program report for the preparation of secondary mathematics … · 2012-03-05 · scores (a minimum...

Program Report for the Preparation of Secondary Mathematics Teachers

National Council of Teachers of Mathematics (NCTM)Option A

NATIONAL COUNCIL FOR ACCREDITATION OF TEACHER EDUCATION

COVER SHEET

1. Institution NameKennesaw State University

2. StateGeorgia

3. Date submitted

MM DD YYYY

/ /

4. Report Preparer's Information:

Name of Preparer:

Phone: Ext.

E-mail:

5. NCATE Coordinator's Information:

Name:

Phone: Ext.

E-mail:

6. Name of institution's programSecondary Mathematics Education (612)

7. NCATE CategoryMathematics Education

8. Grade levels(1) for which candidates are being prepared

(1) e.g. 7-12, 9-12

6-12

9. Program Type

nmlkji First teaching license

10. Degree or award level

nmlkji Baccalaureate

nmlkj Post Baccalaureate

nmlkj Master's

nmlkj Post Master's

nmlkj Specialist or C.A.S.

nmlkj Doctorate

nmlkj Endorsement only

11. Is this program offered at more than one site?

nmlkj Yes

nmlkji No

12. If your answer is "yes" to above question, list the sites at which the program is offered

13. Title of the state license for which candidates are prepared

14. Program report status:

nmlkji Initial Review

nmlkj Response to One of the Following Decisions: Further Development Required or Recognition with Probation

nmlkj Response to National Recognition With Conditions

15. State Licensure requirement for national recognition:NCATE requires 80% of the program completers who have taken the test to pass the applicable state licensure test for the content field, if the state has a testing requirement. Test information and data must be reported in Section III. Does your state require such a test?

nmlkji Yes

nmlkj No

SECTION I - CONTEXT

1. Description of any state or institutional policies that may influence the application of NCTM standards. (Response limited to 4,000 characters INCLUDING SPACES)StateAll teacher candidates in Georgia are expected to demonstrate knowledge, skills, and professional dispositions that enable them to address the needs of all learners, as defined by the Georgia Standards for the Approval of Professional Education Units and Educator Preparation Programs. Information from the preparation program review process is used to address the elements of content knowledge, professional and pedagogical knowledge and skills, pedagogical content knowledge, and student learning. The Georgia Professional Standards Commission mandates that teacher candidates complete a minimum of 800 hours of field experience across all teacher education programs. Mathematics teacher candidates are expected to demonstrate the specific learning proficiencies identified in the professional standards of the National Council of Teachers of Mathematics (NCTM) and to demonstrate the professional standards for Mathematics instruction as outlined in the Georgia Performance Standards for grades 6 – 12. In order to receive a professional teaching certificate in the state of Georgia, passing scores (a minimum of 220 on each exam) on the Georgia Assessment Certification Exam (GACE) for mathematics content (Math 022, 023) must be posted. InstitutionThe mathematics education program at Kennesaw State University prepares candidates for certification in mathematics, grades 6-12, in the state of Georgia. Successful completion of the program leads to a Bachelor of Science (B.S.) degree in mathematics education. The Bachelor of Science in mathematics education program, a four-year initial teaching certification program, is housed in the Department of Mathematics and Statistics in the College of Science and Mathematics. As a teacher preparation program, the mathematics education program is also a part of the Professional Teacher Education Unit (PTEU), which is centered in the Bagwell College of Education (BCOE). This cross-college relationship is built on a model of shared responsibility for teacher preparation. Faculty members in the BCOE teach all education courses in the mathematics education program; all other courses, including mathematics methods courses and student teaching, are taught and/or supervised by faculty in the Department of Mathematics and Statistics and the mathematics education program.

At the institution level, all mathematics education candidates are expected to demonstrate the proficiencies described in the PTEU’s conceptual framework, which defines the specific knowledge, skills, and dispositions expected from teacher candidates. In the PTEU at KSU, teacher candidate proficiencies are organized into three conceptual categories/outcomes—Subject Matter Experts, Facilitators of Learning, and Collaborative Professionals—and represent a common core of essential knowledge, skills, and dispositions for effective classroom instruction. General PTEU proficiencies form the basis for specific content-area expectations for mathematics education teacher candidates, and these proficiencies have been mapped on to the relevant NCTM/NCATE standards. Candidates in the B.S. in mathematics education program develop beginning levels of expertise, facilitate learning in all students, and recognize the significance of life-long professional development and collaboration. Proficiencies in each area reflect a continuum of development and expectation as candidates proceed through the program from initial field experiences through student teaching. The evaluation ratings consist of the lowest rating of L1: The candidate’s performance offers little or no evidence of achieving the proficiency, with subsequent ratings of L2: The candidate’s performance provides limited evidence that the proficiency has been met, L3: The candidate’s performance provides evidence that the proficiency has been met, and L4: The candidate’s performance provides consistent and convincing evidence that the proficiency has been met.

2. Description of the field and clinical experiences required for the program, including the number of hours for early field experiences and the number of hours/weeks for student teaching or

internships. (Response limited to 8,000 characters INCLUDING SPACES)

KSU teacher candidate field experience programs are carefully structured and sequenced in an effort to provide candidates with opportunities to observe and participate in teaching-learning processes and to develop the instructional skills that will enhance their effectiveness as professional facilitators of learning. Toward that end, field experiences are organized in stages that are developmentally sequenced and integrated with specific courses. In total, candidates complete 900 hours of field and clinical experiences.

The B.S. mathematics education program has a learner-centered, field-based focus. The purpose of educational field experiences is to provide each mathematics teacher education candidate with multiple opportunities to engage in the practical aspects of teaching in real classroom settings. These school-based field experiences continue throughout the program and culminate in Student Teaching where students assume full-time teaching responsibilities under the supervision of a public school collaborating teacher and a specialist in mathematics education. Mathematics education candidates complete six separate field experiences. The first four of these experiences, while limited in scope, are designed to provide candidates with a variety of instructional interaction with diverse groups of students. These initial experiences take place within the following education foundation courses:

• EDUC 2110, Investigating Critical and Contemporary Issues in Education: This course, an introductory student of education, includes 15 hours of observation and participation in an appropriate middle grades or secondary setting. • EDUC 2120, Sociocultural Influences on Teaching and Learning: This course includes 15 hours of observation of English language learners (ELLs) in the regular or ESOL classroom, assisting ELLs in understanding content, participating in class activities, and assisting/tutoring ELLs in learning English. • EDUC 2130, Exploring Teaching and Learning: This course includes 10 hours of one-on- one interaction working with P-12 students in ways that support students’ unique growth and developmental needs. • INED 3304, Education of Exceptional Students: This course includes 10 hours of observation and active participation with diverse populations, primarily students with special needs in an inclusive educational setting.

(The education courses described above are taught by faculty housed in the BCOE. Because of the collaborative nature of the PTEU, mathematics education faculty members were involved in the decision-making process when these courses were conceived and continue to participate in discussions about these education foundation courses in order to align and reinforce relevant concepts within mathematics education).The final two field experiences for mathematics education candidates occur in MAED 4417 (Teaching of Mathematics 6-12 Practicum, 100 hours) and MAED 4475 (Student Teaching: Mathematics 6-12, 750 hours).

MAED 4417: Practicum (100 hours)Candidates enroll in MAED 4417 (Practicum) concurrently with MAED 4416: Teaching of Mathematics (6-12). MAED 4416 is the capstone methodology course and is designed for the developing professional; it focuses on the connection between the discussion of the theory of teaching and the implementation of theory in practice within the mathematics classroom. Mathematics education candidates split their time in this course between regular class meeting and a four-week practicum (MAED4417) in a middle school or high school setting with a diverse range of students. The combination of in-depth class explorations of pedagogical theory and practice, curriculum, lesson planning, assessment, classroom management, parent communication, and diversity with a practical experience that allows candidates to implement concepts learned through the program with actual students provides for a rich experience. During the course, the candidates design lesson plans for a

mathematics unit which they will teach and assess during the (MAED 4417) four-week practicum. When candidates return to campus for the remaining weeks of MAED 4416, they have the opportunity to discuss the intersection between theory and practice as they experienced it, and to address a variety of related questions prior to moving into the more sustained Student Teaching experience the following semester.

During the four-week practicum (MAED 4417), candidates work with a university field experience supervisor and a collaborating teacher who advises and guides this first full-class teaching experience. Candidates also remain in contact with their university professor and class peers through regular online discussions. Candidates spend five hours each day in the collaborating teacher’s classroom, initially observing and assisting the teacher for two weeks before eventually teaching their mathematics unit in two classes for two weeks. The candidates are observed and advised both by their collaborating teacher (a teacher who has at least 3 years of secondary mathematics teaching experience) and the university supervisor (a mathematics education professor, instructor, or master teacher who has at least 3 years of secondary school mathematics teaching experience). Through the use of the unit-level Candidate Performance Instrument (CPI) and the program-level Mathematics Observation Instrument, the candidate receives frequent formative assessments from the collaborating teacher and university supervisor. At the end of the teaching experience, the candidate, the collaborating teacher, and the university supervisor also complete the CPI electronically as a summative assessment

MAED: 4475 Student Teaching Mathematics (750 hours)In the final comprehensive clinical field experience, MAED: 4475 Student Teaching Mathematics, candidates are placed in a high school or middle school for the entire university semester. Candidates are placed in the opposite grade level from the previous initial MAED 4417 four-week practicum. During the student teaching experience, candidates assume full responsibility for instruction (full day, for approximately 16 weeks), with at least ten weeks of full-time teaching.

Supervision is done by both the collaborating teacher and the university supervisor. Candidates embrace a full range of teaching and assessment duties and decisions, including selection of instructional strategies and resources; selection of strategies for managing time, materials, and students; selection of activities and instructional technologies; and selection of means for assessing student learning and personal teaching. Evaluation of teacher candidates occurs throughout the field experience using informal techniques and the formal unit-level CPI and Mathematics Observation Instrument, assessments also used during the MAED 4417 practicum. Candidates are observed by the collaborating teacher and university supervisor and are provided with written as well as oral feedback regarding the effectiveness of instructional decisions made.

In addition to mid-term and final evaluations from the collaborating teacher and university supervisor, the candidate receives 4 formal observations from both. At all stages of the student teaching field experience, collaborating teacher evaluations are reviewed by the university supervisor and the mathematics education program coordinator for possible problems or issues. In the event that a candidate is in need of remediation, the collaborating teacher and university supervisor will develop a remediation plan stipulating the conditions for successful completion of student teaching. If necessary, the Director for Educational Placements and Partnerships will join the discussion. Administrative options include a second formal remediation plan for the candidate, removal from the placement, reassignment to a new placement, and in extreme cases, dismissal from the program.

3. Please attach files to describe a program of study that outlines the courses and experiences required for candidates to complete the program. The program of study must include course titles. (This information may be provided as an attachment from the college catalog or as a student advisement sheet.)

Kennesaw State University Undergraduate Math Program of Study

See Attachments panel below.

4. This system will not permit you to include tables or graphics in text fields. Therefore any tables or charts must be attached as files here. The title of the file should clearly indicate the content of the file. Word documents, pdf files, and other commonly used file formats are acceptable.

5. Candidate InformationDirections: Provide three years of data on candidates enrolled in the program and completing the program, beginning with the most recent academic year for which numbers have been tabulated. Report the data separately for the levels/tracks (e.g., baccalaureate, post-baccalaureate, alternate routes, master's, doctorate) being addressed in this report. Data must also be reported separately for programs offered at multiple sites. Update academic years (column 1) as appropriate for your data span. Create additional tables as necessary.

(2) NCATE uses the Title II definition for program completers. Program completers are persons who have met all the requirements of a state-approved teacher preparation program. Program completers include all those who are documented as having met such requirements. Documentation may take the form of a degree, institutional certificate, program credential, transcript, or other written proof of having met the program's requirements.

Program:

Academic Year# of CandidatesEnrolled in the

Program

# of ProgramCompleters(2)

AY2010

AY2009

AY2008

6. Faculty InformationDirections: Complete the following information for each faculty member responsible for professional coursework, clinical supervision, or administration in this program.

Faculty Member Name

Highest Degree, Field, & University(3)

Assignment: Indicate the role of the faculty member(4)

Tenure Track

Scholarship(6), Leadership in Professional Associations, and Service(7):List up to 3 major contributions in the past 3 years(8)

Teaching or other professional experience in

12 schools(9)

Faculty Member Name



Faculty Rank(5)

Tenure Track


Teaching or other professional experience in P-12 schools(9)

Faculty Member Name



Faculty Rank(5)

Tenure Track YESgfedc



Faculty Member Name



Faculty Rank(5)

Tenure Track

Scholarship(6), Leadership in Professional Associations, and

Service(7):List up to 3 major contributions in the past 3 years(8)


Faculty Member Name



Faculty Rank(5)

Tenure Track



Faculty Member Name



Faculty Rank(5)

Tenure Track





Faculty Member Name



Faculty Rank(5)

Tenure Track



Faculty Member Name



Faculty Rank(5)

Tenure Track



12 schools(9)

Faculty Member Name



Faculty Rank(5)

Tenure Track


Faculty Member Name



Tenure Track



Faculty Member Name



Faculty Rank(5)

Tenure Track



Faculty Member Name



Tenure Track



Faculty Member Name



Faculty Rank(5)

Tenure Track



Faculty Member Name

Highest Degree, Field, &

University(3)


Faculty Rank(5)

Tenure Track



Faculty Member Name



Faculty Rank(5)

Tenure Track



Faculty Member Name



Faculty Rank(5)



12 schools(9)

Faculty Member Name



Faculty Rank(5)




Faculty Member Name



Faculty Rank(5)

Tenure Track


Faculty Member Name



Faculty Rank(5)

Tenure Track



,

Faculty Member Name



Faculty Rank(5)




Faculty Member Name



Faculty Rank(5)

Tenure Track



Faculty Member Name


Assignment: Indicate the role

of the faculty member(4)

Faculty Rank(5)

Tenure Track



Faculty Member Name



Faculty Rank(5)




Faculty Member Name



Faculty Rank(5)




Faculty Member Name

Highest Degree, Field, &

(3) e.g., PhD in Curriculum & Instruction, University of Nebraska. (4) e.g., faculty, clinical supervisor, department chair, administrator (5) e.g., professor, associate professor, assistant professor, adjunct professor, instructor (6) Scholarship is defined by NCATE as systematic inquiry into the areas related to teaching, learning, and the education of teachers and other school personnel. Scholarship includes traditional research and publication as well as the rigorous and systematic study of pedagogy, and the application of current research findings in new settings. Scholarship further presupposes submission of one's work for professional review and evaluation. (7) Service includes faculty contributions to college or university activities, schools, communities, and professional associations in ways that are consistent with the institution and unit's mission. (8) e.g., officer of a state or national association, article published in a specific journal, and an evaluation of a local school program. (9) Briefly describe the nature of recent experience in P-12 schools (e.g. clinical supervision, inservice training, teaching in a PDS) indicating the discipline and grade level of the assignment(s). List current P-12 licensure or certification(s) held, if any.

