & N. Stehlikova (Eds.), Proceedings of the 30th International Conference for the Psychology of Mathematics Education (Vol. 3, pp. 257–264). Prague, Czech Republic: Program Committee. Beaton, D., & Hegedus, S. (2006). Constructing an architecture for an interactive educational research database: Issues of design and implementation. (2006, May). Proceedings of the IADIS Virtual Multi Conference on Computer Science and Information Systems. Hegedus, S. (2006). Dynamic representations: A new perspective on instrumental genesis. (2005) In M. Bosch (Ed.), Proceedings for the Fourth Congress of the European Society for Research in Mathematics Education. Sant Feliu de Guíxols, Spain: Authors. Hegedus, S., & Davis, G. (2005). How prepared do students think they are for calculus? (2005, February) In Proceedings of the 8th Conference on Research in Undergraduate Mathematics Education, Phoenix, Arizona. Hegedus, S., & Kaput, J. (2004). An introduction to the profound potential of connected algebra activities: Issues of representation, engagement and pedagogy. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 129-136). Bergen, Norway: Program Committee. Hegedus, S., & Kaput, J. (2003). Improving understanding of core algebra and calculus ideas in a connected SimCalc classroom. Proceedings of the 7th Conference on Research in Undergraduate Mathematics Education, Phoenix, AZ. Kaput, J., & Hegedus, S. (2003). The effect of SimCalc connected classrooms on students’ algebraic thinking. In N. A. Pateman, B. J. Dougherty & J. Zilliox (Eds.), Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education held jointly with the 25th Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 47–54). Honolulu, Hawaii: College of Education, University of Hawaii. Hegedus, S., & Kaput, J. (2003). Exciting new opportunities to make mathematics an expressive classroom activity using newly emerging connectivity technology. In N. A. Pateman, B. J. Dougherty & J. Zilliox (Eds.), Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education held jointly with the 25th Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 293). Honolulu, Hawaii: College of Education, University of Hawaii. Roschelle, J., Vahey, P., Kaput, J., & Hegedus, S., (2003). Five key considerations for networking in a handheld-based mathematics classroom. In N. A. Pateman, B. J. Dougherty, & J. Zilliox (Eds.), Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education held jointly with the 25th Conference of the PME-NA (Vol. 4, pp. 71–78). Honolulu, Hawaii: University of Hawaii.

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Hegedus, S. (2002). The nature of reflective thinking in multi-variable calculus. In D. Mewborn, et al (Eds.), Proceedings of the 24th Conference Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 271–281). Columbus, OH: ERIC Clearinghouse Hegedus, S., & Kaput, J., (2002). Exploring the phenomenon of classroom connectivity. In D. Mewborn, et al. (Eds.), Proceedings of the 24th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 422–432). Columbus, OH: ERIC Clearinghouse. (with J. Kaput) Stroup, W., Kaput, J., Ares, N., Wilensky, U., Hegedus, S., Roschelle, J., Mack, A., Davis, S., & Hurford, A. (2002). The nature and future of classroom connectivity: The dialectics of mathematics in the social space. In D. Mewborn, et al. (Eds.), Proceedings of the 24th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 195–213). Columbus, OH: ERIC Clearinghouse. Kaput, J., & Hegedus, S. (2002). Exploiting classroom connectivity by aggregating student constructions to create new learning opportunities. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th Annual Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 177–184). University of East Anglia: Norwich, UK. Hegedus, S., (2001). Problem solving in integral calculus: One role of metacognitive thinking. In R. Speiser, C. A. Maher & C. N. Walter (Eds.), Proceedings of the 23rd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 491–500). Columbus, OH: ERIC Clearinghouse. Kaput, J., & Hegedus, S. (2001). New activity structures exploiting wirelessly connected graphing calculators. In R. Speiser, C. A. Maher, & C. N. Walter (Eds.), The Proceedings of the 23rd Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 1017–1018). Columbus, OH: The ERIC Clearinghouse for Science, Mathematics, and Environmental Education. Hegedus, S., Tall, D., & Eisenberg, T. (2001). Symbolic cognition in advanced mathematics (Discussion Group). (2001, July) In M. van den Heuvel-Panhuizen (Ed.), Proceedings for the 25th Conference of the International Group for the Psychology of Mathematics Education. (Vol. 1, pp. 268). Utrecht, Netherlands: Program Committee. Hegedus, S. (2001). Is there RUME for ROME? (2001, September) Proceedings of the Sixth Annual Conference on Research in Undergraduate Mathematics Education presented. Special Interest Group of the MAA on Research in Undergraduate Mathematics Education. (Cancelled) Jaworski, B., Nardi, E., & Hegedus, S. (1999, July). Characterizing undergraduate mathematics teaching. In O. Zaslavsky (Eds.), Proceedings of the 23rd Conference the Psychology of Mathematics Education (Vol. 1, pp. 121-128). Haifa, Israel: Program Committee. Jaworski, B., Nardi, E., & Hegedus, S. (1999, July). Characterisations of undergraduate mathematics teaching: An ongoing study. In Proceedings of the Conference for the British Congress for Mathematics Education. Northampton, UK. Hegedus, S. (1999, February). Advanced mathematical thinking. In L. Bills (Ed.), Proceedings of the Conference of the British Society for Research into Learning Mathematics (pp. 89-94). London: King's College. Hegedus, S., (1998, July). The construction of the ROME model for analysing the metacognitive behaviour of mathematics undergraduates. (1998, July) Proceedings of the International Conference for the Teaching of Mathematics, Samos98. Samos, Greece, John Wiley & Sons. Hegedus, S. (1997). Advanced mathematical thinking, metacognition and the calculus. (1997) In R. Sutherland (Ed.), Proceedings of the Conference of the British Society for Research into Learning Mathematics. Bristol, UK.

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Hegedus, S. (1996, July). Analysing the metacognitive behaviour of undergraduates. In Proceedings of the 8th International Conference of Mathematics Education (ICME), Seville, Spain. Hegedus, S. (1996). Analysing the metacognitive behaviour of undergraduates in the domain of calculus. In R. Sutherland (Ed.), Proceedings of the Joint Conference of the British Society for Research into Learning Mathematics and the Association of Mathematics Education Tutors. Loughborough, UK. Hegedus, S. (1996). Analysing verbal data. In R. Sutherland (Ed.), Proceedings of the Joint Conference of the British Society for Research into Learning Mathematics and the Association of Mathematics Education Tutors. Loughborough, UK. Non-Refereed Research Reports/Books Hegedus, S., Kaput, J., Dalton, S., Moniz, R., & Roschelle, J. (2007, December). Understanding classroom interactions among, diverse, connected classroom technologies—Overview of the present findings of a 4-year study. Technical Report 1:1. Dartmouth, MA: James J. Kaput Center for Research and Innovation in Mathematics Education, University of Massachusetts Dartmouth. Roschelle, J., Tatar, D., Shechtman, N., Hegedus, S., Hopkins, B., Knudsen, J., & Dunn, M. (2007, December). Extending the SimCalc approach to grade 8 mathematics. Technical Report 02. Menlo Park, CA: SRI International. Roschelle, J., Tatar, D., Shechtman, N., Hegedus, S., Hopkins, B., Knudsen, J., & Stroter, A. (2007, May). Can a technology enhanced curriculum improve student learning of important mathematics? Technical Report 01. Menlo Park, CA: SRI International. Hegedus, S., (2002, May). Enhancing pedagogical awareness. Professional Development Guide for Higher Education Faculty with accompanying DVD. Dartmouth, MA: Center for Teaching and Learning, University of Massachusetts Dartmouth. Non-Refereed Curriculum I have developed the following packages with my colleagues for use with the SimCalc MathWorlds™ software: Hegedus, S., Kaput, J., Dalton, S., Moniz. R. (2007). A Day At the Races: Linear Functions, Linearity and Slope as Rate. University of Massachusetts Dartmouth: James J Kaput Center for Research and Innovation in Mathematics Education Hegedus, S., Kaput, J., Dalton, S., Moniz. R. (2007). Exciting Sack Races: An Introduction to Algebra—Qualitative & Quantitative Approaches to Slope. University of Massachusetts Dartmouth: James J Kaput Center for Research and Innovation in Mathematics Education Hegedus, S., Kaput, J., Dalton, S., Moniz. R. (2007). Adventures in Space, Time and Money: Systems of Linear Equations and Simultaneity. University of Massachusetts Dartmouth: James J Kaput Center for Research and Innovation in Mathematics Education Hegedus, S., Kaput, J., Dalton, S., Moniz. R. (2007). Faster and Faster: Exploring Quadratic Relationships and Motions Through Linear Rate Graphs. University of Massachusetts Dartmouth: James J Kaput Center for Research and Innovation in Mathematics Education Hegedus, S., Kaput, J., Dalton, S., Moniz. R. (2007). Algebra I. University of Massachusetts Dartmouth: James J Kaput Center for Research and Innovation in Mathematics Education Editor