University(3)


Faculty Rank(5)




Faculty Member Name



Tenure Track



SECTION II - LIST OF ASSESSMENTS

In this section, list the 6-8 assessments that are being submitted as evidence for meeting the NCTM standards. All programs must provide a minimum of six assessments. If your state does not require a state licensure test in the content area, you must substitute an assessment that documents candidate attainment of content knowledge in #1 below. For each assessment, indicate the type or form of the assessment and when it is administered in the program.

1. Please provide following assessment information (Response limited to 250 characters each field)

Type and Number of Assessment

Name of Assessment (10)

Type or Form of Assessment (11)

When the Assessment Is Administered (12)

Assessment #1: Licensure assessment, or other content-based assessment (required)

GACE [Georgia Assessments for

the Certification of Educators]

State Licensure Exam

Candidates take the exam in the

third or fourth year of the program. Each candidate

must take and pass the GACE test

before teacher (6 –12) certification is

awarded.

Assessment #2: Content knowledge in secondary mathematics education (required)

Content GPACoursework in

Math Content and Math Education

GPA is an ongoing assessment

throughout the Program

(Freshman –Senior). Candidates must have a 2.75

before entering the MAED 4417

practicum which occurs the

semester prior to the final Student

Teaching experience.

Assessment #3: Candidate ability to plan instruction(required)

MAED4416 Unit Planning

Unit of Lesson Plans/Reflections

This is a course-based assessment that occurs during the (MAED 4416) methods course, which candidates take the semester prior to the final Student Teaching

experience.

Assessment #4: Student teaching (required)

Math Observation Summary

Instrument

Final Evaluation of Student Teaching

Performance

This assessment occurs during the

final Student Teaching

experience.

Assessment #5: Candidate effect on student leaning (required)

Impact on Student Learning

Assessment of Student Learning

(11) Identify assessment by title used in the program; refer to Section IV for further information on appropriate assessment to include. (12) Identify the type of assessment (e.g., essay, case study, project, comprehensive exam, reflection, state licensure test, portfolio). (13) Indicate the point in the program when the assessment is administered (e.g., admission to the program, admission to student teaching/internship, required courses [specify course title and numbers], or completion of the program).

Candidates complete this

assessment during their final Student


Assessment #6: Additional assessment that addresses NCTM standards (required)

CPI [Candidate Performance Instrument]

Assessment of the candidate’s

knowledge, skills and dispositions


assessment during the final Student


Assessment #7: Additional assessment that addresses NCTM standards (optional)

MATH 3495 [Problem Analysis

Project]

Problem Analysis Assignment


assessment the semester before they enroll in the

(MAED 4416) methods course.

Assessment #8: Additional assessment that addresses NCTM standards (optional)

MATH 3475[Historical &

Modern Approaches to Mathematics]

Assessment of the candidate’s

knowledge and understanding of

the history of mathematics as

well as their ability to use a variety of technological tools.


assessment the semester before they enroll in the

(MAED 4416) methods course.

SECTION III - RELATIONSHIP OF ASSESSMENT TO STANDARDS

1. For each NCTM standard on the chart below, identify the assessment(s) in Section II that address the standard. One assessment may apply to multiple NCTM standards.

#1 #2 #3 #4 #5 #6 #7 #8

Mathematics Preparation for All Mathematics Teacher Candidates. gfedc gfedc gfedc gfedc gfedc gfedc gfedc gfedc

1. Knowledge of Problem Solving. Candidates know, understand and apply the process of mathematical problem solving. [Indicators are listed at http://www.nctm.org/about/ncate/secondary_indic.htm]

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2. Knowledge of Reasoning and Proof, Candidates reason, construct, and evaluate mathematical arguments and develop as appreciation for mathematical rigor and inquiry. [Indicators are listed at http://www.nctm.org/about/ncate/secondary_indic.htm]

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3. Knowledge of Mathematical Communication. Candidates communicate their mathematical thinking orally and in writing to peers, faculty and others. [Indicators are listed at http://www.nctm.org/about/ncate/secondary_indic.htm]

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4. Knowledge of Mathematical Connections. Candidates recognize, use,

and make connections between and among mathematical ideas and in contexts outside mathematics to build mathematical understanding. [Indicators are listed at http://www.nctm.org/about/ncate/secondary_indic.htm]


5. Knowledge of Mathematical Representation. Candidates use varied representations of mathematical ideas to support and deepen students' mathematical understanding. [Indicators are listed at http://www.nctm.org/about/ncate/secondary_indic.htm]


6. Knowledge of Technology. Candidates embrace technology as an essential tool for teaching and learning mathematics. [Indicators are listed at http://www.nctm.org/about/ncate/secondary_indic.htm]

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7. Dispositions. Candidates support a positive disposition toward mathematical processes and mathematical learning. [Indicators are listed at http://www.nctm.org/about/ncate/secondary_indic.htm]

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8. Knowledge of Mathematics Pedagogy. Candidates possess a deep understanding of how students learn mathematics and of the pedagogical knowledge specific to mathematics teaching and learning. [Indicators are listed at http://www.nctm.org/about/ncate/secondary_indic.htm]

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9. Knowledge of Number and Operations. Candidates demonstrate computational proficiency, including a conceptual understanding of numbers, ways of representing number, relationships among number and number systems, and the meaning of operations.[Indicators are listed at http://www.nctm.org/about/ncate/secondary_indic.htm]

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10. Knowledge of Different Perspectives on Algebra. Candidates emphasize relationships among quantities including functions, ways of representing mathematical relationships, and the analysis of change. [Indicators are listed at http://www.nctm.org/about/ncate/secondary_indic.htm]

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11. Knowledge of Geometries. Candidates use spatial visualization and geometric modeling to explore and analyze geometric shapes, structures, and their properties. [Indicators are listed at http://www.nctm.org/about/ncate/secondary_indic.htm]

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12. Knowledge of Calculus, Candidates demonstrate a conceptual understanding of limit, continuity, differentiation, and integration and a thorough background in techniques and application of the calculus. [Indicators are listed at http://www.nctm.org/about/ncate/secondary_indic.htm]


13. Knowledge of Discrete Mathematics. Candidates apply the fundamental ideas of discrete mathematics in the formulation and solution of problems. [Indicators are listed at http://www.nctm.org/about/ncate/secondary_indic.htm]


14. Knowledge of Data Analysis, Statistics and Probability. Candidates demonstrate an understanding of concepts and practices related to data analysis, statistics, and probability. [Indicators are listed at http://www.nctm.org/about/ncate/secondary_indic.htm]


15. Knowledge of Measurement. Candidates apply and use measurement concepts and tools. [Indicators are listed at http://www.nctm.org/about/ncate/secondary_indic.htm]


2. 16.1 Field-based Experience. Engage in a sequence of planned opportunities prior to student teaching that inculdes observing and participating in secondary mathematics classrooms under the supervision of experienced and highly qualified teachers.

Information should be provided in Section I (Context) to address this standard.

3. 16.2 Field-based Experience. Experienced full-time student teaching secondary-level mathematics that is supervised by experienced and highly qualified teacher and a university or college supervisor with mathematics teaching experience.

Information should be provided in Section I (Context) to address this standard.

4. For the NCTM standard on the chart below, identify the assessment(s) in Section II that address the standard. One assessment may apply to multiple NCTM standards.

#1 #2 #3 #4 #5 #6 #7 #816.3 Field-Based Experience. Demonstrate the ability to increase students' knowledge of mathematics. gfedc gfedcb gfedc gfedcb gfedcb gfedcb gfedcb gfedc

SECTION IV - EVIDENCE FOR MEETING STANDARDS

DIRECTIONS: The 6-8 key assessments listed in Section II must be documented and discussed in Section IV. Taken as a whole, the assessments must demonstrate candidate mastery of the SPA standards. The key assessments should be required of all candidates. Assessments and scoring guides and data charts should be aligned with the SPA standards. This means that the concepts in the SPA standards should be apparent in the assessments and in the scoring guides to the same depth, breadth, and specificity as in the SPA standards. Data tables should also be aligned with the SPA standards. The data should be presented, in general, at the same level it is collected. For example, if a rubric collects data on 10 elements [each relating to specific SPA standard(s)], then the data chart should report the data on each of the elements rather that reporting a cumulative score..

In the description of each assessment below, the SPA has identified potential assessments that would be appropriate. Assessments have been organized into the following three areas to be aligned with the elements in NCATE’s unit standard 1:• Content knowledge (Assessments 1 and 2)• Pedagogical and professional knowledge, skills and dispositions (Assessments 3 and 4)• Focus on student learning (Assessment 5)

Note that in some disciplines, content knowledge may include or be inextricable from professional knowledge. If this is the case, assessments that combine content and professional knowledge may be considered "content knowledge" assessments for the purpose of this report.

For each assessment, the compiler should prepare one document that includes the following items:

(1) A two-page narrative that includes the following:a. A brief description of the assessment and its use in the program (one sentence may be sufficient);

b. A description of how this assessment specifically aligns with the standards it is cited for in Section III. Cite SPA standards by number, title, and/or standard wording.c. A brief analysis of the data findings;d. An interpretation of how that data provides evidence for meeting standards, indicating the specific SPA standards by number, title, and/or standard wording; and

(2) Assessment Documentatione. The assessment tool itself or a rich description of the assessment (often the directions given to candidates);f. The scoring guide for the assessment; andg. Charts that provide candidate data derived from the assessment.

The responses for e, f, and g (above) should be limited to the equivalent of five text pages each , however in some cases assessment instruments or scoring guides may go beyond five pages.

Note: As much as possible, combine all of the files for one assessment into a single file. That is, create one file for Assessment #4 that includes the two-page narrative (items a – d above), the assessment itself (item e above), the scoring guide (item f above, and the data chart (item g above). Each attachment should be no larger than 2 mb. Do not include candidate work or syllabi. There is a limit of 20 attachments for the entire report so it is crucial that you combine files as much as possible.

1. State licensure tests or professional examinations of content knowledge. NCTM standards addressed in this entry could include all of the standards 1-7 and 9-15. If your state does not require licensure tests or professional examinations in the content area, data from another assessment must be presented to document candidate attainment of content knowledge. (Assessment Required)

Provide assessment information as outlined in the directions for Section IV

Assessment #1: Georgia Assessments for the Certification of Educators (GACE)


2. Assessment of content knowledge in mathematics. NCTM standards addressed in this entry could include but are not limited to Standards 1-7 and 9-15. Examples of assessments include comprehensive examinations, GPAs or grades, and portfolio tasks(13). For post-baccalaureate teacher preparation, include an assessment used to determine that candidates have adequate content backgroud in the subject to be taught.(Assessment Required)


(14) For program review purposes, there are two ways to list a portfolio as an assessment. In some programs a

Assessment #2: Grade Point Average (GPA) in Required Mathematics Courses


portfolio is considered a single assessment and scoring criteria (usually rubrics) have been developed for the contents of the portfolio as a whole. In this instance, the portfolio would be considered a single assessment. However, in many programs a portfolio is a collection of candidate work—and the artifacts included

3. Assessment that demonstrates candidates can effectively plan classroom-based instruction. NCTM standards that could be addressed in this assessment include but are not limited to Standard 8. Examples of assessments inculde the evaluation of candidates' abilities to develop leasson or unit plans, individualized educational plans, needs assessments, or intervention plans. (Assessment Required)


Assessment #3:Mathematics Teaching Unit Plan


4. Assessment that demonstrates candidates' knowledge, skills, and dispositions are applied effectively in practice. NCTM standards that could be addressed in this assessment include but are not limited to standard 8. An assessment instrument used in student teaching or an internship should be submitted. (Assessment Required)


Assessment #4: MAED Observation Summary Instrument--Student Teaching Evaluation


5. Assessment that demonstrates candidate effects on student learning. NCTM standards that could be addressed in this assessment include but are not limited to Standard 8. Examples of assessments include those based on student work samples, portfolio tasks, case studies, follow-up studies, and employer surveys. (Assessment Required)


Assessment #5: Impact on Student Learning Assignment


6. Additional assessment that addresses NCTM standards. Examples of assessments include evaluations of field experiences, case studies, portfolio tasks, licensure tests not reported in #1, and follow-up studies. (Assessment Required)


Assessment #6: Candidate Performance Instrument (CPI)


7. Additional assessment that addresses NCTM standards. Examples of assessments include evaluations of field experiences, case studies, portfolio tasks, licensure tests not reported in #1, and follow-up studies. (Optional)


Assessment #7:MATH 3495 Problem Analysis (PA)


8. Additional assessment that addresses NCTM standards. Examples of assessments include evaluations of field experiences, case studies, portfolio tasks, licensure tests not reported in #1, and follow-up studies. (Optional)


Assessment #8:MAED 3475 Historical Development Assignment


SECTION V - USE OF ASSESSMENT RESULTS TO IMPROVE PROGRAM

1. Evidence must be presented in this section that assessment results have been analyzed and have been or will be used to improve candidate performance and strengthen the program. This description should not link improvements to individual assessments but, rather, it should summarize principal findings from the evidence, the faculty's interpretation of those findings, and changes made in (or planned for) the program as a result. Describe the steps program faculty has taken to use information from assessments for improvement of both candidate performance and the program. This information should be organized around (1) content knowledge, (2) professional and pedagogical knowledge, skill, and dispositions, and (3) student learning.

(Response limited to 12,000 characters INCLUDING SPACES)

Introduction

KSU requires annual evaluation of each program’s efforts to ensure students’ learning through our Assurance of Learning (AOL) program improvement as part of KSU’s compliance with SACS accreditation requirements pertaining to the institutional effectiveness of all educational programs. AOL reports also address specific information about how the program is meeting the global learning outcomes addressed in the Quality Enhancement Plan (QEP).

At the Professional Teacher Education Unit (PTEU) level, improvements and changes in all programs and curricula as well as service units supporting teacher education are dependent on a reflective process that has become an established culture among PTEU candidates, program faculty, and support personnel. This process enables members of the program to engage in thoughtful and data-based decision-making.

Mathematics education faculty review and reflect on data from the previous semester each fall and spring semester and develop a plan for change as warranted by the results. In fall semester, we review spring and summer data. In spring semester, we review fall data. We review data from the BS in

Mathematics Education and the MAT in Mathematics together to see what one program can learn from the other. Data used includes teacher candidate evaluations, teacher candidate surveys, faculty evaluations and teaching notes, principal surveys, collaborating and supervising teacher evaluations and surveys, and feedback from the Mathematics Education Advisory Board. These rich and varied sources of information support triangulation and the formulation of specific changes to better support teacher candidate learning and program improvement.

In fall and spring meetings, student data and other program concerns are discussed with our Mathematics Education Advisory Board, which includes recent graduates, teachers who have mentored our students, building level administrators, system administrators, and, very often, state DOE-level mathematics educators. In those meetings, we share program data, ask for advice on program-level decisions, and learn about what what’s going on in the schools.

At the departmental level, monthly mathematics education meetings are attended by all faculty and mathematics education advisor Marie Powell. Curricular or policy changes agreed upon there must go before the departmental Policies and Curriculum Committee for approval. Policy and curricular changes then go to the Teacher Education Council and the Graduate Policies and Curriculum Committees before the changes are finalized.

Knowledge of Content (Assessments #1, #2, #7, #8)

Mathematics Education faculty are confident that our candidates demonstrate the mathematics content knowledge needed to become certified to teach secondary mathematics. In reflecting over assessment data for content knowledge, mathematics education faculty members discovered that our candidates are quite successful. During the assessment period of 2007 – 2009, all candidates who took the GACE passed both test. Upon reviewing the Grade Point Average (GPA) data, we discovered that all of our candidates meet or exceed the minimum GPA (2.0) rating for all required mathematics coursework. Candidates’ mean grade point averages ranged from 2.25 – 4.0.

Data from the 2008 academic year showed the value of the Problem Analysis (Assessment #7) assignment and the undergraduate course MATH 3495 for undergraduate teacher candidates. The data showed that this course was an opportunity for teacher candidates to make connections between various areas of their mathematical knowledge and between their college mathematics and the mathematics they would teach. After careful reflection over the data for the current assessment periods, two faculty members who teach these courses realized that there was not sufficient consistency in grading the Problem Analysis projects during the two periods of assessment. Two different faculty members taught the course and graded the assignments causing concern for inter-rater reliability. As a result, several changes were made in the assessment of the problem analysis in the spring of 2010. During spring 2010, a new, more specific rubric was piloted with several changes made with respect to when candidates submitted the assignment and how it was scored. The spring semester instructor allowed a draft to be turned in for each section during various times throughout the semester allowing candidates to receive feedback and make changes before submitting the entire project. Candidates were given a grade on each section allowing them to keep up with their final PA grade throughout the semester. Having this progress report seemed to help candidates succeed in subsequent sections if they had not done well on a previous section. During the spring 2010, all candidates met or exceeded the rubric criteria relevant to the NCTM standards. Over both periods, 94% of all candidates met minimum rubric requirements relevant to the NCTM standards.

The Mathematics Historical Development assignment (Assessment #8) provides candidates with the opportunity to select and describe what they consider to be three significant steps/events/contributions in the historical development of each of the content areas of Number & Operation, Algebra & Trig,

Geometry & Measurement, Data Analysis, Statistics & Probability, Discrete Mathematics, and Calculus. This assessment specifically addresses the candidate’s knowledge of the historical development of the mathematical content areas as well as cultural contributions. Spring 2010 was the first time we piloted the Assessment #8: Math 3475 Mathematics Historical Development rubric. Our initial rubric for this assessment was not useable because the rubric was not aligned with the NCTM standards in a significant way. After applying the old rubric for two semesters (spring/summer 2009), we discovered that the assessment needed to provide students with a format for the assignment, a more detailed description of the assignment, and new alignment with relevant NCTM standards. The current rubric is now aligned with standards 9 – 15. After one application of the new rubric and analysis of assessment data, we discovered that 100% of our candidates met or exceeded the minimum acceptable rating for Standards 9 – 15.

Professional and Pedagogical Knowledge, Skill, and Dispositions (Assessments #3 and #4)

Mathematics education faculty reviewed multiple sources of data for professional and pedagogical knowledge, skill, and dispositions. We discovered that all candidates met or exceeded the minimum acceptable rating for each rubric criterion on Assessment #4: MAED Observation of Teaching Summary during fall 2009 and spring 2010. However, Mathematics Education faculty discovered that in some areas candidates are simply meeting, rather than exceeding, the requirements. The Observation Summary Instrument showed a less frequent use of (a) culturally relevant, real world connections, (b) appropriate use of technology, and (c) using concrete materials. Faculty will address these areas during the candidates’ mathematics methods course (MAED 4416) and during other mathematics education coursework. To enhance the quality of teaching and learning in this area, the faculty will make changes in how we address connecting content to other disciplines and applying it to the real-world by modeling and emphasizing these areas within mathematics education coursework. We plan to include topics of discussion related to culturally relevant and responsive pedagogy within the mathematics methods course (MAED 4416) and to engage the candidates in real-world, culturally relevant mathematical problem solving situations. In fall 2010, we made changes in Assessment #3: Unit Planning. We now require candidates to design a lesson that is culturally relevant and one that includes differentiation. We will reflect upon data from the Assessment#3: Unit Planning rubric at the end of fall semester 2010.

Less frequent use of technology and concrete materials can be attributed to the limited availability of technology and manipulatives in the field. Candidates include the use of technology and manipulatives within their lesson plans, but are unable to utilize them during instruction because of the lack of available technology and manipulatives in assigned schools. The mathematics education program currently has a library of manipulatives available for candidates to check-out and utilize during their field experience. We will continue to discuss in our regular Mathematics Education meetings and Mathematics Education Advisory Board meetings the lack of technology and hands-on manipulatives available in the schools and how we can work together to make resources available for candidates to use while in the field.

Student Learning (Assessments #5 and #6)

In the assessment of our candidates’ dispositions, mathematics education faculty members found that the majority of our candidates scored at the L3 or L4 level for each rubric criterion on Assessment #5: Impact on Student Learning. A large percentage of all candidates scored at an L3 or above on elements/criteria associated with communicating the results of their data analysis in writing. Equity is an issue that is one aspect of the Impact on Student Learning assignment because candidates are asked to describe the educational setting, classroom resources, and classroom diversity and use this information to design lessons, assessments, and differentiate learning. Over two assessment periods, data from Assessment #5 indicated at least of all candidates addressed equity and lesson differentiation, used

various assessments, and compared the effectiveness of their instruction across different subgroups of students.

Evidence from Assessment #6: Candidate Performance Instrument (CPI) indicates that students are collaborative professionals. Candidate data on the CPI reflect strengths in all three areas assessed: Subject Matter Expert, Facilitator of Learning, and Collaborative Professional. As we reviewed CPI data on all three outcomes we could see that no candidate scored below the minimum requirement. The majority of our candidates ( performed at a level of L3 or higher for outcome3: collaborative professionals. Data on the CPI in fall 2009 and spring 2010 showed some variability in the candidates related to other collected data on the candidate. This variability was initially hard for faculty to understand until feedback from the university supervisors indicated that the variability was due to differences in the university supervisors’ understanding of the rating instrument. Since that time, additional efforts have been made to train the supervisors on the use of the instrument. Another factor that has improved this variability is that we have been able to develop a core of university supervisors who have become familiar with the program’s assessments and expectations.

Overall, the Mathematics Education faculty feels satisfied with the results in the areas of content knowledge, professional and pedagogical knowledge, skill, and dispositions, and student learning. We will continue to reflect upon candidate data and seek ways to enhance/improve our program.

SECTION VI - FOR REVISED REPORTS OR RESPONSE TO CONDITIONS REPORTS ONLY

1. For Revised Reports: Describe what changes or additions have been made to address the standards that were not met in the original submission. Provide new responses to questions and/or new documents to verify the changes described in this section. Specific instructions for preparing a Revised Report are available on the NCATE web site at http://www.ncate.org/institutions/resourcesNewPgm.asp?ch=90

For Response to Conditions Reports: Describe what changes or additions have been made to address the conditions cited in the original recognition report. Provide new responses to questions and/or new documents to verify the changes described in this section. Specific instructions for preparing a Response to Conditions Report are available on the NCATE web site at http://www.ncate.org/institutions/resourcesNewPgm.asp?ch=90

(Response limited to 24,000 characters. INCLUDING SPACES)

Please click "Next"

This is the end of the report. Please click "Next" to proceed.

KSU #:

Matriculation

(Please forward your student email to the email that you check most frequently.)

Advisor: Phone #

Title Hrs Course HrsComposition I 3 MATH 2595 3Composition II 3 MATH 3260 3Precalculus** 3 MATH 3322 3Social Issues: Perspectives in ...

2 MATH 3332 3

3 MATH 3390 3

World Literature 3 MATH 3395 3Arts in Society: ... 3 MATH 4361 3

Calculus I 4 MATH 3495 3

4 MATH 4495 3

3 or 4

American Govt 3World Civilization 3 INED 3304 3America since 1890 3 EDUC 2120 3Global Economics 3 MAED 3475 3

KS

U Fitness for Living 3 MAED 4416 6

MAED 4417 TOSS Practicum 3MAED 4475 12

++++No other course should be taken during Student Teaching.

Calculus II 4 Electives KSU 1101 can be used here 3Calculus III 4 Differential Equations 3

Programming Princip. I 4 Real Analysis I 3Invest Crit/Cont Issues in Educ

3 IS 2101**** Computers & Your World 3

Expl Tch & Learn 3 CS 2302**** Programming Princip. II 4CSED 4416**** Teaching of Computer Science 3CSED 4417**** Practicum 1

***Required for a Mathematics Major and Teacher Certification

8/10/10

GENERAL EDUCATION (45* hours) TEACHING FIELD (27 Hours)Title

Are

a A Mathematics for Middle Grades

Linear AlgebraDiscrete Modeling I

Course

Department of Mathematics & StatisticsBACHELOR OF SCIENCE IN MATHEMATICS EDUCATION (6-12)

Requirements Effective Fall 2007 - present

Are

a B

Probability and Statistical Inference

Introduction to Mathematical Systems

Are

a C Geometry

Modern Algebra

COM 1109/FL 1002/ PHIL 2200

ENGL 2110ART/ DANC/ MUSI/ TPS 1107

Advanced Perspectives on School Mathematics II

Are

a E

PROFESSIONAL EDUCATION (30 hours)Educ of Exceptional StudentsSoc Infl Teach & LearnHistorical & Modern Approaches to Math

Are

a D

ECON 1100

MATH 1190

+++ Must pass or exempt GACE Basic Tests I, II and III for admission to Teacher Education

HPS 1000

MATH 2202MATH 2203

Teaching Mathematics Grades 6-12 (TOSS)

**See advisor if have already taken Calculus I

Admitted to TOSS

Applied to Student Teaching

****Required for Computer Science Endorsement

Name:

email:

ENGL 1101ENGL 1102MATH 1113ANTH/ GEOG/ PSYC/SOCI 2105

LOWER DIVISION MAJOR (18 Hours)

Admitted to Teacher Education

Advanced Perspectives on School Mathematics I

FREE ELECTIVES (3 Hours)

Area

F

MATH 3310***

MATH 4381***

EDUC 2110++

EDUC 2130*one hour from gen. educ. is carried over to lower division

CS 2301****

++++ Must pass GACE Content Tests I and II in order to Student Teach

BS____MATH__

SCI 1101 (or most sciences with labs)

SCI 1102 (or most sciences)

POLS 1101HIST 1110HIST 2112

Student Teaching++++

++ EDUC 2110 is required for admission to Teacher Education

Assessment #1: GACE Licensure Exam 1

Assessment #1: Georgia Assessment for the Certification of Educators (GACE)

1a) Description of the assessment

In taking the GACE content assessment in mathematics, candidates are assessed in a variety of content knowledge areas. Test I (022) includes questions in three subareas: number concepts and operations, algebra, precalculus and calculus. Test II (023) includes questions in three subareas: geometry and measurement, data analysis and probability, and mathematical processes and perspectives. Teacher candidates must pass both tests in order to meet the state of Georgia certification grade 6-12 requirements. The publisher of the GACE, the National Evaluation Systems (NES), allowed a group of college mathematics/mathematics education faculty and two high school teachers to complete the alignment of GACE Content Tests to NCTM indicators. The alignment in the table below was agreed upon by members of the Georgia Professional Standards Commission (Georgia’s certification agency), representatives from NES, and representative Georgia mathematics educators (secondary and post-secondary). 1b) Alignment of NCTM Standards and Indicators with the GACE

NCATE/NCTM Standards/Indicators

GACE Test

Assessment Alignment with NCTM Standards/ Indicators

Standard 1: Knowledge of Mathematical Problem-solving [NCTM 1.1, 1.2]

Test 023

Candidates apply and adapt a variety of appropriate strategies to solve problems that arise in mathematics and those involving other mathematics context

Standard 2: Knowledge of Reasoning and Proof [NCTM 2.2, 2.3,2.4]

Test 023 Candidates make and investigate mathematical conjectures, develop and evaluate mathematical arguments and proofs and are able to communicate their mathematical thinking orally and in writing.