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Hegedus, S., & Moreno-Armella, L. (to appear April 2009). Invited Editor for Special Issue on Dynamic Mathematics. ZENTRALBLATT FÜR DIDAKTIK DER MATHEMATIK (ZDM). Hegedus, S. (2008). Editor of Special Issue of Educational Studies in Mathematics: Democratizing Access to Mathematics through Technology—Issues of design and Implementation. Licensed Educational Software Educational Statistics Relational Database – Stand-alone, updatable application for Educational performance statistics. Final Release May 2000. Published: DfEE, UK Government. Published at http://kaputcenter.umassd.edu via Texas Instruments at http://education.ti.com under a license agreement with the University of Massachusetts: SimCalc MathWorlds® for the TI-83/84 Plus Graphing Calculators* v.6.1 – released October 2006 SimCalc MathWorlds® for the TI-73 Explorer™ Graphing Calculators* v.2.0 – released March 2007 SimCalc MathWorlds® for the TI-92 Plus/Voyage™ 200 Graphing Calculators* v1.0 – released August 2007 SimCalc MathWorlds® for Windows* (for use with the TI-Navigator™ Learning System)* v4.1 – released October 2006. SimCalc MathWorlds® for the Mac v4.1 – released October 2006. Under Development: SimCalc MathWorlds® for the Computer-to-Computer Environment – target release Spring 2004 Development of a Haptic Device (force feedback) System with a Graphical User Interface to allow students to “touch and feel” three-dimensional mathematical objects to enable deeper, conceptual access to attributes of surfaces and the mathematics of 3d phenomenon. Target release Summer 2008. Invited Talks/Leadership at Conferences & Workshops Vision and Mission of Democratizing Access to Mathematics. Presentation to the Kauffman Foundation. February 7, 2008. Kansas City, MO. (with J. Roschelle) Organizer and Leader of Working group on Research perspectives of the impact of dynamic mathematics on teaching and learning, First Central and Eastern European Conference on Computer Algebra and Dynamic Geometry Systems in Mathematics Education. June 2007. Pecs, Hungary. (with L. Moreno) Invited Plenary on Dynamic Mathematics, Invited Conference on Semiotics in Mathematics Education, July 2007. Melle, Germany. (with L. Moreno) Organizer and Leader of Working Group on Algebra and Calculus. Thirteenth International Conference on the Teaching of Mathematical Modelling and Applications: Modelling student modelling competencies. July 2007. Bloomington, Indiana. Classroom Connectivity and 21st Technology in Mathematics Education. Invited talk to over 40 PhD students at Harvard Graduate School of Education, April 30, 2007. Harvard University, Cambridge, MA. (with J. Burke) Technology that Mediates and Participation in Mathematical Cognition. Invited presentations at the 5th Congress of the European Society for Research in Mathematics Education (CERME) Conference, Larnaca, Cyprus, February 2007. Faster and Faster: Introducing Quadratic Functions via Linearly Varying Speed. Workshop presented at the Association of Teachers of Mathematics in Massachusetts (ATMIM) 2007 Spring Conference, April 5, 2007. Marlborough, MA. (with S. Dalton)

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Teachers and Researchers Talk About Classroom Connectivity. Workshop presented at the Annual Meeting and Exposition of the National Council of Teachers of Mathematics, March 21-24, 2007. Atlanta, GA. (with S. Dalton, C. Marchessault, J. Sunderland & N. Thuestad) New Forms of Participation with Wireless Classrooms. Workshop presented at the Annual Meeting and Exposition of the National Council of Teachers of Mathematics, March 21-24, 2007. Atlanta, GA. (with J. Burke) Topologies and Pedagogies: Learning in and from Connected Classrooms. Research symposium at the Research Presession of the Annual Meeting of the National Council of Teachers of Mathematics, March 20-21, 2007. Atlanta, GA. (with T. White, N. Ares & A. Bellman) Scaling Up a Technology-rich Innovation Using a Multi-tiered Trainers Model. Working session at the Research Presession of the Annual Meeting of the National Council of Teachers of Mathematics, March 20-21, 2007. Atlanta, GA. (with R. Schorr, J. Roschelle, J. Knudsen, M. Dunn, S. Hemphill & R. Lesh) New Forms of Participation with Wireless Classrooms. Workshop presented at the 19th International Conference on Technology in Collegiate Mathematics (ICTCM), February 15-18, 2007. Boston, MA. (with S. Dalton & J. Burke) The Role of Gesture as a Form of Participation in Networked Classrooms. Poster presentation at the Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education, November 9-12, 2006. Mérida, Yucatán. (with S. Rodriguez) Patterns of Participation in Networked Classrooms. Research report presented at the 30th Annual Conference of the International Group for the Psychology of Mathematics Education, July 16-21, 2006. Prague, Czech Republic. (with S. Dalton, L. Cambridge & G. Davis) Modeling Teacher’s Questions in High School Mathematics Classes. Poster presentation at the 30th Annual Meeting of the International Group for the Psychology of Mathematics Education, July 16-21, 2006. Prague, Czech Republic. (with S. Dalton & G. Davis) Analyzing the Impact of Dynamic Representations and Classroom Connectivity on Participation, Speech and Learning. Invited talk at the conference on the Promises and Problems of a Semiotic Approach to Mathematics, the History of Mathematics and Mathematics Education, July 13-15, 2006. Bielefeld (Germany) SimCalc Connected Classrooms: New forms of Learning, New Forms of Teaching Anytime Anywhere Learning Foundation. Invited Symposium leader, AALF 4i Conference, June 21, 2006. Northeastern University, Boston, MA. Representational and Connectivity Infrastructure. Making a difference with attention to content, technology, and scale: A session honoring the memory of Jim Kaput. Invited Symposium leader at the International Conference for the Learning Sciences, June 27- July 1, 2006. Indiana University, Bloomington, IN. (with J. Roschelle, R. Lesh, C. Brady, R. Pea) Classroom Connectivity and 21st Technology in Mathematics Education. Invited talk to over 50 PhD students at Harvard Graduate School of Education, May 1, 2006. Harvard University, Cambridge, MA. Noted Invited talks to the National University of Columbia, Bogota. A series of 3 talks on Technology in Mathematics Education over 2 days to members of the Faculty of the National University of Columbia, local teachers and the Ministry of Education. March 22-24, 2006. Bogota, Columbia. Engaging Students' Minds by Bringing Trigonometry to Life! Workshop at the 2006 Annual Meeting of the NCTM, April 26-29, 2006. St. Louis, MO. (with S. Dalton) Dynamic Motion Simulations + Wireless Networks = Amazing Algebra Learning. Workshop presented at the 2005 Western Regional NCTM Conference, November 10-12, 2005. Denver, CO. (with D. Beaton)

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Dynamic Motion Simulations + Wireless Networks = Amazing Algebra Learning. Workshop presented at the 2005 Southern Regional NCTM Conference. October 20-22, 2005. Birmingham, AL. (with J. Sylvia) The Profound Power of Classroom Networks: From Pre-algebra through Calculus. Workshop presented at the 2005 Eastern Regional NCTM Conference. October 6-8, 2005. Hartford, CT. (with S. Dalton) Discovering Pre-Calculus through Dynamic Simulations + Classroom Connectivity. Invited Calculator Workshop Leader for the 17th Annual International Conference on Technology in Collegiate Mathematics, October 29-31, 2004. New Orleans, LA. Discovering Algebra & Pre-Calculus through Dynamic Simulations + Classroom Connectivity. Invited Calculator Workshop Leader for Association of Teachers in Mathematics in New England (ATMNE), October 23, 2004. Boston, MA. (with D. Beaton) Working Group for Symbolic Cognition in Advanced Mathematics (www.symcog.org). Leader & Coordinator of the 28th International Meeting of the Psychology of Mathematics Education, July 2004. Bergen, Norway. 13th Topic Study Group for Research and Development in the Teaching and Learning of Advanced Mathematical Topics. Leader & Team Chair at the 10th International Congress on Mathematical Education (ICME), July 2004. Copenhagen, Denmark. Using SimCalc software to Investigate Rate Graphs by a Secant Visualizer. Invited speaker at the 22nd Annual Meeting of the National Council for Teachers of Mathematics, April 2004. Philadelphia, PA. (with J. Kaput) Feeling Algebraic! Using CBR and MathWorlds to Understand Linear and Quadratic Functions. Invited Workshop Leader for Association of Teachers in Mathematics in Massachusetts, April 2004. Marlborough, MA. (with J. Kaput & D. York) Integrating Navigator, SimCalc and CBR in Pre- and In-Service Courses. Workshop at the 16th Annual International Conference for Teachers Teaching with Technology, March 2004. New Orleans, LA. Integrating SimCalc with TI-Navigator in grades 6-12. Co-leader of 3 workshops at the15th Annual International Conference for Teachers Teaching with Technology, March 2004. New Orleans, LA. (with J. Kaput, C. Phillips, D. York, R. Lancaster) The advent of classroom connectivity and new relations between individual and socially mediated work. Invited guest to the DataFest Symposium, part of the 15th Annual Winter Text Conference on Discourse, Text and Cognition, January 2004. Jackson Hole, WY. New Kinds of Whole Class Activities in Algebra and Pre-Calculus Using TI-Navigator. Invited Calculator Workshop Leader for the 16th annual International Conference on Technology in Collegiate Mathematics, October 2003. Rosemont, IL. (with J. Kaput) Improving Understanding of Core Algebra and pre-Calculus Ideas in a Connected SimCalc Classroom: Invigorating and Transforming Mathematics Education using Dynamic Connected Classrooms. Main speaker at the 7th International Conference for Research in Undergraduate Mathematics Education, October 2003. Scottsdale, AZ. Symbolic Cognition in Advanced Mathematics (www.symcog.org). Working Group leader at the 27th International Meeting of the Psychology of Mathematics Education. July 2003. Honolulu, Hawaii, US. How Can Classroom Connectivity Advance Standards-Based Teaching? Presentation at the Research Presession of the Annual Meeting of the the National Council of Teachers of Mathematics, April 2003. San Antonio, TX. New Mathematical Activities in Connected Classrooms using Motion Detectors. Leader of Research Insights Workshop at the Annual Meeting of the National Council of Teachers of Mathematics, April 2003. San Antonio, TX.

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Integrating Navigator, SimCalc and CBR in Pre- and In-Service Courses. Workshop at the15th Annual International Conference for Teachers Teaching with Technology, March 2003. Nashville, TN. Integrating SimCalc with TI-Navigator in Grades 6-12. Co-leader of 6 workshops presented at the15th Annual International Conference for Teachers Teaching with Technology, March 203. Nashville, TN. (with J. Kaput) SimCalc and TI-Navigator. Co-leader of 3 professional development workshops presented at the15th Annual International Conference for Teachers Teaching with Technology, March 2003. Nashville, TN. (with J. Kaput) Classroom Connectivity: What Is It and What Can It Do For Us? Presentation at the Regional Conference for the National Council of Teachers of Mathematics, November 2002. Boston, MA. (with J. Kaput & K. Zeppenfeld). The Nature And Future Of Classroom Connectivity: The Dialectics Of Mathematics In The Social Space. Co-leader of the Discussion Group at the 24th Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, October 2002. Athens, GA. (with W. Stroup, J. Kaput, N. Ares, U. Wilensky, J. Roschelle, A. Mack, S. Davis, & A. Hurford) Symbolic Cognition in Advanced Mathematics (www.symcog.org). Coordinator of the Discussion Group at the 26th International Meeting of the Psychology of Mathematics Education. July 2002. Norwich, UK. Classroom Connectivity: Opportunity Spaces. International workshop for the German-USA Early Career Research Exchange: Research on Learning Technologies and Technology-Supported Education, May 2002. Tampa, FL. SimCalc. Co-leader of a workshop at Annual Meeting for the National Council for Teachers of Mathematics, April 2002. Las Vegas, NV. A Spectrum of Pedagogic Development. Leader of Workshop for University faculty held at the University of Massachusetts Dartmouth, October 2001. Dartmouth, MA. Symbolic Cognition in Advanced Mathematics (www.symcog.org). Founder and Coordinator of the Discussion Group, First meeting at the 25th International Meeting of the Psychology of Mathematics Education, July 2001. Utrecht, Netherlands. Core Ideas of Pre-Algebra and Algebra I to Life Using Dynamical Motion Simulations and Visualization Tools on Graphing Calculators. Content Institute at Fairhaven High School, July 2001. Fairhaven, MA. Integrating SimCalc Flash Software and the TI Navigator Classroom Network Technology. Invited presentation at the Teachers Teaching with Technology International Conference, March 2001. Columbus, OH. (with J. Kaput) SimCalc. Co-leader of workshop at the Annual International Conference for Teachers Teaching with Technology, March 2001. Columbus, OH. (with J. Kaput) Exploring Students’ Engagements with New Mathematical Activity Structures in Connected SimCalc Classrooms. International workshop for the German-USA Early Career Research Exchange: Research on Learning Technologies and Technology-Supported Education, October 2001. Tuebigen, Germany. Empowering mathematics students. Interview talk presented to the Department of Matheamtics, University of Massachusetts Dartmouth, February 14, 2000. Dartmouth, MA. Towards a Good Research Practice—One Opinion. Plenary talk at British Society for Research into Learning Mathematics' New Researchers Day, University of Warwick, November 12, 1999. Coventry, UK. An aesthetic approach to inequalities. Presentation made to the Working Group on Algebra: Epistemologies, Cognition and New Technologies at the 23rd International Conference for the Psychology of Mathematics Education, July 1999. Haifa, Israel.

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A Painting of a Reflective Aesthetician. Inaugural lecture, Centre for Mathematics Education Research, University of Oxford, February 23, 1999. Oxford, UK. Characterisations of Undergraduate Mathematics Teaching: Tutors' Reflections on the Teaching of Proof. Presentation at the Joint Mathematics Association of America/American Mathematics Society Conference, January 1999. San Antonio, TX. The Issue of the Submission of Electronic Theses and Dissertations. Public Lecture, University of Southampton, June 1998. Southampton, UK. Electronic Theses and Dissertations. Coordinator of Meeting and host to visiting Professor Edward Fox, Virginia Tech, USA, University of Southampton, September 1998. Southampton, UK. The Construction of the ROME Model for Analysing the Metacognitive Behaviour of Mathematics Undergraduates. Presentation at the International Conference for the Teaching of Mathematics, Samos98, July 1998. Samos, Greece. A Study of the Metacognitive Behaviour of Mathematics Undergraduates in Solving Problems in the Integral Calculus. Defense of Doctoral Thesis. February 14, 1998. University of Southampton, Southampton, UK. Advanced Mathematical Thinking and the Calculus—A Summary of Tall (1992) and Its Applications to Students' Knowledge of the Calculus. Presentation at the Centre for Research in Mathematics Education, School of Education, University of Southampton, July 1997. Southampton, UK. Advanced Mathematical Thinking, Metacognition and the Calculus. Presentation at the Centre for Research in Mathematics Education, School of Education, University of Southampton, November 1997. Southampton, UK. Advanced Mathematical Thinking, Metacognition and the Calculus. Presentation at British Society for Research into Learning Mathematics, University of Bristol, November 1997. Bristol, UK. Metacognition - Knowledge of what exactly? Presentation at the Centre for Research in Mathematics Education, School of Education, University of Southampton, April 1996. Southampton, UK. Analysing the Metacognitive Behaviour of Undergraduates in the Domain of Calculus. Faculty Presentations, School of Education, University of Southampton, May 1996. Southampton, UK. Analysing the Metacognitive Behaviour of Undergraduates. Presentation at ICME8, International Conference of Mathematics Education, July 1996. Seville, Spain. Escaping the Constraints of Linearity - Presenting Data Using HTML. - A Discussion of the Internet and Its Origins and How It Can Be Used As a Presentation Tool in Research. Faculty Presentations, School of Education, University of Southampton, November 1996. Southampton, UK. Analysing the Metacognitive Behaviour of Undergraduates in the Domain of Calculus. Presentation at the Joint Conference of the British Society for Research into Learning Mathematics and the Association of Mathematics Education Tutors, November 1996. Loughborough, UK. Analysing Verbal Data. Presentation at the Working Group on Interviewing at the Joint Conference of the British Society for Research into Learning Mathematics and the Association of Mathematics Education Tutors, November 1996. Loughborough, UK.

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Curriculum Vitae LUIS ENRIQUE MORENO ARMELLA

Publicaciones (selección) Moreno, L.; Hegedus, S. & Kaput, J. (2008). From Static to Dynamic Mathematics: Historical and Representational

perspectives. Educational Studies in Mathematics, 68(2), pp. 99-112, June 2008. Moreno, L & Hegedus, S. (2008). Analyzing the impact of dynamic representations and classroom connectivity as

participation, speech and learning. In the book: Semiotics in Mathematics Education, epistemology, history, classrooon and culture. Sense Publishers.

Kaput, J: Blanton, M. & Moreno, L. (2008). Algebra From a Symbolization Point of View In: Algebra in the Early Grades, L. Erlbaum, New York, pp. 19-55.

Moreno, L. & Santos, M. (2008). Democratic access and use of powerful mathematics in an emerging country. In: Handbook of International Research in Mathematics Education, 2nd edition; L. English (ed). pp. 319-351, chapter 14th. Routledge, Taylor & Francis.

Moreno, L. & Santos, M. (2008). Mathematical Practices and new potential instructional trajectories. In TSG22, New technologies in the teaching and learning of Mathematics, ICME 11, Monterrey, México.

Moreno, L. & Sriraman, B. (2007). On “Intelligence and technology; the impact of tools on the nature and development of human abilities” (Sternberg & Preiss eds). ZDM, Mathematics Education, (39) 191-194. Ensayo de revisión. Moreno, L & Hegedus, S & Dalton, S. (2007). Technology that Mediates and Participation in Mathematical Cognition. CERME, Cyprus.

Moreno, L. (2006). Nociones matemáticas, constitución del símbolo y evolución del campo de referencia. En: Matemática Educativa, XXX Años. E. Filloy (ed). Aula XXI, Santillana. ISBN10: 970-29-1753-0.

Moreno, L. & Waldegg, G. (2006). Tecnología y Cognición, Postcriptum. Capítulo IX. En: Rojano, T. (Ed.). Enseñanza de la Física y las Matemáticas con tecnología. SEP-OCDE, México. ISBN 970-790-885-8

Moreno, L., Sriraman, B. & Waldegg, G. (2006). Mathematical Objects and the Evolution of Rigor. Mediterranean Journal for Research in Mathematics Education, vol. 5, 1, pp. 17-28.

Moreno, L. & Kaput, J. (2005). “Aspectos Semióticos de la divergencia de la Aritmética y el álgebra”. En: Alvarado, M & Brizuela, B.(Eds.) Haciendo Números, serie: Paidós, Educador. México.

Moreno, L. & Sriraman, B. (2005). Dynamic geometry and situated proofs. International Reviews of Mathematical Education (ZDM), Vol. 37 No. 4, pp. 130-139. Moreno, L. & Sriraman, B. (2005). The articulation of Symbol and Mediation. The International Reviews of mathematics Education ZDM (2005) vol. 37 (6) pp. 476-486, 8600.