Standard 4: Knowledge of Mathematical Connections [NCTM 4.1, 4.2]

Test 023 Candidates recognize and apply connections among mathematics and mathematical ideas in contexts in and outside of mathematics

Standard 5: Knowledge of Mathematical Representations [NCTM 5.2]

Test 023 Candidates create and use representations to organize, record, and communicate mathematical ideas

Standard 9: Knowledge of Number and Operation [NCTM 9.1, 9.3, 9.4, 9.5, 9.6, 9.8, 9.9]

Test 022 Candidates use manipulatives to develop a conceptual understanding of integer, rational number, and complex number operations; represent ratios using fractions, decimals, and quotients; solve and apply proportions, percents, simple and compound interest problems.

Standard 10: Knowledge of Different Perspectives on Algebra

Test 022 Candidates explore, analyze, and represent patterns, relations, and functions; determine coordinates and associated reference angles on the unit circle manipulate transformations basic


[NCTM 10.1, 10.2, 10.4]

trigonometric functions, inverse trigonometric functions, model quantitative relationships

Standard 11: Knowledge of Geometries [NCTM 11.2, 11.3, 11.5, 11.6]

Test 023 Candidates demonstrate knowledge of axiomatic systems and proofs in geometry; analyze geometric shapes and structures; describe spatial relationships and apply transformations and use symmetry, similarity and congruence to analyze math situations

Standard 12: Knowledge of Calculus [NCTM 12.1, 12.3]

Test 022 Candidates use models to solve problems and justify why applications work.

Standard 13: Knowledge of Discrete Mathematics [NCTM 13.1]

Test 022 Uses graphs, recurrence relations, finite differences, combinatorics, and linear programming to solve problems.

Standard 14: Knowledge of Data Analysis, Statistics, and Probability [NCTM 14.1, 14.2, 14.3, 14.4, 14.7]

Test 023 Candidates use statistical methods and technology to describe and analyze data; and to draw conclusions

Standard 15: Knowledge of Measurement [NCTM 15.1, 15.2]

Test 023 Candidates convert within and across English and Metric measurements.

1c) Analysis of the data findings Data for the GACE were reported to us from the Georgia Department of Education for the 2007-2008 and 2008-2009 academic years. The data tables indicate a strong performance of our candidates on the licensure exams with passing rates of % on each exam for both the 2007-08 and 2008-09 testing years. The candidates who pass the licensure exams are then fully eligible for certification in the state of Georgia.

1d) An Interpretation of how the data provides evidence for meeting standards These data indicate that candidates are successful in demonstrating the knowledge, skills and dispositions relative to the frameworks for the Georgia Assessment for the Certification of Educators [GACE] exam. The standards table demonstrates that the GACE exam is aligned with the NCTM standards (listed above) and provides evidence of candidate competence.


1e) Assessment #2: GACE Description Listed below are the frameworks for these two licensure exams as described by the Georgia State Education Department.

022 Mathematics Test I and 024 Mathematics Test II Framework

1f) GACE Scoring Information All test results are reported as scaled scores being a combination of the number of scorable questions answered correctly on the selected-response questions and the scores received on the constructed-response questions. These scores are converted to a scale from 100-300 where a score of 220 is passing.

Test Subarea Objective 022 SUBAREA 1 Number Concepts and Operations

022 0001 Understand number operations and basic principles of number theory.

022 002 Understand the real and complex number systems. 022 SUBAREA 2 Algebra 022 003 Understand algebraic operations and properties of functions and relations. 022 004 Understand properties of linear equations and linear systems. 022 005 Understand properties of quadratic functions. 022 SUBAREA 3 Precalculus and Calculus 022 006 Understand properties of nonlinear functions. 022 007 Understand properties of trigonometric functions and identities. 022 008 Understand principles and applications of calculus.

023 SUBAREA 1 Geometry and Measurement 023 009 Understand the principles of measurement. 023 0010 Understand principles of Euclidean geometry. 023 0011 Understand coordinate and transformational geometry. 023 SUBAREA 2 Data Analysis and Probability 023 0012 Understand methods of collecting, organizing, and describing data. 023 0013 Understand the theory and applications of probability. 023 0014 Understand the process of analyzing and interpreting data to make statistical

inferences. 023 SUBAREA 3 Mathematical Processes and Perspectives 023 0015 Understand how to use a variety of representations to communicate

mathematical ideas and concepts and connections between them. 023 0016 Understand mathematical reasoning, the construction of mathematical

arguments, and problem-solving strategies in mathematics and other contexts.


1g) Candidate data derived from Assessment #2: Georgia Licensure Exam

Table G1

2009 Annual Program Completer GACE Pass Percentages

Certification Field Level Test Code Test Description

# Tested

# Passed

% Passing

MATH B.S. GACE 022 GACE Test 1 % GACE 023 GACE Test 2 %

Table G2

2008 Annual Program Completer GACE Pass Percentages

Certification Field Level Test Code Test Description

# Tested

# Passed

% Passing

MATH B.S. GACE 022 GACE Test 1

GACE 023 GACE Test 2

Assessment #2: GPA 1

Assessment #2: Grade Point Average (GPA) in Mathematics Courses 2a) Description of the assessment:

This assessment is comprised of GPAs in the secondary level (grades 6-12) mathematics content courses that teacher candidates take for undergraduate mathematics education program completion. In the mathematics courses below, candidates are assessed based on their ability to solve problems on homework assignments, quizzes, examinations, and in some cases, projects. A student’s grade in a course is based on the learning outcomes for that course, which are aligned with the SPA Standards as shown below. Nine content courses, selected for the GPA assessment, prepare teacher candidates to teach in a rigorous secondary level mathematics program that supports a deep understanding of mathematics. All courses are each worth three credits, except Calculus II, and III, which are each worth four credits. MATH 2595 and MATH 4495 are not required for students who matriculated before fall 2003 and fall 2007 respectively. A grade of C (2.0 GPA) or better in each of the required content courses shows a student has met those learning outcomes, and is a prerequisite for advancement to the next required course in the program. A primary objective of the required mathematics content courses is for candidates to learn academic content knowledge of mathematics and meet a required specified performance level. In order for instructors and candidates to know if candidates are achieving this academic knowledge at the required level of performance, instructors assess candidates’ knowledge, specify, and summarize the performances required in their courses into a letter grade or points which represent the quality of the candidates’ work.

2b) Alignment of NCTM Standards/Indicators with Teacher Candidate GPAs

Course Course Description NCTM Indicators

MATH 2595: Math for Middle Grades and Secondary Teachers

Number and operation, algebra, and measurement. The process standards of communication, connections, problem solving, reasoning and proof, and representation are emphasized. Appropriate use of manipulatives, calculators and software are integrated.

1.1, 2.1, 9.1. 9.2, 9.3, 9.4, 9.5, 9.6, 9.7, 10.1, 10.4, 10.5, 15.1, 15.2, 15.3

MATH 4495: Advanced Perspectives on School Math II

The study of algebraic structures, analytic geometry, and trigonometry, including conic sections, complex numbers, polynomials and functions.

1.3, 3.1, 3.2, 3.3, 3.4, 4.1,4.2, 4.3, 5.1, 5.2, 5.3, 6.1, 9.1, 9.8, 10.1, 10.3, 10.5, 11.5, 12.2

MATH 3260: Linear Algebra I

Systems of linear equations, vector spaces, linear transformations, and diagonalization. Some use of technology in performing matrix computations.

9.9, 10.1, 10.2

MATH 4361: Modern Algebra

Fundamental structures of groups, fields, and rings and their connections with elementary algebra.

10.3


MATH 3395: Geometry

An axiomatic system from synthetic, transformation, and algebraic perspectives. Finite, infinite projective, Euclidean and Non-Euclidean.

11.1, 11.2, 11.3, 11.6, 11.7

MATH 2202: Calculus II

Integral Calculus and infinite sequences and series. Applications of the integral, techniques of integration, and Taylor Series.

12.1, 12.3, 12.4

MATH 2203: Calculus III

Concepts of single Variable calculus are extended to functions of more than one variable. Vector calculus, partial derivatives, multiple integrals, and applications of these concepts.

12.1, 12.3

MATH 3322: Discrete Modeling I

Topics (matrices, graphs, counting and recursion) and methods in discrete mathematics motivated by a series of real-world problems.

13.1, 13.2, 13.3

MATH 3332: Probability & Statistical Inference

Topics include random variables, properties of estimators, exploratory data techniques, confidence intervals, hypothesis test for population mean and proportion, Statistical Process control, chi-square goodness of fit, contingency table analysis. MINITAB used.

14.1, 14.2, 14.3, 14.4, 14.5, 14.6, 14.7

2c) Analysis of the data findings

A careful analysis of the data for the period summer 2009 – spring 2010 shows a strong alignment to the standards with a significant number of the indicators met. A candidate’s grade point average (GPA) for mathematics content courses is based on a possible 4.0 GPA. Candidates must earn at least a 2.0 grade point average in each required mathematics course. The data table indicates that, over three assessment periods (summer 2009, fall 2009, and spring 2010), each completer met or exceeded the minimum expectation of a C (2.0 quality points) or better in all required mathematics courses for the undergraduate mathematics education program. The data on the required mathematics course grades indicate that all candidates enrolled in the undergraduate mathematics education program are earning grades in the range of A to C.

2d) An Interpretation of how the data provides evidence for meeting standards These data indicate that all of our candidates are successful in demonstrating the knowledge and understanding of the mathematics content needed for certification. As the chart demonstrates, these classes are aligned with the NCTM content standards (listed above).


2e) Assessment Documentation

Grading System

All completers must have a GPA of 2.0 or better in all required mathematics coursework in the program to be eligible to student teach. The university is organized on the semester system, with two semesters extending 15 weeks (plus exams) and a summer term extending approximately eight weeks. The semester hour is the unit of credit in any course. Kennesaw State University complies with the University System of Georgia uniform grading system. The final grades and their definitions are as follows:

Final Grades Quality Points per Credit Hour A Excellent 4 B Good 3 C Satisfactory 2

D Passing, but less than satisfactory 1

F Failing 0


2f) The scoring guide for the assessment Not appropriate for this assessment 2g) Charts that provide candidate data derived from Assessment #2:

Candidates’ Grades in Required Mathematics Courses Undergraduate Mathematics Candidates

Table 1

Grades: A=4 points, B= 3 points, C=2 points, D=1 point, F= 0 points

2009-2010 (Su 2009, Fa 2009, Sp 2010)

Mean Course

Grade (Range)

Candidates Meeting Minimum Expectations

MATH 2202 Calculus II

MATH 2203 Calculus II

MATH 2595 Math for Middle Grades and Secondary Teachers

MATH 3260

Linear Algebra I MATH 3322

Discrete Modeling I MATH 3332

Probability & Statistical Inference

MATH 3395 Geometry

MATH 4361 Modern Algebra

MATH 4495 Advanced Perspectives on School Mathematics

II

Assessment #3: Mathematics Teaching Unit Plan 1

Assessment #3: Mathematics Teaching Unit Plan 3a) Description of the assessment

In MAED 4416/4417 (methods course/4 week field experience), candidates design and implement a unit of lesson plans for teaching important mathematical ideas in a middle or high school. The unit is a chapter of lesson plans for each day the candidate will be teaching, including all assessments (quizzes, unit tests) the candidate will incorporate into the unit. At least one lesson plan incorporates the investigative use of electronic technology. In their initial practicum (MAED 4417), candidates teach these units and are asked to reflect upon them 3b) Alignment of NCTM Standards with the Mathematics Teaching Unit

NCTM Standards/Indicators Addressed

Assessment Alignment with NCTM Standards/Indicators

Standard 3: Knowledge of Mathematical Communication [NCTM 3.1, 3.2, 3.3, 3.4]

The candidate writes a well-written, organized, insightful, reflective overview that addresses the required mathematical topics in their unit plan. The candidate uses correct mathematical symbols, language, and conventions.

Standard 5: Knowledge of Mathematical Representation [NCTM 5.1, 5.2, 5.3

The candidate represents the mathematics using correct symbols, language, and conventions throughout the teaching unit.

Standard 6: Knowledge of Technology [NCTM 6.1]

The candidate includes investigative use of technology that provides opportunities for students to build deep mathematical understanding.

Standard 7: Dispositions [NCATM 7.2, 7.3, 7.4, 7.5, 7.6]

The candidate supports mathematical processes and learning by using stimulating curricula, effective teaching, various assessments, and teaching tools including technology throughout the teaching unit.

Standard 9: Knowledge of Number and Operation [NCTM 9.1, 9.2]

The candidate uses mathematical symbols, language, and conventions correctly throughout the unit. Mathematical problems and exercises are well-planned and worked correctly, and mathematics is represented accurately throughout the unit.

Standard 8: Knowledge of Mathematics Pedagogy [NCTM 8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 8.8, 8.9]

The candidate participates in and uses research, print, and online resources from professional math organizations while incorporating problem-solving and a wide variety of mathematics curricula, concrete materials, listening, and assessments in their lesson plans to help all students build a deep understanding of mathematics.

Standard 16: Field-Based Experiences [NCTM 16.1]

The candidate teaches a unit of lesson plans during a 4-week practicum while observing and participating in both middle and high school mathematics classrooms under the supervision of experienced and highly qualified teachers.


3c) Analysis of data findings

The Mathematics Teaching Unit Rubric results are displayed in Data Tables A3.1 and A3.2 for two assessment periods fall 2009 and spring 2010. The tables depict the percentage of candidates as well as the number of candidates scoring at each level of the Mathematics Teaching Unit Plan criteria. A candidate can score in the range of L1 – L4. The evaluation ratings consist of the lowest rating of L1: The candidate’s performance offers little or no evidence of achieving the proficiency, with subsequent ratings of L2: The candidate’s performance provides limited evidence that the proficiency has been met, L3: The candidate’s performance provides evidence that the proficiency has been met, and L4: The candidate’s performance provides consistent and convincing evidence that the proficiency has been met. A minimum acceptable rating for each Mathematics Teaching Unit Plan Rubric criteria is L3. Looking at the combined scores on all relevant rubric criteria shows that at least 87% of candidates scored at L3 or higher L3. The results from the two assessment periods show that the NCTM standards outlined above are clearly satisfied by the candidates in our program. During spring 2010, all candidates scored at L3 or higher for all rubric criteria. During the fall of 2009, a large percentage of our candidates ( are successful in meeting the minimum passing score of L3 or higher for each criteria of the Mathematics Teaching Unit Plan rubric. For 7 out of 10 criteria, all candidates (for both periods of assessment) score at L3 or above, indicating that their performance on these criteria has been consist, accurate , and convincing. Although the majority of candidates ( met the minimum requirements for all rubric criteria, faculty members are aware that a small percentage ( ) scored L2 during fall 2009. A small number of candidates demonstrated limited evidence for the rubric criteria “materials and curriculum” [Standard 8.2, 8.5] and the criteria related to “pedagogical strategies” [Standards 7.2, 7.3, 8.1, 8.6, 8.7]. scored at L2 or less on the criteria associated with the “appropriate use of technology” [Standards7.6, 8.9]. While these are not major weaknesses, mathematics education program faculty members continue to provide opportunities for candidates to improve in areas where they scored lower than an L3. 3d) Interpretation of how the data provides evidence for meeting standards

This data shows that our candidates are well prepared in pedagogy and constructing unit plans in mathematics as evidenced in the Mathematics Teaching Unit P lan rubric criteria relevant to the NCTM standards/indicators listed above. This demonstrates that the majority of our candidates use print and online resources from professional organizations and the correct mathematical symbols, language, conventions, and they also have knowledge of different types of instructional strategies in planning mathematics lessons. Our candidates create a unit of lesson plans that incorporate a wide variety of appropriate student-centered instructional strategies, mathematics curricula, and teaching materials grounded in research and appropriate for all students.


3e) Description of the assessment

MAED 4416/4417

Mathematics Teaching Unit

Two weeks before entering your field experience you will be submitting the unit plan for your field experience. The TOSS instructors will be returning your units within one week of submission with comments and guidance on revisions (if needed). Any necessary adjustments should be resubmitted before you enter the field. After the Instructor grades your unit, you will submit the lesson plan for your cooperating teacher’s approval when you arrive on the first day of your field experience [NCTM 16.1]. Note: A score of 80% must be achieved on the unit plan in order to be approved to complete the field experience. If the initial score is lower than 80%, the student is required to revise and submit for a re-grade. Students with scores above 80% should complete requested revisions and may submit for re-grade if desired. If a unit plan has been submitted for re-grade, the final score will be the average of the initial grade and the re-grade. Essentially, the unit is a set of lesson plans for each day that you will be teaching plus an overview and all of the assessments (quizzes, unit tests) that you will incorporate into the unit. Attached is the evaluation rubric on which you will be scored. In addition, you will submit one of the unit lesson plans on an earlier due date as your third individual lesson plan assignment. The TOSS instructors realize that cooperating teachers will have certain expectations of you and that you will have to work within their parameters. Ultimately, they are accountable for their students’ success. If you experience any conflicts between their expectations and ours, please discuss these issues with us so that we can work out a reasonable compromise. Please submit the following items as your unit plan:

1. Overview (narrative or bulleted list). Create a brief (one to two pages) summary of your unit plan that includes your overarching goals and justification for your selection of activities and teaching methods. Specifically, how does your unit conform to the process standards endorsed by NCTM and GPS? What measures are you taking to promote conceptual understanding, and how will you assess conceptual and procedural understanding? Finally, we understand that inevitably some decisions for your unit will be dictated by school and cooperating teacher expectations. Please address in your overview how you would change your unit plan if this were your own class.

2. Complete lesson plans for each day that you will be teaching [NCTM 16.1]. Use the lesson plan template that has been required for all group and individual lesson plans in class. Please be sure to indicate whether you are planning for block or traditional schedules, and always include time estimates for the major parts of your lessons. You are required to incorporate mathematics curricula and teaching materials from print and on-line resources of professional organizations where appropriate (cite your source). At least one lesson plan should incorporate the investigative use of electronic technology (e.g., Geometer Sketchpad demonstration, graphing calculator or computer activity). [NCTM 7.6]

3. Copies of all handouts that you create to support your lessons.


4. Copies of all classwork and homework assignments, completely worked out. If you are giving homework assignments out of the textbook, please include copies of the textbook pages so that we can see your choices in problems.

5. Completely worked out copies of your unit test and quizzes, with point values and scoring policies indicated. Include your rubrics for grading these assessments.

You will be evaluated on the following dimensions (see rubric for point values):

1. Conceptual understanding– the extent to which your unit addresses conceptual understanding. [NCTM 7.4, 8.7, 8.8]

2. Student engagement –the extent to which your unit elicits students’ thinking, active participation, and engagement. [NCTM 7.2, 7.3, 8.6, 8.7, 8.8]

3. Formative and summative assessment– the extent to which your assessment plans provide usable information about student understanding and achievement that is aligned with your instructional plans. [NCTM 3.4, 7.5, 8.3]

4. Clarity – the extent to which your lesson plans are readable, clear, and easy to follow. [NCTM 3.1, 3.2, 3.3]

5. Mathematical correctness – the extent to which your unit is mathematically correct. [NCTM 3.2, 3.3, 5.2, 5.3, 9.1, 9.2]

6. Completeness – the extent to which your lesson plans contain required elements (learning outcomes, standards alignment, materials and resources, motivation/warm up, lesson procedure (all activities clearly detailed and problems completely worked out), closure, and assignment (completely worked out). [NCTM 7.1, 7.2, 8.1, 8.2, 8.4]


3f) Scoring Guide for Assessment # 3: Mathematics Teaching Unit Plan Secondary Mathematics Education – MAED 4416/4417 Teaching Unit Scoring Rubric

Overview (NCTM 3.1)

0 po ints No overview was provided

1-4 po ints An overview was provided, but it failed to address some of the required topics. It was poorly wr itten and lacked insight and reflection.

5-8 points An overview that addressed the required topics was provided, but it was poorly written and/or lack ed insight and reflection.

9-10 points A well-wr itten, ins ightful, reflective overview that addressed required topics was provided.

Po ints Earned

Materials and Curriculum

(NCTM 8.1, 8.2)

0-8 points All lessons are teacher-centered and textbook-based. No mater ials beyond overhead projector/board are requir ed.

9-12 po ints The unit includes little to no variety of mathematics curr icula and teaching mater ials. The unit does not include the use of appropriate concrete materials for learning mathematics or uses materials in a way that does not enhance instruction.

13-17 points The unit includes a limited var iety of mathematics curr icula and teaching mater ials. The unit includes some appropriate use of concrete materials for learning mathematics.

18-20 points The unit includes a wide variety of mathematics curr icula and teaching mater ials appropriate for all students, including pr int and on-line resources from profess ional organizations. The unit includes the use of appropriate concrete materials for learning mathematics.

Pedagog ical Strategies

(NCTM 7.2, 7.3, 8.6, 8.7)

0-8 points All lessons are teacher-centered and lecture-oriented.

9-15 points More than half of the lessons are teacher -centered and lecture-oriented. Activities requir ing s tudent participation do not enhance instruction.

16-24 po ints More than half of the lessons in the unit include student-centered instructional strateg ies, grounded in research related to the teaching and learning of mathematics.

25-30 points A wide variety of appropriate student-centered instructional strateg ies, grounded in research related to the teaching and learning of mathematics, is used throughout the unit.

Learning Goals/

Outcomes

(NCTM 8.4)

0 po ints Learning outcomes are not provided.

1-4 po ints Learning outcomes stated, however they were not aligned with local, s tate, and national s tandards. There were many stated learning outcomes that were not thoroughly addressed in the unit and/or there were many k ey concepts addressed in the unit that were not s tated as learning outcomes.

5-8 points Throughout the unit, appropriate learning outcomes (including local, state, and national mathematics standards and legis lative mandates) were included. There were some stated learning outcomes that were not thoroughly addressed in the unit and/or there were some key concepts addressed in the unit that were not stated as learning outcomes.

9-10 points Throughout the unit, appropriate learning outcomes (including local, state, and national mathematics standards and legis lative mandates) were included. The stated learning outcomes were thoroughly addressed in all lessons, and all key concepts in the unit were specified in the learning outcomes.

Conceptual Understanding

(NCTM 7.4, 8.7)

0-9 points No opportunities are provided for students to engage in problem-solving or in developing in-depth conceptual understanding of mathematics. The teacher poses and so lves all problems with a purely procedural approach.

10-1 8 po ints The unit pr imar ily addresses procedural unders tanding. Attempts are made in the unit to provide opportunities for students to engage in mathematical problem solving and in developing in-depth conceptual understanding of mathematics; however, it is unlikely that students will develop an in-depth conceptual unders tanding through the activities provided in the unit.

19-28 points The unit thoroughly addresses procedural unders tanding. There are opportunities provided in the unit for students to engage in mathematical problem so lving and in developing in-depth conceptual understanding of mathematics; however, the activities do not consistently support the development of students’ in-depth conceptual understanding of mathematics.

29-35 points Frequent opportunities are provided throughout the unit for students to engage in mathematical problem so lving and in developing in-depth conceptual understanding of mathematics. Procedures and generalizations are developed thoroughly and with understanding through pattern identif ication, conjecture, and testing. The activities provided in the unit will foster students’ in-depth conceptual understanding and procedural understanding of mathematics.

Formative Assessment (NCTM 3.4, 7.5, 8.3)

0-3 po ints All ques tions in the lessons and assignments are procedural or requir e memorization and do not provide opportunities to gauge s tudent understanding.

4-7 points In fewer than half of the lessons and assignments, questions are provided that will provide the TOSS intern opportunities to lis ten to and understand the ways students think about mathematics in an effor t to assess students’ mathematical knowledge.

8-12 po ints In more than half of the lessons and assignments, questions are provided that will provide the TOSS intern opportunities to listen to and understand the ways students think about mathematics in an effort to assess students’ mathematical knowledge.

13-15 points In each lesson and ass ignment, questions are provided that will provide the TOSS intern opportunities to lis ten to and to understand the ways students think about mathematics in an effort to assess s tudents’ mathematical knowledge.


Unit Test and Quizzes (Summative Assessment) (NCTM 7.5, 8.3)

0-3 po ints All ques tions on the

assessment instruments are procedural and do not

provide opportunities to gauge s tudent understanding. No scoring rubric is provided.

4-7 points Assessment instruments include

predominantly procedural exercises and provide few or no opportunities for

students to demonstrate a conceptual unders tanding of mathematics. The

scoring rubric is inappropriate and/or unclear.

8-12 po ints Assessment instruments include a major ity of

exercises that are procedural but provide limited opportunities for students to

demonstrate a conceptual understanding of mathematics. The scor ing rubric is somewhat

lacking in clar ity and/or appropriateness.

13-15 points Assessment instruments include oppor tunities

for students to demons trate a conceptual unders tanding of mathematics appropr iately balanced with exercises that assess procedural

unders tanding. The scor ing rubric is clear and appropriate for the test items.

Mathematical Correctness (NCTM 3.2, 3.3, 5.2, 5.3, 9.1, 9.2)

0-9 points There are fr equent serious

errors in mathematical symbols, language, and

conventions throughout the unit. Problems and exercises

have not been planned in advance and are not worked out or are worked incorrectly

and/or inef ficiently. The progression of mathematical topics presented is illogical.

10-1 8 po ints In more than half of the lessons, there are

errors in the use of mathematical symbols, language, and conventions.

Mathematical problems and exercises are not well-planned and are occas ionally worked incorrectly and/or ineff iciently. The topics are disorganized and are

frequently not presented in a mathematically logical progress ion.

19-28 points Mathematical symbols, language, and

conventions are used correctly throughout the unit, with only an occas ional lapse.

Mathematical problems and exercises are planned in advance and worked correctly, and

mathematics is r epresented accurately throughout mos t of the unit. The topics are

organized and generally presented in mathematically logical progress ion.

29-35 points Mathematical symbols, language, and

conventions are used correctly throughout the unit. Mathematical problems and exercis es are well-planned and worked correctly, and

mathematics is r epresented accurately throughout the unit. The topics are

thoughtfully organized and presented in mathematically logical progress ion.

Appropr iate Use of Techno logy (NCTM 7.6, 8.9, 6.1, 8.1)

0-8 points No opportunities are provided to inves tigate mathematical concepts with technology

9-12 po ints The unit includes attempts at inves tigative

uses of technology, but activities are inappropr iate and/or fail to provide

students opportunities to build unders tanding of mathematical concepts and to develop important mathematical

ideas.

13-17 points The unit includes attempts at inves tigative

uses of technology; however, the oppor tunities provided could be improved in order to

promote conceptual understanding and the development of mathematical ideas.

18-20 points The unit includes some inves tigative use of technology that provides opportunities for

students to build understanding of mathematical concepts and to develop

important mathematical ideas.

Clar ity (NCTM 3.1, 3.2, 3.3)

0 po ints The unit was very diff icult to

follow. It was poorly organized, poorly wr itten, and contained many grammar and spelling errors that affected the meaning or clar ity of the

lessons.

1-4 po ints The unit was challeng ing to read. I t was

often disorganized and contained fr equent grammar and spelling errors that affected

the meaning or clar ity of the lessons.

5-8 points The unit was usually easy to read and fo llow, with a few exceptions. I t was organized and

well-written. It contained occas ional grammar and spelling errors that did not affect the

meaning or clarity of the lessons.

9-10 points The unit was easy to read and follow. It was well-organized, well-written, and contained

very few grammar and spelling errors.