Moreno, L. & Santos, M. (2004). Students Explorations of Powerful Mathematical Ideas through the use of Algebraic Calculators. In McDougall, D.E.& Ross, J.A.(eds), Proceeedings of the XXII- PME-NA, Toronto, ISBN 92-990027-0-3.

Moreno, L & Santillán, M. (2004). “Variation, variables and Semiotic Mediation in a Dynamical Environment”. McDougall, D.E.& Ross, J.A.(eds), Proceeedings of the XXII- PME-NA, pp. 223-228. Toronto, ISBN 92-990027-0-3.

Moreno, L. (2004). “Stabilitá strutturale et geometría dinamica: alcune idee sulle prove”. Progetto Alice, vol. V (14) pp. 407-430, Roma.

Moreno, L. (2004). Mathematical Reasoning and its formalization within a dynamic world. En: Technology and its Integration into Mathematical Education, (TIME) Montreal, julio 2004. Publicación Electrónica (CD).

Moreno, L. (2004). Mathematical Thinking and technology: Some views on their co-evolution. En: TSG15 del ICME-10, Copenhagen.

Najera, V., Moreno, L. & Santillán, M. (2004). “The variation in the understanding of the literal as a variable”. McDougall, D.E.& Ross, J.A.(Eds.), Proceeedings of the XXII- PME-NA, pp. 1497-1503. Toronto, ISBN 92-990027-0-3.

Moreno, L. y Sacristan, A. (2003). “Abstracciones y Demostraciones contextualizadas: conjeturas y generalizaciones en un micromundo computacional” En Matemática Educativa: aspectos de la investigación actual. pp. 280-294, México 2003, Fondo Cultura Económica, ISBN 968-16-7028-0.

Moreno, L. (2003). “El Espacio Indiscreto” En Alvarez, C. y Barahona, A. (Eds.) La continuidad en física y matemáticas México, Fondo de Cultura Económica, 121-132, ISBN 968-16-6543-0.

Moreno, L. (2003). “Cognición y mediación instrumental”. En Libro de Conferencias Magistrales, pp. 257-274, COMIE, 2003. ISBN 968-7542-34-9.

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Moreno, L. (2003). “Evolución y Tecnología”. En Uso de Nuevas Tecnologías en el Curriculum de Matemáticas, pp.67-80, Ministerio de Educación Nacional (MEN), Colombia, 2002. ISBN 958-97013.

Moreno, L. (2003). “Instrumentos matemáticos computacionales”. En Uso de Nuevas Tecnologías en el Curriculum de Matemáticas, pp.81-86, Ministerio de Educación Nacional (MEN), Colombia, 2002. ISBN 958-97013.

Moreno, L. (2003). “Calculadoras algebraicas y aprendizaje de las matemáticas”. En Uso de Nuevas Tecnologías en el Curriculum de Matemáticas, pp.93-98, Ministerio de Educación Nacional (MEN), Colombia, 2002. ISBN 958-97013.

Moreno, L. (2003). “Graficación de Funciones”. En Uso de Nuevas Tecnologías en el Curriculum de Matemáticas, pp.110-140, Ministerio de Educación Nacional (MEN), Colombia, 2002. ISBN 958-97013.

Moreno, L. (2003). “Ideas geométricas del currículo mediante Cabri-geometre”. En Uso de Nuevas Tecnologías en el Curriculum de Matemáticas, pp.141-150, Ministerio de Educación Nacional (MEN), Colombia, 2002. ISBN 958-97013.

Moreno, L. (2003). “La Nueva Matemática Experimental”. En Uso de Nuevas Tecnologías en el Curriculum de Matemáticas, pp.269-280, Ministerio de Educación Nacional (MEN), Colombia, 2002. ISBN 958-97013.

Moreno, L. y Block, D. (2002). “Democratic access to Powerful Mathematics in a Developing Countries” En Lyn English (Ed.) Handbook of International Research In Mathematics Education, Lawrence Erlbaum Publishers, 301-321.

Moreno-Armella L. y Santos–Trigo, M. (2001). “The Students’ Processes of Transforming the Use of Technology in Mathematics Problem Solving Tools”, Proceedings XXIII-PME, pp. 12-18, Utrecht, The Netherlands.

Moreno, L. y Santos, M. (2001). “De la herramienta al instrumento: una perspectiva informática”, Educación Matemática, 13 (2) 78-97.

Lupiáñez, J. y Moreno, L. (2001). “Tecnología y Representaciones Semióticas en el Aprendizaje de las Matemáticas”. En Iniciación a la Investigación en Didáctica de la Matemática. Homenaje al Profesor M. Castro, 291-300. P. Gómez & L. Rico (Eds.), Granada, ISBN 84-338-2752-9.

Moreno, L. y Waldegg, G. (2000). “An Epistemological History of Number and Variation” En Katz, V. (ed). Using History to Teach Mathematics, Mathematical Association of America, pp. 183-190.

Moreno, L. y Santos, M. (2000). “The use of hand-held calculators as cognitive tools in mathematical problem solving”. En Hand-held Technology in Mathematics and Science Education, 117-122, Ohio State University, Ed Laughbaum (Ed.).

Moreno, L.; Rojano, T.; Bonilla, E. y Perrusquía, E. (1999). “The incorporation of new technologies to school culture: the teaching of mathematics in secondary school” Proceedings of XXI PME-NA, vol. 2, pp. 827-833. ERIC Clearing House for Science and Mathematics.

Moreno, L. (1999). “Acerca del conocimiento y sus Mediaciones en la Educación Matemática”, Revista EMA, 4 (2) 101-114.

Moreno, L. (1999). “Epistemologia Ed Educazione Matematica”, Revista La Matematica e la sua Didattica, No. 1, 43-59. Bologna, Italia.

Moreno, L. y Waldegg, G. (1998). “La epistemología constructivista y la enseñanza de las ciencias: ¿coincidencia o complementariedad?”, Enseñanza de las Ciencias, 16 (3), 421-429. Barcelona.

Moreno, L. (1998) “La Construcción del Espacio Geométrico” en Libro Conmemorativo del 35 Aniversario del Cinvestav, 157 – 171, México, Grupo Editorial Iberoamérica, ISBN 970-625-151-0.

Moreno, L. (1998). “El Postulado de las Paralelas”, Revista de la Academia Colombiana de Ciencias, XXII (84) 393-405.

Moreno, L. (1997). “Weierstrass: cien años después”, Miscelánea Matemática, (Sociedad Matemática Mexicana), vol. 25, 11-27. (Artículo por invitación con arbitraje, publicación especial de la Sociedad Matemática Mexicana, para conmemorar los cien años del fallecimiento de Weierstrass.

Moreno, L. (1997). “La Educación matemática hoy”, Revista EMA, Investigación e Innovación educativa, 2 (2) 101-114. Bogotá (Existe versión electrónica de esta revista, lo cual le ha dado un considerable impacto internacional: http://ued.uniandes.edu.co).

Moreno, L. (1997). “La Enseñanza de la Matemática: un enfoque constructivista” en: Piaget en la Educación, 163-193,México, Editorial Paidós,ISBN968-853-381-5.

Moreno, L. (1996). “Mathematics: A Historical and Didactic Perspective”, Int. Journal for Education in Science and Technology, 27 (5) 633-639.

Moreno, L. y Sacristán, A. (1996). “Representaciones Conceptuales y Procesos recursivos. Revista EMA, Investigación e Innovación en educación matemática, 1 (2) 83-96, Colombia. Existe versión electrónica: http://ued.uniandes.edu.co)

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Moreno, L. (1996). “Una Perspectiva sobre la Demostración”, Revista Mexicana de Investigación Educativa, I (1) 123-136.

Moreno, L. (1996). “Matemáticas: Explicar y Comprender”, Revista de la Academia Colombiana de Ciencias, Vol. XX (78), 539-547.

Moreno, L. (1996). “La Epistemología Genética: una interpretación”, Educación Matemática, 8 (3) 5-23. Moreno, L. (1996). “Matemáticas y Educación: Matemática Educativa” en: Sanchez, E. y Santos, M. (Eds.)

Perspectivas en Educación Matemática, 45-57. México, Grupo Editorial iberoamérica, ISBN 970-625-137-5. Moreno, L. (1996). “Calculus and Cognition”, en Historia e Educaçao Matematica, 294-300, Portugal, ISBN: 972-

9053-55-3. Moreno, L. y Waldegg, G. (1995). “Variación y representación: del número al continuo” en Educación Matemática,

7 (1) 12-28, México. Moreno, L. (1995). “La Educación Matemática en México” en: Artigue, M., Douady, R., Moreno, L. y Gómez, P.

(Eds.) Ingeniería Didáctica en Educación Matemática, México, Grupo Editorial Iberoamérica, ISBN 970-625-119-7.

Moreno, L. y Sacristan, A. (1995) “On Visual and Symbolic Representations” en: Exploiting Mental Imagery with Computers Springer-Verlag, R. Sutherland & J. Mason (eds), 178-189.

Moreno, L. (1994). “La Geometría del Desorden y un Nuevo Desarrollo Curricular”, Educación Matemática, 6 (3) 52-64.

Moreno, L. (1994). “Comunicación y Enseñanza de las Ciencias” en: Ramirez de Alvarez, E. (Ed.) Ciencia para el despliegue de la Creatividad, 177-182. Bogotá, Colciencias, ISBN 958-9037-34-8.

Moreno, L. y Waldegg, G. (1993). “Constructivism and Mathematical Education”, International Journal of Mathematics Education in Science and Technology. 24(5) 653-661. Version en español: Moreno, L. y Waldegg, G. (1992). “Constructivismo y Educación Matemática” en: Educación Matemática 4 (2) 7-15, México.

Reproducido en La enseñanza de las matemáticas en la escuela secundaria, dentro del Programa Nacional de Actualización Permanente SEP, México, 1995, pp 49-66 y en La enseñanza de las matemáticas en la escuela primaria. Programa Nacional de Actualización Permanente SEP, México, 1995, pp 27-39.

Traducido al portugués como Moreno, L. y Waldegg, G.: “Constructivismo e Educaçao Matemática” en Matemática(s) em rede. Formação de acompanhantes locais da região centro. Departamento do Ensino Secundário, Lisboa, Portugal. Disponible en http://membros.aveiro-digital.net/adam/oficina/textos/constructo.pdf

Moreno, L. y Waldegg, G. (1991). “The Conceptual Evolution of Actual Mathematical Infinity”. Educational Studies in Mathematics, 22 (5) 211-231.

Moreno, L. (1991). “En torno a las nociones de número y variación”, Mathesis, 7, 189-204. Bromberg, S. y Moreno, L. (1990). “Tres hitos en la fundamentación de la geometría”. Mathesis, 6 (3) 281-306. Moreno, L. y Waldegg, G. (1987). “El análisis matemático y su aritmetización”. MATHESIS, III (1) 49-72,

México. Moreno, L. (1982). “Perpendicularidad y Localizaciones de Whitney”, Boletín de la Sociedad Mexicana de

Matemáticas, 27 (1) 1-24. Albis, V. y Moreno, L. (1976). “Una Hipótesis Equivalente al Postulado de las Paralelas” Boletín de la Sociedad

Colombiana de Matemáticas, 10, 78-85. Publicaciones en extenso en memorias de congresos Internacionales y Nacionales (selección) 1) Moreno, L. (2004). “Argumentación y Formalización mediadas por Cabri”. En Congreso Internacional (2002):Tecnologías Computacionales en el currículo de Matemáticas. ISBN 958-97013-9-6. Ministerio de Educación de Colombia. Conferencia Plenaria. 2) Moreno, L. & Santillán, M. (2002). “Visualizing and Understanding Variation”. En XXIV PME-NA, pp. 907-914, Atlanta, Georgia. ERIC Clearing House for Science and Mathematics. 3) Moreno,L. (2002). “From Tools to Mathematical Instruments” World Conference T3, Columbus, Ohio. Publicación Electrónica (CD). 4) Moreno, L. (2000). “Computational Tools and Executable Representations:The construction of mathematical meaning”. Worldwide T^3, Dallas, Texas. Publicación electrónica (CD). 5) Bourges, P.; Rojano, T. y Moreno, L. (2000). The Role of Usability on the Implementation of Educational Technology. Proceedings of the 33th Annual International Conference on System Sciences, Hawai, 2000. Publicación electrónica (CD).

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6) Moreno, L. y Santos, M. (2000). “An exploration of mathematical tasks via the use of Technology”. Proceedings of the International Conference on Technology in Mathematics Education, (ICTME), July 5-7, Unesco, Libano. pp. 190-200. 7) Moreno, L. (1999). On Representations and Situated Tools. Conferencia Plenaria PME-NA. 8) Moreno, L. (1999). “Mediación Instrumental y Tecnología Informática”. VII Simposio Internacional en Educación Matemática, México, Grupo Editorial Iberoamérica. 9) Bourges, P., Moreno L. y Rojano T. (1999). “Cultural Differences In Mathematics Education”. Cultural Diversity in mathematics Education, CIEAEM 51, pp. 192-198, Chichester, Inglaterra. En: Ahmed, Afzal; Williams, Honor; and Kraemer, Jean Marie (Eds.) Horwood Publishing Limited, International Publishers in Science and Technology, Coll House, Westergate, Chichester, West Sussex, 2000. ISBN 1-898563-68-3. 10) Bourges, P.; Moreno, L.; y Rojano, T. (1999). “The Role of Usability on the Implementation of Educational Software”. Proceedings of the 1st International Workshop, Designing for Global Markets, Rochester, NY, pp. 113-122. 11) Moreno, L. y Sacristan. A. (1998). “A Logo-based microworld as a window on the infinite”. Berenson, S. Dawkins, K. (Eds.) XX PME-NA , pp. 121-130. ERIC Clearing House for Science and Mathematics. 12) Moreno, L. (1998). “History of Calculus and Technology: the construction of mathematical meaning”. Proceedings of the Cieaem 50, Neuchatel, Suiza pp.421-425. ISBN 88-7967-036-0. 13) Moreno, L. (1995).”Continuity and Variation: the Transfer from a Visual to a Symbolic Representation”. Actes de la Premiere Universite d´ete europeenne sur Histoire et Epistemologie des Mathematiques, Montpellier, Francia, pp. 97-103. Moreno, L. (1995). “Windows and Executable Representations”, Keitel, K. (Ed.) Mathematics Education and Common Sense, CIEAEM 47, Berlín, pp. 370-374. Ponencias en Congresos Internacionales y Nacionales(selección) History and Pedagogy of Mathematics (HPM-ICMI), University of Toronto, 12-14 August 1992, Ponencia:

Calculus: A Historical and Didactic Perspective. VI Reunión Centro Americana y del Caribe sobre Formación de Profesores e Investigación en Educación

Matemática. Cuernavaca, 23-25 julio, 1992. Ponencia: Cálculo, una perspectiva histórica y didáctica. Memorias del IV Simposio Internacional sobre Investigación en Educación Matemática, Juárez, 4-6 agosto, 1992.

Ponencia: Visualización y Recursividad: un enfoque computacional. HIMED 94, University of Winchester, King Alfred´s College,U.K. March 1994. Ponencia: Mathematics: A

Historical and Didactic Perspective Congreso Internacional de Historia de la Matemática, UNAM (sede) 1994. Ponencia: La Demostración en

Perspectiva Annual Meeting American Mathematical Society and Mathematical Association of America, San Francisco enero

1995. Ponencia: Proof in History and Proof in the Classroom. Coloquio internacional sobre Razonamiento Matemático, México, octubre 1997. Ponencia: (con: Waldegg, G.),

Mathematical objects and the evolution of rigor. Tecnologías de la Información y Comunicación: su impacto en la Educación. OCDE, 2001. Santander España.

Ponencia en: las mesas redondas “Las infraestructuras tecnológicas”, y “La experimentación y la evaluación de las Tecnologías de la Información y la Comunicación (TIC)”.

Libros Moreno,L. (1983). Funciones Logarítmica y Exponencial, México,Limusa-Wiley, ISBN 968-18-1473-8. Moreno,L. y Waldegg,G. (1985). La Transición del Cálculo al Análisis, México, SEP / CINVESTAV. Moreno,L. y Waldegg,G. (1986). Cálculo Avanzado, México, Programa Nacional de Formación de Profesores. González, J. L., Moreno, L. y Salinas, P. (1986). Variable Compleja, México, Programa Nacional de Formación de

Profesores. Bromberg, S. y Moreno,L. (1987). Fundamentación de la Geometría:de Euclides a Hilbert, México, Programa

Nacional de Formación de Profesores. Los textos anteriores han sido empleados sistemáticamente, a través de diversas ediciones, como materiales dentro

del Programa de Maestría (y del Programa Nacional de Formación y Actualización de Profesores de Matemáticas) que el Departamento de Matemática Educativa mediante convenio con la SEP, ha impartido en mas de 16 universidades e institutos tecnológicos del país. El programa forma parte del proyecto estratégico No

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4: Formación de Profesores para el nivel medio superior y superior de la Unidad Coordinadora de Proyectos Estratégicos de la Subsecretaría de Planeación de la SEP.

Bromberg,S. y Moreno, L. (1989). Anillos de Funciones Diferenciables, Publicación de la Sociedad Colombiana de Matemática en su XXV Aniversario, 110 pags.

Moreno, L. (1989). Introducción al Análisis Matemático, Publicación UAM-I, Depto de Matemáticas y Sección de Matemática Educativa, Marzo / diciembre.

Ha sido empleado sistemáticamente en el Departamento de Matemáticas de la UAM--Iztapalapa, como libro de texto.

Moreno, L. (1989). Aplicaciones de Categoría y Medida en el Análisis, México, VI Coloquio Depto de Matemáticas, CINVESTAV.

Moreno, L. (1989) Matemáticas. Temas selectos por computadora: Cálculo, México, Sección de Matemática Educativa- CONACYT.

Moreno, L. & Waldegg, G. (2004). Aprendizaje, matemáticas y tecnología: una visión integral para el maestro. Editorial Santillana. ISBN 970-29-1198-2

Moreno, L. (et al.) (2004). Tecnología Informática: Innovación en el Currículo de Matemáticas. Ministerio de Educación Nacional de Colombia, ISBN 958-97013-9-5.