3g) Candidate data derived from Assessment #3: Mathematics Teaching Unit

Assessment #3: Data Table A3.1 Fall 2009

Fall 2009

L1 Little or

No Evidence

L2 Limited Evidence

L3 Clear

Evidence

L4 Clear,

Consistent &

Convincing Evidence

Total

Percent Scoring

at L3/L4

Percent Scoring

at L1/L2

Elements/Criteria % N % N % N % N % N % % Overview (3.1) Materials and Curriculum (8.2, 8.5) Pedagogical Strategies (7.2, 7.3, 8.1, 8.6, 8.7) Learning Goals/Outcomes (8.4) Conceptual Understanding (7.4, 8.7) Formative Assessment (3.4, 7.5, 8.3) Unit Test and Quizzes (Summative Assessment) (7.5, 8.3) Mathematical Correctness (3.2, 3.3) Appropriate Use of Technology (7.6, 8.9) Clarity (3.1, 3.2, 3.3) Formative Assessment (3.4, 7.5, 8.3)

Candidate data derived from Assessment #3: Mathematics Teaching Unit


Assessment #3 Data Table A3.2

Spring 2010

Spring 2010

L1 Little or

No Evidence

L2 Limited Evidence

L3 Clear

Evidence

L4 Clear,

Consistent &

Convincing Evidence

Total

Percent Scoring

at L3/L4

Percent Scoring

at L1/L2

Elements/Criteria % N % N % N % N % N % % Overview (3.1) Materials and Curriculum (8.2, 8.5) Pedagogical Strategies (7.2, 7.3, 8.1, 8.6, 8.7) Learning Goals/Outcomes (8.4) Conceptual Understanding (7.4, 8.7) Formative Assessment (3.4, 7.5, 8.3) Unit Test and Quizzes (Summative Assessment) (7.5, 8.3) Mathematical Correctness (3.2, 3.3) Appropriate Use of Technology (7.6, 8.9) Clarity (3.1, 3.2, 3.3)

Assessment #4: MAED Observation Summary 1

Assessment #4: MAED Observation Summary--Student Teaching Evaluation

4a) Description of the assessment

The observation summary is composed of ten indicators that must be observed “at least one time” during the capstone experience of student teaching. The capstone experience is designed to provide the student with teaching practice in the field in which the major aspects of content knowledge, pedagogy, and pedagogical content knowledge interact. It ties together several pieces of instruction from courses required in the program by: 1) communicating performance results to others, 2) determining the effect of instruction on students’ learning, and 3) guiding decisions about future instruction, the effectiveness of the courses required in the program, and plans to improve on student performance during student teaching. Candidates are assessed four times during their student teaching—twice before midterm and twice before the conclusion of student teaching. The student teaching Mathematics Observation Summary evaluation is completed by the University Supervisor and Collaborating Teacher who dates and provides a description of observed criteria/indicators.

4b) Alignment of NCTM Standards/Indicators with the MAED Observation Summary

NCTM Standards

NCTM Indicators Addressed


Standards 3: Knowledge of Mathematical Communication

3.4

The candidate interacts daily with students and listens carefully to individual students’ thinking.

Standard 4: Knowledge of Mathematical Connections

4.2, 4.3 The candidate is required to use real-world applications that show the relevance of mathematics to daily life and how these applications tie together different arenas such as geometry and algebra.

Standard 5: Knowledge of Mathematical Representation

5.1, 5.3 Within the lesson, the candidate uses various representations of mathematics, including, but not limited to picture models, graphs, and algebraic expressions/equations. The contexts might refer to physical, social, or mathematical phenomena.

Standards 6 Knowledge of Technology,

6.1 The candidate designs lessons that incorporate technology such that the use of technology builds and enhances the mathematical understanding of the student.

Standards 7: Dispositions

7.1, 7.4, 7.5, 7.6

The candidate connects mathematical learning to real-life situations relevant to students’ lives and cultures. This attention to diversity in the classroom promotes equity among students that the candidate is teaching. The candidate uses technology as a tool for instruction and develops important mathematical concepts with understanding. The candidate assesses (formative and summative) student knowledge and understanding during the lesson in ways that include quizzes, tests, or homework in addition to questioning, the use of instructional tools such as technology, individual student white boards, or simple monitoring of student work as they progress through the lesson. In doing so, the candidate gains knowledge


of student thinking and understanding. Standard 8: Knowledge of Mathematics Pedagogy

8.1, 8.2, 8.3, 8.7, 8.8, 8.9

The candidate plans/designs lessons using curriculum materials outside of the textbook for all students and uses concrete materials that enable students to build mathematical understanding by forming and testing generalizations that will lead students to a deeper understanding of mathematical concepts. Candidates listen carefully to students during instruction which gives the candidate insights into the students’ mathematical thinking and understanding.

4c) Analysis of data findings

Rubric results are displayed in Tables: A4.1 and A4.2 for the periods of fall 2009 and spring 2010. Results are combined for all candidates evaluated during each period and delineated for indicator and rating. Data tables depict the percentage of candidates as well as the number of candidates scoring at each rubric level for each indicator. The Mathematics Observation Summary shows that each indicator has been observed at least one time during a candidate’s student teaching experience. A minimum acceptable rating for each indicator is L2 (indicator observed 1 time during student teaching). Looking at the overall Observation Summary Instrument Rubric tables for both periods, all ratings (100%) are at L2 or above indicating that all candidates were observed demonstrating each NCTM indicator at least once over a period of four different observations. During fall 2009, 90% of the candidates exceeded minimum requirements scoring at L3 or above for 7 out of 10 rubric criteria. This indicates that during the candidates’ student teaching instruction, university supervisors observed them (a) listening carefully to individual students’ mathematical thinking [standards 3.4, 8.3], (b) connecting mathematical ideas and mathematical learning to real-life situations relevant to students’ lives and cultures [standards 4.2, 4.3, 7.1], (c) using technology in an investigative way[standards 6.1, 7.4, 7.6, 8.9], (d) providing opportunities for students to develop and test generalizations while engaged in problem-solving [standard 8.8], and(e) authentically assessing students [standard 7.6] two or more times. During this same period, although 100% of the candidates met the minimum requirement (scoring L2 for each indicator), less frequent observations were made of candidates demonstrating use of concrete materials [8.2], real-world connections [4.2, 7.1], or providing opportunities for students to make conjectures [7.4]. During spring 2010, at least 50% of the candidates exceeded the minimum requirements for 7 out of 10 indicators. Fewer candidates demonstrated use of concrete materials (29%), use of investigative technology (46%), and problem-solving (42%) more than one time. However, 100% of candidates demonstrated all rubric indicators at least one. 4d) An Interpretation of how the data provides evidence for meeting standards Data from the Student Teaching Evaluation clearly indicate that our candidates understand and successfully apply the NCTM standards during their student teaching. Looking at both periods, all candidates (100%) scored at L2 or above demonstrating each rubric criterion at least once over a 16 week period.


4e) Assessment # 4 Documentation

The student teaching Mathematics Observation Summary evaluation is completed by the University Supervisor and Collaborating Teacher who date and provide a description of observed criteria/indicators. It is composed of ten indicators each of which must be observed “at least one time” during the capstone experience of student teaching. Candidates are assessed four times during their student teaching—twice before midterm and twice before the conclusion of student teaching.

MATHEMATICS EDUCATION OBSERVATION SUMMARY Kennesaw State University

Student’s Name: KSU Course: Semester: Collaborating Teacher: University Supervisor: School: Observer (Circle): Unvsty Supervisor Collab. Teacher SMT Self Peer Each indicator must be observed at least one time during student teaching. NCTM Indicator

Date

Observed

Description (if observed multiple times describe

each instance, indicating the date of each)

The candidate listened carefully to individual students’ mathematical thinking (3.4, 8.3).

The candidate’s instruction helped students connect new learning to prior learning (4.1, 4.3).

The candidate connected mathematical learning to real-life situations that were relevant to their students’ lives and cultures (4.2, 7.1).

The candidate used technology in an investigative way to provide opportunities for students to build mathematical understanding (6.1, 7.6, 8.9).

The candidate required students to develop and test generalizations (8.8).

The candidate required students to engage in problem solving (situations in which a solution strategy was not known) (8.8).

The candidate used concrete (hands-on) materials that enabled students to build mathematical understanding (8.2).

The candidate represented mathematics in a variety of ways (5.1, 5.2, 5.3).

The candidate designed a lesson using curriculum materials outside of the textbook or other curricula provided by the school that enabled students to build mathematical understanding (7.2, 7.4, 8.1, 8.7).

The candidate assessed students’ understanding in an authentic way other than a quiz, a test, or homework (7.5, 8.3)


4f) Scoring Guide for Assessment # 4 L1 L2 L3 L4 The Indicator is Observed 0 times during Student Teaching

The Indicator is Observed 1 time during Student Teaching

The Indicator is Observed 2 or 3 times during Student Teaching

The Indicator is Observed 4 or more times during Student Teaching


4g) Candidate data derived from Assessment # 4

Assessment #4 Data Table A4.1 Fall 2009

Fall 2009

L-1

Indicator Observed

0 times

L-2

Indicator Observed

1 time

L-3

Indicator Observed

2 or 3 times

L-4

Indicator Observed 4 or more

times

Total

% at L3/L4

Indicator Observed

More than 2 times

% at L2

Indicator Observed

1 time

% at L1

Indicator 1: Listening to

Students [NCTM 3.4, 8.3]

Indicator 2: Mathematical Connections

[NCTM 4.1, 4.3] Indicator 3:

Culturally RelevantReal-World

Connections [NCTM 4.2, 7.1]

Indicator 4: Investigative Technology

[NCTM 6.1, 7.6, 8.9]

Indicator 5: StudentConjectur ing [NCTM 8.8] Indicator 6:

Problem Solving [NCTM 8.8] Indicator 7:

Concrete Materials[NCTM 8.2]

Indicator 8: Varietyof Representations

[NCTM 5.1, 5.2, 5.3]

Indicator 9: Engaging Curriculum

[NCTM 7.2, 7.4, 8.1, 8.7]

Indicator 10: Authentic

Assessment [NCTM 7.5, 8.3]


Assessment #4 Data Table A4.2 Spring 2010

Spring 2010

L-1

Indicator Observed

0 times

L-2

Indicator Observed

1 time

L-3

Indicator Observed

2 or 3 times

L-4

Indicator Observed 4 or more

times

Total

% at L3/L4

Indicator Observed

More than 2 times

% at L2

Indicator Observed

1 time

% at L1

Indicator 1: Listening to

Students [NCTM 3.4, 8.3]

Indicator 2: Mathematical Connections

[NCTM 4.1, 4.3] Indicator 3: Culturally

Relevant Real-World

Connections [NCTM 4.2, 7.1]

Indicator 4: Investigative Technology

[NCTM 6.1, 7.6, 8.9]

Indicator 5: Student

Conjectur ing [NCTM 8.8] Indicator 6:

Problem Solving [NCTM 8.8] Indicator 7: Concrete Materials

[NCTM 8.2] Indicator 8: Variety of

Representations [NCTM 5.1, 5.2,

5.3] Indicator 9: Engaging Curriculum

[NCTM 7.2, 7.4, 8.1, 8.7]

Indicator 10: Authentic

Assessment [NCTM 7.5, 8.3]

Assessment #5: Student Learning 1

Assessment #5: Impact on Student Learning Assignment (ISLA) 5a) Description of the assessment:

This assessment is designed to give students the opportunity to a) determine the effect of their instruction on all students’ learning, b) guide decisions about future instruction and plans to improve upon every student’s performance, and c) communicate performance results to others. In the assignment, students are required to design a method of collecting data (such as pre-test/post-test) to analyze the impact of their instruction on a particular group of students. Specifically candidates assess student learning before and after planned instruction and write an analysis of student learning on three levels: whole group, two subgroups, and two individuals. They also describe the educational setting, create and administer assessments, and write a reflection about their planning and teaching impact on student learning.

5b) Alignment of NCTM Standard/Indicators with the ISLA

NCTM Standards/Indicators


Standard 3: Knowledge of Mathematical Communication [NCTM 3.1, 3.2]

The analysis in the assignment is at least partially mathematical. Candidates must communicate the results of their data analysis in writing, using the language of mathematics. Candidates describe statistical techniques, charts, or other representations and to provide the rationale for each of the statistical techniques used. Candidates provide a description of the findings, and a meaningful interpretation (finding and matching patterns, categorizing, drawing inferences, and making meaning from the data) of the findings.

Standard 7: Dispositions [NCTM 7.1, 7.3, 7.5]

Candidates address equity and lesson differentiation, students with exceptionalities, etc. They compare the effectiveness of their instruction across different subgroups of students. The candidates analyze how effective their teaching was by analyzing students' learning.

Standard 14: Knowledge of Data Analysis, Statistics, and Probability [NCTM 14.1, 14.3, 14.4]

Candidates select or design assessments, collect data, and then report the analysis of the data. Candidates use appropriate statistical methods (typically descriptive statistics) to describe their data.

Standard 16: Field-Based Experiences [NCTM 16.3]

As part of the assignment, candidates analyze the extent to which they are able to increase their students' knowledge of mathematics. In the event that their analysis indicates that they did not increase their students’ knowledge of mathematics, the candidates develop professional learning goals that would help them increase the impact of their teaching on student learning.