Publicados en extenso en otras revistas especializadas con arbitraje Moreno, L. (1974). “Construcción de una función no-singular”, Actas del III Coloquio del Dpto Matemáticas

CINVESTAV, 117-125 Moreno,L. (1975). “La Función de Polya”, Boletín de la Sociedad Colombiana de Matemáticas, vol 9,1975. Moreno. L. (1977). “Conteo y Probabilidad”, Matemática y Enseñanza, vol IX , 30-48 (Sociedad Matematica

Mexicana). Moreno, L. (1979). “La Curvatura de una Superficie”, Matemática y Enseñanza, vol XII 13-24 (Sociedad

Matematica Mexicana). Moreno, L. y Bromberg, S. (1990). “Determinación contextual de la práctica y enseñanza de la matemática”.

Ciencia y Educación, 4 (2). Universidad de San Carlos, Guatemala. Alarcón, J.; Bonilla, E.; Moreno, L.; Parra, BM.; Rigo, M. y Waldegg, G. (1991). “La enseñanza de las ciencias y la

comunidad científica” en Avance y Perspectiva 10, 83-92. Moreno, L. (1991). “Una Alternativa de Aprendizaje”, Notas de Matemática, vol. 31, Bogotá , Colombia. Bromberg, S. y Moreno, L. (1991) “La Organización Global de la Geometría y el Quinto Postulado Naturaleza”,

Notas de Matemática, vol. 5, 63-71. Universidad Nacional de Colombia. Moreno, L. (1992). “Fractales y Recursividad con Logo”, Micro-Aula, septiembre-octubre, 13-18. Moreno, L. (1993). “Cálculo: una perspectiva histórico-didáctica”, Matemáticas: Enseñanza Universitaria (Nueva

serie), 3, (1), 71-78, Bogotá, Colombia. Moreno, L. (1994). “¿Qué es educación matemática?”, Ciencia y Educación, 6 (1) Guatemala. Moreno, L. (1997). “Auto-nomía”, Avance y Perspectiva, marzo-abril. Moreno, L. y Rojano, T. (1998). “Las Nuevas Tecnologías en el Aula de Matemáticas y Ciencias”, Avance y

Perspectiva, vol. 17. Moreno, L. (1998). “Una hoja perdida”, Avance y Perspectiva, vol. 17, 391-393 Moreno, L. y Rojano, T. (1999). “Educación Matemática: Investigación y Tecnología en el Nuevo Siglo”, Avance y

Perspectiva, vol. 18. Moreno, L. (1999). “El Quinteto de Cambridge”, Avance y Perspectiva, vol. 18, 187-189. Moreno, L. (2001). “Cognición, Mediación y Tecnología”, Avance y Perspectiva vol. 20 Moreno, L. (2002). “Cerebro e Ideas. Ideas y cerebro”, Educacion Matemática, 14 (1) 132-138 TESIS DIRIGIDAS Maestría Fidel Sánchez S. (1981). Problemas de la Enseñanza/Aprendizaje de la Matemática Cinvestav, Departamento de

Matemática Educativa. Guillermina Waldegg (1981) Historia y Enseñanza del Cálculo, Cinvestav, Departamento de Matemática Educativa. Alejandro Ruiz (1982). Un Enfoque de la Trigonometría (vía un ensayo estadístico) Cinvestav, Departamento de

Matemática Educativa. Ricardo Cantoral (1983). Procesos del Cálculo y su Desarrollo Conceptual, Cinvestav, Departamento de

Matemática Educativa.

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Mirna Velásquez (1984). Didáctica de la Geometría, Cinvestav, Departamento de Matemática Educativa (co-dirección : Waldegg, G.)

Manuel Fajardo (1984). Didáctica del Algebra, Cinvestav, Departamento de Matemática Educativa (co-dirección : Waldegg, G.)

Truman Membreño (1984). Análisis Crítico de un Curriculum de Análisis, Cinvestav, Departamento de Matemática Educativa (co-dirección : Waldegg, G.)

Juan A. Alanís (1985). Adquisición del Concepto de Límite de una Función, Cinvestav, Departamento de Matemática Educativa (co-dirección: Waldegg, G.)

Patricia Salinas (1985). Obstrucciones e Imágenes Conceptuales en el Aprendizaje de los Números Reales, Cinvestav, Departamento de Matemática Educativa (co-dirección : Waldegg, G.)

Ana I. Sacristán (1988). Procesos Infinitos : Centración en la Intuición, Cinvestav, Departamento de Matemática Educativa.

Guillermo Bonilla (1988). La Experiencia Numérica en el Cálculo: Diseño y Desarrollo Curricular, Cinvestav, Departamento de Matemática Educativa.

Isaín Mesa Lanza. (enero 21,1992). Simbolización y Graficación: Experiencia Computacional, Cinvestav, Departamento de Matemática Educativa.

Jacobo Núñez, (Agosto 1991). Los Teoremas Fundamentales del Cálculo Integral, Cinvestav, Departamento de Matemática Educativa.

Javier González Mendieta (1992). Geometría: Una Experiencia docente, Cinvestav, Departamento de Matemática Educativa.

Susana Martinez Sánchez (Mayo 1994). Una Herramienta Computacional para el Manejo de Gráficas, Cinvestav, Departamento de Matemática Educativa.

Enrique Farías Martinez (1994). Representaciones Visuales y Simbólicas: un estudio experimental, Cinvestav, Departamento de Matemática Educativa (co-dirección: Sacristán, A.)

José Luis Lupiáñez (2000). Nuevos acercamientos a la Historia de la Matemática a través de la calculadora TI-92, Cinvestav, Departamento de Matemática Educativa.

Ivonne T. Sandoval (2001). Visualización y Razonamiento Geométrico. Cinvestav, Departamento de Matemática Educativa.

Leticia Sanchez (2003). Fluidez Computacional y Conceptual mediante los sistemas algebraicos computacionales (CAS), Cinvestav, Departamento de Matemática Educativa.

Valentín Cruz Oliva (2005). Mediación Instrumental con Calculadora. Cinvestav, Departamento de Matemática Educativa.

Doctorado Guillermina Waldegg Casanova (1o Diciembre 1987). Esquemas de Respuesta ante el Infinito :Transferencia de la

Operatividad de lo Finito a lo Infinito. Cinvestav, Departamento de Matemática Educativa (co-dirección : Alarcón, J.)

Citada en: Núñez Errázuriz, Rafael (1993). En deçà du transfini. Aspects psychocognitifs sous-jacents au concept d’infini en

mathématiques. Friburgo : Editions Universitaires Fribourg (Contributions fribourgeoises en psychologie, vol. 4).

Gonzalez, Gloriana (1995). Students’ Notions of Infinity and their Remembrances of Mathematics Classes: A Study with Latino Students. Tesis de maestría. Cornell University.

D’Amore, Bruno (1996). “El infinito: una historia de conflictos, de sorpresas y de dudas. Un campo fértil para la investigación en didáctica de la matemática” en Epsilon 36, pp 341-360 (artículo de revisión del campo).

Penalva Martínez, M. Carmen (1998). “El mapa cognitivo como recurso de investigación en el estudio de casos” en Educación Matemática, 10 (2) 5-22.

Garbin Dall’Alba, Sabrina (2000). Infinito actual: inconsistencias e incoherencias de estudiantes de 16-17 años. Tesis doctoral. Universidad Autónoma de Barcelona, pp 349.

Garbin, Sabrina y Azcárate, Carmen (2002). “Infinito actual e inconsistencias: Acerca de las incoherencias en los esquemas conceptuales de alumnos de 16-17 años” Gonzalo Zubieta Badillo (1996). Sobre Número y Variación: antecedentes del cálculo. Cinvestav, Departamento de Matemática Educativa.

Gonzalo Zubieta Badillo (1996 ). Sobre Número y Variación: antecedentes del cálculo. Cinvestav, Departamento de Matemática Educativa.

Ricardo Quintero (1996). Arte Analítica e imaginación en la Geometría de Descartes, Cinvestav, Departamento de Matemática Educativa (co-dirección: Garcíadiego, A.)

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Ana Isabel Sacristán (octubre 1997). Windows on the Infinity: Constructing meanings in a Logo-base microworld, Instituto de Educación de la Universidad de Londres, dentro del convenio académico entre dicho instituto y el Programa Nacional de Formación y Actualización de Profesores de Matemáticas. (co-direccion: Noss, R.)

Marco Antonio Santillán (2002). Mediación Instrumental con Calculadora Graficadora, Cinvestav, Departamento de Matemática Educativa.

Eugenio Diaz Barriga (2002). Transparencia y Opacidad de los Objetos Geométricos. El Desarrollo de algunos procesos fundamentales del pensamiento matemático en ambientes de resolución de problemas. Cinvestav, Departamento de Matemática Educativa.

David Benitez Mojica (2006). Formas de razonamiento que desarrollan estudiantes universitarios en la resolución de problemas con el uso de tecnología. Cinvestav, Departamento de Matemática Educativa (Co-dirección: Santos, M.).

Ivonne T. Sandoval, (2005). Sobre la Argumentación y la Demostración en ambientes de Geometría Dinámica”. Cinvestav, Departamento de Matemática Educativa. Octubre 2005. Tesis premiada con el galardón Arturo Rosenblueth, a la mejor tesis doctoral del Cinvestav, en el area de Ciencias Sociales y Educación.

Invitaciones: Conferencias y Grupos de Trabajo (2007-2008) Keynote lecture: Digital Semiotic Theory: An evolutionary and epistemological perspective. (with S. Hegedus) 16th July, 2007, Melle, Germany. In: Promises and problems of a Semiotic approach to Mathematics. Inaugural lecture of the Kaput Center: From Symbolic Cognition to Digital Environments-a long term perspective. 26th October, 2007. 3) Invited Plenary address: A perspective on proof and situated proof. For the Conference: Research Paradigms on the Teaching and Learning of Proof. Providence, November 6th, 2007. 4) Invited lecture: Some reflections on digital tools and mathematical signs. Tufts University, March 2008. 5) Workshop (4 sessions): Dynamic Mathematics, during the First Central –Eastern European Conference on Computer Algebra and Dynamic Geometry Systems in Math Education. University of Pécs, Hungary, 20-23 June, 2007. (With S. Hegedus) 6) Directions for research on modeling in Algebra and Calculus. In: ICTMA 13, July 22-26, 2007. (With S.Hegedus). Concurrent sessions (4). Indiana University. Conferencias Plenarias (Selección) Stabilita strutturale e geometria dinamica: alcune idee sulle prove. Third Cabri Geometry International conference:

Cabriworld 2004, Italia. Matemática dinámica y sus procesos de validación. Segundo Congreso Internacional Iberocabri 2004, México. Cognición y Mediación Instrumental. Conferencia Magistral en VI Congreso Nacional de Investigación Educativa

(COMIE) 2003. México. Mathematical Thinking and technology: Some views on their co-evolution (2004). En TSG15 (The role and use of

technology in the teaching and learning of mathematics) del ICME-10, Copenhagen. La publicación es en formato electrónico en el site del ICME, puede verse en: http://www.icme-organisers.dk/tsg15/

La demostración en un contexto dinámico (2002). Primer Congreso Internacional Iberocabri 2002, Santiago de Chile.

Otras conferencias por Invitación (Selección)

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Ciclo de cuatro conferencias por invitación: "La Evolucion del Análisis Matemático". Departamento de Análisis Matemático, Universidad de La Laguna, Tenerife, España, 14-17 abril 1993.

Ciclo de conferencias sobre Epistemología y Constructivismo en Matemáticas Universidad Nacional de Colombia 25 agosto-5 septiembre 1991.

Ciclo de conferencias sobre Infinito Matemático y Constructivismo en Educación. Universidad del Valle, Cali, Colombia, 6-9 septiembre 1991.

Educación Matemática y Nuevas Tecnologías. Ciclo de conferencias en la Univ. del Norte, Barranquilla, Colombia, julio, 1995.

Estado Actual y perspectivas de la Educación Matemática. Ciclo de conferencias en la Univ. del Tolima, Colombia, 1995.

Didáctica de la Matemática. Curso impartido durante la III Reunión de Matemáticas e Informática en Sabanalarga, Colombia, enero 1996 (Reunión organizada por la Sociedad Colombiana de Matemáticas).

Sobre Representaciones Ejecutables y Calculadoras. Curso impartido durante la IV Reunión de Matemáticas e Informática en Sabanalarga, Colombia, enero1997 (Reunión organizada por la SCM como parte de la celebración de su 40 aniversario).

Se realizaron en el marco de diversas invitaciones financiadas por el BID-ICFES (Instituto Colombiano para el Fomento de la Educación Superior) dentro del proyecto "Desarrollo de la Capacidad de Investigación". Mi participación fué en calidad de "Asesor Internacional". Estas tareas equivalen a la formación de recursos humanos en el area estratégica de la educación.

Subvención otorgada Otorgamiento por concurso, de una beca de investigación (con financiamiento completo) de la Fundación Archivos

Jean Piaget, de Ginebra, para adelantar trabajos sobre la Constitución del Espacio Geométrico, durante un trimestre a partir de septiembre de 1997.

Otras contribuciones a la vida académica Dr. Moreno-Armella pertenece al Editorial Board de la revista internacional Mathematical Thinking and Learning, una de las revistas líderes en el campo de la educación matemática. La investigación sobre geometría dinámica del Dr. Moreno-Armella ha dado pie a diversas invitaciones para presentar su trabajo como conferencista plenario a nivel internacional. Fue invitado como conferencista plenario al International CabriWorld 2004, Roma, Italia. Una versión especial de su conferencia apareció publicada como Stabilitá Strutturale e geometria dinamica: alcune idee sulle prove en la revista italiana Progetto Alice (Rivista de matematica e didattica). La tesis de doctorado de Ivonne Sandoval, dirigida por el Dr Moreno-Armella, Sobre la Argumentación y la Demostración en ambientes de Geometría Dinámica, sustentada en octubre de 2005, recibió el premio Arturo Rosenblueth a la mejor tesis doctoral en Cinvestav.

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APPENDIX F: REPORTS OF EXTERNAL EVALUATORS, INSTITUTIONAL RESPONSES

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REPORT FROM THE UNIVERSITY CURRICULUM COMMITTEE MEETING (11/4/08) AND RESPONSES FROM THE PROPOSERS

p. 7 Build connections specific to math/ education /both incorporate p.41 last sentence into this section Response: see revision; p. 7 of proposal at http://www.kaputcenter.umassd.edu/phd/ p. 23 MAE650 – delete reference to cross-listing need to remove cross-listing of SOC 401 and as cited in other areas of proposal Response: deletion made; see revision p. 23 of proposal p. 41 Section 6C- make reference to student selection / admission as part of Cohort model is cited in other areas of proposal but should be emphasized in this section Response: The nature of the cohort model and the necessity of it is explained in more detail on p41 Section 6C. p. 42 1st paragraph Second to the last sentence listed twice (typo) Response: deletion made; see revision p. 42 of proposal p. 42 1st sentence should be restated in admission criteria to emphasize prior math knowledge expectations Response: see revision; p. 42 of proposal. Please note that the program requires a Bachelors in Mathematics or a related area. Specific mathematics requirements are not a major requirement of the program because of its interdisciplinary focus. p. 42 1st paragraph, last sentence can be structured into p. 7 Response: see addition; p. 7 of proposal p.42 & 43 GPA 3.0 and 4.0 : possibly review change in GPA requirements to be consistent with other grad programs on campus…cite GPA expectations for Bachelors and Masters level . Use College of Nursing outline as defined in Grad Office posting on UMassD website Response: The STEM department respects the concern of the UCC but GPA will remain at 3.0 based on the following: • There is no campus criteria for GPA expectations-graduate programs • The Academic Council and Dean of SEPPCE did not offer any concern with a 3.0 GPA • A review of other UMass Graduate Programs found undergraduate GPA requirements as low as

2.75 for various programs • The GPA is only one requirement. We will expect more than just a 3.0 GPA and the application

procedure is expected to be competitive. p. 51 Define how state appropriation amount is projected (how did you calculate this specific amount)

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Response: State appropriation funds are dependent on student enrollment. The formula and figures were supplied by the Associate Provost for Graduate Affairs. It should be noted that the program is sustainable without such projected funds. p. 50 & 51 Library resources: proposal cites $5,000.00 yearly…Where will these funds come from? Response: The Dean of SEPPCE will allocate funds to the library to establish supporting material. It should be noted that students will use existing resources (especially electronic resources) and the archive of literature and scholarly journals available at the Kaput Center. Also, 5% of indirect funds generated by grants will continue to support LSIRT and indirect funds recovered to the SEPPCE will also be used to help support the acquisition of these resources. p. 52 Current status of faculty ’09 positions/ searches? Response: The Position Authorizations for the Assistant or Associate Professor (Math Education) (#09057) has been approved. This is part of a long-term strategic agenda beginning in 2004 – see page 1 – to support the growth of the Math Ed Research Group to sustain a PhD and research program.

p. 52 AY’11 : $80,000 – Where will these funds come from? Campus? Grant/Research supported? Response: As explained on pg 47 the AY’11 position will be funded through enrollment-produced income as well as research grant expansion. General concern: If existing faculty are instructing/ developing new courses…who will instruct their prior/current courses? Where will the additional funds come from to support such additional required units? What strain will this cause on the needs of the MAT and undergrad. education programs on campus? Response: It is expected that students on the program with TAs will have sufficient background to instruct these ongoing pre- and in-service courses to serve both the MAT and undergraduate education programs that the faculty partly taught before. Faculty taught approximately 4 MAT/Pre-service courses per year previously. Faculty will still teach some MAT courses but the focus will be on the effective and efficient delivery of the proposed PhD program. We believe that the program will actually provide more opportunity to deliver education courses and it will be a collaborative effort of the SEPPCE, adjunct expert faculty from the region (through Kaput Center outreach initiatives) and students on the program.

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RESPONSE TO OTHER QUESTIONS FROM CAMPUS OFFICIALS AND

PRESIDENT’S OFFICE STAFF

1. What are the math requirements?

Answer: See page 42. We appreciate that this a non-standard approach to listing "relevant"

content but mathematics education is a field with many paradigms and it is not just the education

of mathematics. Our work is not a sub-set of the department of mathematics or the field of

mathematics, yet content, is deeply important to our program. Content and pedagogy are deeply

intertwined. We alert the reader to the structure of our program and the content of our proposed

courses that reaches across various disciplines but nowhere addresses content directly, e.g.

Teaching Calculus. Our program requires a level of mathematics competence as outlined on pg

42 AND more so skills to research deep and complex problems at the cognitive, social and

professional level.

In our approach we are taking a deep epistemological stance on the nature of knowledge in

educational paradigms that is different from that of a traditional mathematics department. As

such we expect our students to develop an awareness and/or build models of mathematical

cognition and theories of teaching at the micro and macro level.