5c) Analysis of the data findings Rubric results are displayed in the Tables A5.1 and A5.2 for each semester the assessment was implemented (fall 2009 and spring 2010). The results are combined for all candidates evaluated each term and delineated for each criterion and rating. Data tables depict the percentage of candidates as well as the number of candidates scoring at each rubric level for each Impact on Student Learning rubric element/criterion. Level 1 (L1): the candidate’s performance offers little or no evidence of


that the element/criterion has been met. Level 2 (L2): the candidate’s performance provides limited evidence that the element/criterion has been met. Level 3 (L3): the candidate’s performance provides evidence that the element/criterion has been met. Level 4 (L4): the candidate’s performance provides consistent and convincing evidence that the element/criterion has been met. Candidates must attain at least a Level 3 (L3) for each rubric criterion. Candidates complete this assignment typically the semester prior to student teaching during their MAED4417 four-week practicum. They have received prior feedback and generally do well during student teaching. Looking at scores across all candidates for both fall 2009 and spring 2010 shows or fewer candidates scoring below the L3/L4 level. At least of all candidates scored at L3 or above in the appropriate use of statistical techniques, charts, and graphs. Over both assessment periods, only four candidates ( in fall 2009 and

spring 2010) scored at the L1/L2 level indicating that they did not do a sufficient job in providing a whole class summary of student scores. However, a range of of candidates were able to analyze and explain/describe how effective their teaching was by analyzing whole class, subgroups, and individual students' learning and successfully analyze the extent to which they were able to increase their students' knowledge of mathematics. Finally, after collecting pre-post assessment evidence during the field-based experience, candidates write a reflection about their teaching and its impact on students’ learning. In the event that their analysis indicates that they did not increase their students’ knowledge of mathematics, the candidates develop professional learning goals that will help them increase the impact of their teaching on student learning. At least of all candidates scored at L3 or better in the area of reflection. 5d) An Interpretation of how the data provides evidence for meeting standards Standards are clearly satisfied by the candidates in our program. A large percentage of all candidates ( scored at an L3 or above on elements/criteria associated with communicating the results of their data analysis in writing. Equity is an issue that is one aspect of the assignment because candidates are asked to describe the educational setting, classroom resources, and classroom diversity and use this information to design lessons, assessments, and differentiate learning. At least

of all candidates scored at the L3/L4 level for criteria associated with designing quality, purposeful assessments aligned with instructional objectives, and using assessment results to analyze student learning.


5e) Description of the Assessment #5

Impact on Student Learning Assignment Purpose: This assessment is to give you the opportunity to tie together many pieces of the assessment process to help you: determine the effect of instruction on all your students’ learning (NCATE/PSC Standards 1, 3, 4) guide decisions about future instruction and plans to improve upon every student’s performance

(NCATE/PSC Standards 1, 3, 4) communicate performance results to others (NCATE/PSC Standard 2) Method: Select a class/group of students whom you are teaching and a lesson/activity/unit/skill on which to evaluate

the impact on every student’s learning. Decide on a method of collecting data on your impact upon student learning using an assessment that will generate data suitable for analysis, such as a pre- and post-test. The assessment(s) you choose should be aligned with your objectives. The assessments can be of the authentic/alternative or traditional nature or a combination of both.

In assessing the impact of your lesson on all students’ learning, you should interpret the results within the contexts of the setting and student diversity. Contextual factors are important for teachers to know because they often help explain student behaviors and achievements. In your analysis, you need to investigate these contextual factors of the class you evaluated:

o geographic location, community and school population, socio-economic profile and race/ethnicity, o physical features of setting, availability of equipment/technology and other resources, o student characteristics such as age, gender, race/ethnicity, exceptionalities (disability and giftedness),

achievement/developmental levels, culture, language, interests, learning styles or skill levels.

Analyzing and Reporting the Data: Perform the analysis on the three levels below. For each level, justify your choices in statistical and analytical methods. Discuss potential reasons why these results are the way they are and future actions that you may take as a result.

Whole group: Compile the data as a whole group by using simple descriptive techniques. If you gave a pre-test, compare the pre-and post-test results. Sub groups: You should compile the data into groups for comparison (select two) from those identif ied under student characteristics. This analysis should include the contextual factors of exceptionalities, ethnicity, race, socioeconomic status, gender, language, religion, sexual orientation, and geographical area (NCATE/PSC Standard 3, Element 3; Standard 4, Elements 1 & 4). Individuals: Select two students who represent different levels of performance and examine the data you have on them.

Reflecting on the Data: After analyzing and reporting the data, reflect on your performance as a teacher and link your performance to student learning results using the “Impact on Student Learning” Rubric as a guide for reflection. Evaluate your performance and identify future action for improved practice and professional growth.

Additional Prompts for Reflection: Select the learning objective where your students were most successful, and discuss. Select the learning objective where your students needed more opportunity to grow, and discuss. Consider the individual items on your assessment and their effectiveness in measuring student

learning. Upon which items were your students most successful? Least successful? Reflect on


reasons for the levels of performance on those items, including student prerequisite knowledge, student motivation, instructional strategies, and item design.

What instructional strategies did you use in this unit? Reflect on relationships between teaching strategies and performance on related objectives.

What other forms of assessment did you use during this unit (including informal assessment)? Reflect on relationships between the feedback you got from those assessments and performance on related objectives.

In each case, provide two or more possible reasons for these outcomes. Consider your objectives, instruction, and assessment along with student characteristics and other contextual factors that you can influence to continue to have a positive impact on student learning. Finally, reflect on the possibilities for professional development. Describe at least two professional learning goals that emerged from your insights and experiences with this assignment. Identify two specific steps you will immediately take to improve your performance in the critical areas(s) you identified. Organization of the Paper for Submission (refer to preceding sections for specific information):

Introduction - In this section, describe the occasion, the setting, the students and the instructional unit they were engaged in. Provide an outline of the content of the unit you taught. It is also here that contextual factors are described. Assessments - Provide a complete description of each assessment including, but not limited to purpose, instructions, scoring (provide copy of rubric if one was used), score sheet, equipment, administrator details, and connection with the instructional unit. Analyzing and Reporting Data - Wherever statistical techniques, charts or other representations are used, describe them adequately in the narrative. Provide the rationale for each of the statistical techniques used, a description of the findings, and meaningful interpretation (finding and matching patterns, categorizing, drawing inferences, and making meaning from the data). Reflection on What You Learned - Using the section above on “Reflecting on the Data” as a guide, Insert more here on Reflecting on the Data – Based on the results you obtained and analyzed, write a reflection on what you think the results say about what students learned as a result of the instructional unit. Discuss the implications of the results to instruction and what should be changed or given different or greater emphasis if the unit were to be taught again. Be specific about the implications to a teaching method, assignments/activities that students might complete to minimize knowledge gaps or increase understanding. Identify any changes you would make in preparation, procedures and data collection if you were able to administer the assessments again.


5f) The scoring guide for Assessment #5

IMPACT ON STUDENT LEARNING ANALYSIS RUBRIC

1 – Candidate provides little or no evidence. Little understanding of expectations with regard to criterion. Description missing or

poorly communicated. No data reported. Analysis lacking, incomplete, or done using inappropriate methods. Descriptive reflection only.

2 – Candidate provides limited evidence. Criterion is addressed minimally or apparently misunderstood. Description not elaborate enough to provide clear representation. Data reported, but incomplete or poorly organized. Analysis carried out but may be lacking or additional analysis needed. Reflection mostly descriptive with some insights.

3 – Candidate provides sufficient evidence. Narrative provides a rationale for selection of evidence that is clear throughout with only a few exceptions. Evidence exists that proficiencies are adequately addressed. Candidate makes connections between evidence presented and demonstration of expertise in the outcome.

4 – Candidate provides clear, consistent, and convincing evidence. Narrative provides a clear and convincing rationale for selection of evidence. Clear, consistent, and convincing evidence exists that proficiencies are addressed with multiple examples. Candidate consistently assesses impact on student learning and provides multiple examples of adjusting practice accordingly.

CRITERIA L1 L2 L3 L4 Weight Weighted Score

INTRODUCTION – Setting (1.2, 1.4, 2.3, 2.6, 2.8) • School and Community (location, population, SES, etc.) 1 • Classroom and Resources (availability of technology, other

resources) 1

• Student Diversity (age, gender, race/ethnicity, exceptionalities, achievement/developmental levels, culture, language, learning styles, etc. as appropriate)

1

• Unit/Lesson/Content Overview 1 ASSESSMENT(S) (2.1, 2.2, 2.5, 2.9, 3.1,3.4) • Aligned with instructional objectives/learning outcomes 1 • Purpose 1 • Quality of assessment (description given or assessment attached) 1 • Whole class summary sheet of student scores (do not include names) 1

ANALYSIS (2.3, 2.7, 2.9, 3.1, 3.4) • Statistical techniques, charts, graphs included as appropriate 1 • Rationale for use of statistical techniques & representations 2 • Findings (report comparisons-An overall discussion of your findings) 1

Whole group 2 Two subgroups 2 Two individuals 2

• Interpretation of reported data 2 REFLECTION (2.7, 2.10, 3.1, 3.2, 3.4)

• On teacher’s performance 3 • On assessment instruments 3 • On impact on student mathematical learning 3 • Future actions

2 Professional development goals 2 2 Immediate actions 2

TOTAL POINTS (Maximum – 132 pt)

Percentage Score: Score out of 50:


5g) Candidate data derived from Assessment #5

Assessment #5 Data Table A5.1 Math BS ISLA (Impact on Student Learning Analysis)

Fall 2009

Fall 2009

L1 Little or

No Evidence

L2 Limited

Evidence

L3 Clear

Evidence

L4 Clear,

Consistent, and

Convincing Evidence

Total % scoring

at L3/L4

% scoring

at L1/L2

Elements/ Criteria % N % N % N % N % N INTRODUCTION: School and Community INTRODUCTION: Classroom and Resources INTRODUCTION: Student Diversity [NCATE, 7.1] INTRODUCTION: Unit/Lesson/Content

ASSESSMENT(S) : Aligned with instructional objectives/learning Outcomes [NCATE 7.5] ASSESSMENT(S): Purpose [NCATE, 7.5] ASSESSMENT(S): Quality of assessment [NCATE, 7.5] ASSESSMENT(S): Whole class summary sheet of student scores

ANALYSIS: Statistical techniques, charts, graphs included as appropriate [NCATE, 14.1, 14.3] ANALYSIS: Rationale for use of statistical techniques & representations [NCATE 3.1, 3.2, 14.1] ANALYSIS: Findings [NCATE 3.1, 3.2, 14.1] ANALYSIS: Whole group [NCATE 3.1, 3.2] ANALYSIS: Two subgroups [NCATE 3.1, 3.2] ANALYSIS: Two individuals [NCATE 3.1, 3.2] ANALYSIS: Interpretation of reported data [NCATE 3.1, 3.2, 14.4] REFLECTION: On teacher’s performance [NCATE 7.3] REFLECTION: On assessment instruments [ NCATE 7.5] REFLECTION: On impact on all student’s learning [NCATE 7.3]

REFLECTION: Future actions- Professional development goals

REFLECTION: Future actions-Immediate actions


Assessment #5 Data Table A5.2 Math BS ISLA (Impact on Student Learning Analysis)

Spring 2010

Spring 2010

L1 Little or

No Evidence

L2 Limited

Evidence

L3 Clear

Evidence

L4 Clear,

Consistent, and

Convincing Evidence

Total Percent scoring at

L3/L4

Percent scoring at

L1/L2

Elements/ Criteria % N % N % N % N % N INTRODUCTION: School and Community

INTRODUCTION: Classroom and Resources

INTRODUCTION: Student Diversity [NCATE, 7.1] INTRODUCTION: Unit/Lesson/Content

ASSESSMENT(S) : Aligned with instructional objectives/learning Outcomes [NCATE 7.5]

ASSESSMENT(S): Purpose [NCATE, 7.5]

ASSESSMENT(S): Quality of assessment [NCATE, 7.5] ASSESSMENT(S): Whole class summary sheet of student scores

ANALYSIS: Statistical techniques, charts, graphs included as appropriate [NCATE, 14.1, 14.3]

ANALYSIS: Rationale for use of statistical techniques & representations [NCATE 3.1, 3.2, 14.1]

ANALYSIS: Findings [NCATE 3.1, 3.2, 14.1] ANALYSIS: Whole group [NCATE 3.1, 3.2] ANALYSIS: Two subgroups [NCATE 3.1, 3.2]

ANALYSIS: Two individuals [NCATE 3.1, 3.2]

ANALYSIS: Interpretation of reported data [NCATE 3.1, 3.2, 14.4]

REFLECTION: On teacher’s performance [NCATE 7.3]

REFLECTION: On assessment instruments [ NCATE 7.5]

REFLECTION: On impact on all student’s learning [NCATE 7.3]

REFLECTION: Future actions- Professional development goals

REFLECTION: Future actions-Immediate actions

Assessment #6: CPI 1

Assessment #6: Candidate Performance Instrument (CPI)

6a) Description of the assessment The Candidate Performance Instrument (CPI) contains the 18 proficiencies that our professional teacher educators and school professionals agree represent the knowledge, skills and dispositions our candidates should have by the completion of their programs. The proficiencies are separated into three outcomes: Subject Matter Experts (possession of broad, deep mathematical knowledge, ability to correctly represent mathematics, ability to connect to other mathematics and subjects, and effective use of pedagogical content knowledge); Facilitators of Learning (knows how learners develop and think, motivates students to learn, implements instruction that embodies multiple cultures, creates well-managed, active learning environments, maintains high expectations for students, designs effective instruction impacting all students, uses a variety of methods, materials, and technologies, and uses assessment results to improve instruction); and Collaborative Professionals (communicates effectively, reflects on and improves professional performance, builds collaborative and respectful relationships, and displays professional and ethical behavior).

6b) Alignment of NCTM Standards and Indicators with the CPI

NCTM/NCATE Indicators/ Standards

Assessment Alignment with NCTM/NCATE Standards

Standards 3: Knowledge of Mathematical Communication [NCTM 3.4]

Candidates must demonstrate knowledge of how learners develop, learn and think mathematically utilizes a variety of strategies to assess student mathematical learning.

Standard 4: Knowledge of Mathematical Connections [NCTM 4.2, 4.3]

Candidates must connect mathematical content to other disciplines and apply it to common life experiences.

Standards 5: Knowledge of Mathematical Representations [NCTM 5.2]

Candidates must represent mathematical content accurately.

Standards 6: Knowledge of Technology [NCTM 6.1]

Candidates must use a variety of methods, materials, and technologies to enhance students’ mathematical learning.