2. Need to be clear on what we are seeking approval for, i.e. an MS and a PhD - Page 22

Answer: A new sentence is added to pg4 to alert the reader upfront that we are proposing the

need to offer a Masters and PhD in Mathematics Education but students will apply and be

accepted only into the doctoral program and not for a separate master’s degree.

We have added similar statements to clarify this need in the sections on curriculum (4C –

pg25) and admissions (6C – pg40).

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Responses to External Reviewers Report

Institutional Responses in Red

Prepared by: Marilyn Carlson & John Olive Submitted: January 7, 2009

1. Is the proposed curriculum congruent with program goals? Are the content and sequencing of the curriculum appropriate? Is there a sufficient distinction between the doctoral, master's and baccalaureate curricula? Are there any major omissions or problems?

The proposed curriculum has a strong focus on developing students’ research skills, knowledge of research literature, and use of theory to analyze, interpret and report research findings. The faculty voiced that they value authentic research experiences as a primary approach for supporting the development of scholars in mathematics education. The proposed program reflects this stance. The program of study has a heavy focus on research internships, research seminars and doctoral coursework. In year 1 the student completes a research seminar and a course titled, “Developing Research Skills Part I” (6 hours). In Year 2 the student completes an internship (Authentic Learning), a Research Seminar and “Developing Research Skills Part II” (9 hours). In years 3 and 4 the student completes all of her/his coursework (36 hours) engaged in one-on-one research with her/his advisor. Fifty one (of 72) hours of the program’s coursework fall into these categories. The other courses in the program of study appear to be more structured, although many of them also appear to be focused on developing students’ research skills (e.g., Introduction to Qualitative Methods, Introduction to Quantitative Methods, Frameworks for Research Analysis, Developing Theory, Topics In Mathematics Education). The program goal of providing students’ authentic research experiences will be met with the current coursework. We were particularly impressed with the internship component of their program and suggest that coursework for this experience be retained. However the heavy focus in the area of research skills means that other areas of standard Ph.D. programs in mathematics education are deemphasized. The proposed program of study, as currently stated, does not appear to have a strong emphasis on developing students’ advanced mathematical abilities. In our discussions with the faculty we understand that all of the proposed courses will focus on mathematics as the kernel of students’ inquiry and they are planning on including more courses with a mathematical focus based upon our conversations. For example: A K-20 approach to (1) Algebraic thinking, (2) Mathematics of Change and Variation, (3) Proof, (4) Geometric reasoning, (5) Discrete Structures, (6) Number Theory, (7) Mathematical Problem Solving. These courses would be developed by Center faculty in collaboration with many adjunct faculty through the UMass system and the Kaput Center advisory board. The creation of these new courses would certainly go a long way towards meeting our recommendations that all students in the program complete at least 12 hours of graduate coursework that deeply reflects the content

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matter of mathematics from longitudinal perspectives across the K-20 educational system. Further, we recommend that students who are interested in conducting research on secondary mathematics education complete at least 18 hours of such coursework and students interested in conducting research in the area of undergraduate mathematics education complete at least 24 hours of graduate level coursework that deeply reflects the content matter of both pre-college and college mathematics.

Students admitted conditionally based on a deficiency in their mathematical preparation will be

required to take up to 12 credit hours in addition to existing program course requirements to

meet these deficiencies. We will assess the needs on a case-by-case basis upon entrance to the

program. In addition, students will be expected to have the appropriate level of mathematical

knowledge to conduct research in their selected grade domain (e.g., elementary secondary,

tertiary). Students who do not meet this expectation will be advised to take additional

coursework in mathematics courses within the program. Students will be expected to meet any

program deficiencies before qualifying for the Production Phase (Advanced Doctoral Phase).

See revisions on p. 24 Our conversations with various faculty members and administrators suggest that such an adjustment to the current program is possible. We also appreciate that the current mathematics education faculty have exceptionally strong backgrounds in mathematics; as such, they also agree with our view that the mathematical development of their students is critical and should be a central feature of the program. We were impressed with their desire and commitment to have their students take mathematics courses that are relevant and meaningful. We are also confident that the current faculty have the knowledge to collaborate with mathematicians in developing mathematics courses that meet these goals. It also became clear from our conversations that several of the proposed MAE courses would involve the study of advanced mathematics, and this content emphasis needs to be reflected more explicitly in the course descriptions. The development of a Master’s Program in Mathematics at UMass Dartmouth would also help provide options for graduate study in mathematics for the doctoral students in mathematics education. In several Ph.D. programs in mathematics education in the US, students pick up a master’s in mathematics along the way to their doctorate. The opportunity to do so provides these students with stronger backgrounds in mathematics that make them very competitive for the best positions in mathematics education. See titles above. Courses are currently in preparation.

We also suggest that faculty create a plan to support the instructional development of their students’ instructional abilities early in the students’ program of study. In light of the focus on algebra in the current faculty’s various funded projects, and the fact that it is likely that after graduation many of the Ph.D. students will be teaching this content, we believe that students would benefit by teaching and studying student learning in a college algebra course. Is it

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possible to have students complete a teaching internship in college algebra or precalculus during the second or third year of their program? If mathematics education Ph.D. students are able to cover 5-10 sections of college algebra or precalc each semester, this may justify increasing the student numbers and faculty lines in the proposed Ph.D. program. Students who have no K-16 teaching experience will be advised to complete a teaching

internship prior to qualifying for the Advanced Doctoral Phase of the program. See revision on p.

25.

2. Are admission and degree requirements of sufficient rigor to produce graduates who are competitive in the field?

Admission requirements may need to be strengthened, perhaps requiring a master’s level education in an appropriate field or graduate-level teaching certification. Generally, we believe that once the program of study is adjusted to include meaningful, graduate coursework that deeply reflects the content matter of mathematics from longitudinal perspectives across the K-20 educational system (as suggested above), the students will be well prepared to be competitive in the field. However, students admitted to the program without prior teaching experience at the pre-college level may need to have such experiences accommodated within their program. We have found that positions in Mathematics Education often state pre-college teaching as desired (if not necessary) experiences of job candidates.

See pages 41-42 (section 6C) for changes 3. Are the research and teaching credentials of the faculty of sufficient quality,

breadth and depth to mount the proposed program? Are there sufficient faculty to mount the program? The strong faculty team of mathematics educators dedicated to building this program have the research expertise, academic integrity and experiences needed to develop high quality courses and research experiences for their students. All three faculty are highly regarded by their colleagues in the field and have published widely, establishing an admirable research record and reputation for high-quality work. With the expansion of the course requirements to include courses focused on mathematical content and a teaching internship, we believe the total number of mathematics education faculty should be increased to 6 or 7. It seems appropriate that the graduate courses in the MAT program for pre-service and inservice teachers should be taught by faculty, with the Ph.D. students assisting; however, their may be exceptional cases where Ph.D. students could teach some of these courses, although it is not typical that graduate students teach graduate courses prior to completing their degree.

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4. Are facilities, equipment, and library resources adequate to support the

program? Is the program's proposed budget adequate? The facilities, equipment and library are equipped to support mathematics education faculty and graduate students in conducting their research. The technology resources and tech support supplied by the Kaput Center’s funded projects provide exceptional resources for collecting and processing qualitative data. The space seems adequate for the current mathematics education faculty and project staff; however, as more faculty are hired and students are recruited into the program, additional office space will be needed. The income and expense projections for the program indicate that this program has the potential to generate substantial income for the university, although the comparison in Table 5 on page 53 may be somewhat misleading. The income column of this table indicates total income for each year, whereas the expense side only shows new expense added in each year (rather than the total on-going expense for each year). We believe that a more honest comparison of total income against total expenses over the 4 years would show a net gain to the university of more than half a million dollars.

See revisions to Table 5, p. 55. 5. In your opinion, will graduates of this program be employable? Is the evidence of need and demand for such a program compelling?

With the suggested additions to the program we have high confidence that graduates of the program will have many diverse job opportunities upon completion of their degrees. The high-esteem with which the current faculty are regarded in the profession will also add to their graduates’ competitive edge. The evidence for need has been established in the program’s proposal (see Reys 2000, 2002, 2006).

6. Has an adequate process been established to assess the effectiveness of the program in achieving its goals and objectives?

Yes, regular student and external reviewer evaluations will provide feedback for adapting the program. The student e-portfolio’s will be an excellent recourse as the mathematics education faculty assess the program’s impact on the students’ development. The portfolios will also be a source of data for the external advisory board to assist the faculty in monitoring the program’s effectiveness. We encourage the faculty to periodically review the e-portfolios as a group to determine the extent to which the coursework, seminars, internships, etc. are impacting students’ development. We suggest that the faculty regularly reflect on their students’ development as mathematics education researchers and teachers. We suggest that they examine the student portfolios for evidence of growth in students’: i) knowledge of major findings of key mathematics education research studies; ii) ability to use theory

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effectively to analyze data; iii) ability to prepare a tight synthesis of a body of research studies; iii) ability to pose relevant research questions and select optimal research methods to carry out the study; iv) ability to weave together research results to make convincing arguments to support research findings; v) ability to deliver quality instruction and reflect on its impact on student learning; vi) ability to develop new theory in the field.

These are excellent suggestions. We look forward to incorporating these suggestions as we begin to implement the program.

full proposal to develop a phd in mathematics · pdf filephd in mathematics education at the...

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