Standards 7: Dispositions [NCTM 7.1, 7.2, 7.3, 7.5, 7.6]

Candidates must create and implement instruction that embodies multiple cultures and a rich, diverse mathematics curriculum; create effective, well-managed and active mathematical learning environments; implement effective instruction that positively impacts the mathematical learning of all students; utilize a variety of strategies to assess student mathematical learning; and use a variety of methods, materials, and technologies to enhance students’ mathematical learning.

Standard 8: Knowledge of Mathematics Pedagogy [NCTM 8.1, 8.2, 8.3, 8.5, 8.7, 8.9]

Candidates must implement effective instruction that positively impacts the mathematical learning of all students; use a variety of methods, materials, and technologies to enhance students’ mathematical learning; utilize a variety of strategies to assess student mathematical learning; design effective mathematical instruction, including the use of print and on-line resources available through professional mathematical organizations; create and implement instruction that embodies multiple cultures and a rich, diverse mathematics curriculum; and use a variety of methods, materials, and technologies to enhance students’ mathematical learning.


Standards 16: Field-Based Experiences [NCTM 16.2, 16.3]

Candidates must complete a 10 week fulltime student teaching experience that is evaluated by both the University Supervisor and the Collaborating Teacher. Candidates utilize a variety of strategies to assess student mathematical learning and use the results of assessments to improve the quality of mathematical instruction.

6c) Analysis of the Data Findings Rubric results for fall 2009 and spring 2010 are displayed in the Data Tables A6.1 and A6.2. The tables depict the combined results for all candidates evaluated each term and delineated for each criterion and rating. Rubric criteria specific to this standard are located in brackets within each table. Tables depict the percentage of candidates as well as the number of candidates scoring at each rubric level for each proficiency/criteria under each outcome (subject matter experts, facilitator of learning, and collaborative professionals). Candidates must attain at least an average of Level 3 (L3) for each of the three outcomes. Receiving a score of L2 or less for an individual proficiency does not indicate an average of less than L3 for a rubric outcome. A candidate can earn an L2 on a single proficiency and maintain an overall average of L3 for the overall outcome. Candidates are evaluated using the CPI multiple times during their field experiences. The CPI evaluations during student teaching are based on a minimum of 4 formal observations of the candidate teaching. Only results from the final CPI evaluation during student teaching are reported here as the previous evaluations were discussed with each candidate signaling areas where improvement was required. For both periods, looking at the scores across all candidates shows the all candidates met the minimum requirements. Fewer than 4% of candidates earned ratings below L3 on an individual proficiency. Over both periods, results for Outcome1: Subject Matter Experts show that candidates met minimum requirements averaging L3 or higher for Outcome1. or more candidates scored an L3 or higher for 3 out of 4 of Outcome1 proficiencies. One candidate scored an L2 for proficiency 1.3 (spring 2010), indicating that the candidate did not do a sufficient job connecting the content to other disciplines/common life. Careful review of the candidate’s overall average for outcome 1 indicates that each candidate met the minimum requirement by earning an average of L3 for Subject Matter Experts. Over both periods, results for Outcome2: Facilitator of Learning show that candidates met minimum requirements averaging L3 or higher for Outcome2. Results indicate that of the candidates scored at L3 or more for 9 out 10 of the proficiencies. Only one candidate (spring 2010) scored at the L2 level for the proficiency 2.3, indicating that the candidate did not sufficiently create and implement instruction that embodied multiple cultures. Review of the candidate’s overall performance for Outcome2 indicates that each candidate met minimum requirements by scoring an overall average of L3 for the outcome. For both assessment periods, results for Outcome3: Collaborative Professionals indicate that all candidates met minimum requirements averaging L3 or higher for Outcome 3. During the spring 2010 assessment period, one candidate score at L2 for proficiency 3.1 indicating that the candidate demonstrated limited evidence of communicating effectively orally and in writing. 6d) An Interpretation of how the data provides evidence for meeting standards

Overall, our candidates do well on the Candidate Performance Instrument (CPI). CPI proficiencies are aligned with certain NCTM content standards (listed above). Candidate data on the CPI reflect strengths in all three areas assessed. As we reviewed CPI data on all three outcomes we could see that no candidate scored at the L1 level and only one scored at the L2 level. The majority of our candidates ( perform at a level of L3 or higher.


6e) Assessment # 6 Documentation

Candidate Performance Instrument

KSU Candidate: Program: TOSS, ST, or MAT KSU Supervisor: Semester and Year: Collaborating Teacher: Date: Grade Level/Subject: Mid-Term or Final CPI School: Evaluator: School System: If other, explain:

L1 – Little or no evidence L2 – Limited evidence L3 – Evidence L4 – Consistent and convincing evidence OUTCOME 1: SUBJECT MATTER EXPERTS

Proficiency 1.1. Candidate demonstrates broad, in-depth, and current knowledge of mathematical content.

Proficiency 1.2: Candidate represents mathematical content accurately.

Proficiency 1.3: Candidate connects mathematical content to other disciplines and applies it to common life experiences.

Proficiency 1.4: Candidate uses pedagogical content knowledge effectively.

Notable Strengths:

Areas for Improvement:

OUTCOME 2: FACILITATORS OF LEARNING

OUTCOME 3: COLLABORATIVE PROFESSIONALS Proficiency 3.1: Candidate communicates effectively orally and in writing. Proficiency 3.2: Candidate reflects upon and improves professional performance. Proficiency 3.3: Candidate builds collaborative and respectful relationships with colleagues,

supervisors, students, parents and community members. Proficiency 3.4: Candidate displays professional and ethical behavior.

Notable Strengths: Areas for Improvement:

Proficiency 2.1 Candidate demonstrates knowledge of how learners develop, learn and think mathematically.

Proficiency 2.2: Candidate successfully motivates students to learn mathematics . Proficiency 2.3: Candidate creates and implements instruction that embodies multiple cultures and a

rich, diverse mathematics curriculum. Proficiency 2.4: Candidate creates effective, well-managed and active mathematical learning

environments. Proficiency 2.5: Candidate creates environments that reflect high expectations for student achievement

in mathematics . Proficiency 2.6: Candidate designs effective mathematical instruction, including the use of print and

on-line resources available through professional mathematical organizations. Proficiency 2.7: Candidate implements effective instruction that positively impacts the mathematical

learning of all students. Proficiency 2.8: Candidate uses a variety of methods, materials, and technologies to enhance

students’ mathematical learning. Proficiency 2.9: Candidate utilizes a variety of strategies to assess student mathematical learning. Proficiency 2.10: Candidate uses the results of assessments to improve the quality of mathematical

instruction. Notable Strengths: Areas of Improvement:


Other comments:


BAGWELL COLLEGE OF EDUCATION AND PROFESSIONAL TEACHER EDUCATION UNIT

MID-TERM AND FINAL EVALUATION Collaborative Development of Expertise in Teaching and Learning: The Kennesaw State University teacher education faculty is committed to preparing teachers who demonstrate expertise in facilitating learning in all students. Toward that end, the KSU teacher education community strongly upholds the concept of collaborative preparation requiring guidance from professionals within and beyond the university. In tandem with this belief is the understanding that teacher expertise develops along a continuum which includes the stages of preservice, induction, in-service, and renewal; further, as candidates develop a strong research-based knowledge of content and pedagogy, they develop their professional expertise in recognizing, facilitating, assessing, and evaluating student learning. This evaluation instrument contains the 18 proficiencies that our KSU professional teacher educators and school professionals agree represent the knowledge, skills and dispositions our candidates should have by the completion of their programs. Since student teaching is the culminating comprehensive experience for all candidates just prior to graduation, it is altogether appropriate to formally assess our candidates’ proficiencies at this time. KSU requests that the collaborating teacher, KSU supervisor and candidate complete this form independently of each other once during MAED 4417 and MAED 6416L and twice during MAED 4475 and MAED 6475. Self-assessment is important for the candidate in developing a realistic view of personal competency and professional growth.

Rubric and Supporting Explanation Candidate Proficiencies - L1-L4 Performance Characteristics

The purpose of this rubric is to provide guidance in the evaluation of the candidate’s performance during student teaching. The basis for judgment should be evidence from multiple sources such as (but not limited to) assignments, journal entries, lesson plans, observations of teaching, portfolio products, projects, service-learning projects, teacher work samples, unit plans, etc. When determining the proficiency level demonstrated by the candidate, take into account all the evidence relating to the proficiency and strive to make a holistic judgment based upon the sufficiency and quality of the evidence. The goal is to make accurate judgments and ones that are consistent with the judgments of all evaluators. The rubric contains descriptors that describe the criteria for each level. With each subsequent rating beginning with the lowest rating of L1 to the highest rating of L4, the criteria show a progression toward more compelling and better quality evidence. Apply these criteria in your judgment of the candidate’s performance as revealed through the various sources of evidence. Additional information that follows each rating’s criterion is provided to help you make an accurate judgment. Candidates must attain at least an average of Level 3 (L3) for all outcomes to graduate from the undergraduate program. Receiving a rating of less than an average of L3 on any outcome should prompt a plan developed by the program area for remediating the performance.

Level 1 – L1 The candidate’s performance offers little or no evidence of achieving the proficiency. Although there may be occasional points that vaguely suggest the candidate has achieved the expected proficiency, viewed as a whole the candidate’s performance provides little or no evidence of meeting the proficiency. If evidence is presented, the evidence suggests that the actions of the candidate have been carried out solely to fulfill course requirements. Candidate is unable to assess impact on student learning or adjust practice accordingly. Negative opinions and behaviors about students, parents, or other professionals are evident.

Level 2 – L2 The candidate’s performance provides limited evidence that the proficiency has been met. Performance may occasionally hint at a higher level of practice but viewed as a whole the candidate’s performance is either inconsistent, partial, inadequate or incomplete. Candidate shows difficulty identifying the impact of instruction on student learning and has difficulty adjusting practice. Evidence shows that while the candidate may have met course requirements, the candidate fails to meet performance expectations.

Level 3 – L3 The candidate’s performance provides evidence that the proficiency has been met. Performance is coherent, complete, consistent and accurate. Candidate demonstrates the ability to assess the impact of instruction on student learning and adjust practice accordingly. Evidence shows that candidate learning extends beyond course requirements and expectations. These extensions reflect the application of best practices from research. Positive opinions and behaviors about students, parents, or other professionals are evident.

Level 4 – L4 The candidate’s performance provides consistent, and convincing evidence that the proficiency has been met. The performance of this individual is exceptional, with multiple examples of extensions beyond course requirements and expectations.


These extensions reflect the daily application of research-based, best practices. Candidate consistently and accurately assesses the impact of instruction on student learning and demonstrates multiple examples of adjusting practice accordingly. Candidate interacts positively with students, parents, or other professionals; and is positive about the ability to teach all students.


6g) Candidate data derived from Assessment #6

Mathematics Student Teacher CPI Final

Assessment #6: CPI Data Table A6.1 Fall 2009

Fall2009 Fall2009 Fall2009 Fall2009 Total % at L3/L4

% at L1/L2

L-1 Little or No Evidence

L-2 Limited

Evidence

L-3 Clear

Evidence

L-4 Clear, Consistent, and Convincing

Evidence

Elements/ Criteria % N % N % N % N % N

OUTCOME 1: SUBJECT MATTER EXPERTS Proficiency 1.1: Candidate demonstrates broad, in-depth, and current knowledge of discipline content.

Proficiency 1.2: Candidate represents content accurately. [NCTM, 5.2]

Proficiency 1.3: Candidate connects content to other disciplines and applies it to common life experiences. [NCTM, 4.2, 4.3]

Proficiency 1.4: Candidate uses pedagogical content knowledge effectively.

OUTCOME 2: FACILITATORS OF LEARNING

Proficiency 2.1: Candidate demonstrates knowledge of how learners develop, learn and think. [NCTM 3.4]

Proficiency 2.2: Candidate successfully motivates students to learn.

Proficiency 2.3: Candidate creates and implements instruction that embodies multiple cultures and a rich, diverse curriculum. [NCTM 7.1, 8.7]

Proficiency 2.4 Candidate creates effective, well-managed and active learning environments. [NCTM 7.2]


Proficiency 2.5: Candidate creates environments that reflect high expectations for student achievement.

Proficiency 2.6: Candidate designs effective instruction. [NCTM 8.5]

Proficiency 2.7: Candidate implements effective instruction that positively impacts the learning of all students. [NCTM 7.3]

Proficiency 2.8: Candidate uses a variety of methods, materials, and technologies. [NCTM 6.1, 8.2, 8.9]

Proficiency 2.9: Candidate utilizes a variety of strategies to assess student learning. [NCTM 3.4, 7.5, 8.3,16.3]

Proficiency 2.10: Candidate uses the results of assessments to improve the quality of instruction. [NCTM 16.3]

OUTCOME 3: COLLABORATIVE PROFESSIONALS

Proficiency 3.1: Candidate communicates effectively orally and in writing.

Proficiency 3.2: Candidate reflects upon and improves professional performance.

Proficiency 3.3 Candidate builds collaborative and respectful relationships with colleagues, supervisors, students, parents and community members.

Proficiency 3.4: Candidate displays professional and ethical behavior.


Assessment # 6: CPI Data Table A6.2

Spring 2010

L-1 L-2 L-3 L-4 Total Percent scoring at L3/L4

Percent scoring at L1/L2 Little or

No Evidence

Limited Evidence

Clear Evidence

Clear, Consistent,

and Convincing

Evidence

Elements/ Criteria % N % N % N % N % N OUTCOME 1: SUBJECT MATTER EXPERTS Proficiency 1.1: Candidate demonstrates broad, in-depth, and current knowledge of discipline content. Proficiency 1.2: Candidate represents content accurately. [NCTM, 5.2] Proficiency 1.3: Candidate connects content to other disciplines and applies it to common life experiences. [NCTM, 4.2, 4.3] Proficiency 1.4: Candidate uses pedagogical content knowledge effectively. OUTCOME 2: FACILITATORS OF LEARNING

Proficiency 2.1: Candidate demonstrates knowledge of how learners develop, learn and think. [NCTM 3.4] Proficiency 2.2: Candidate successfully motivates students to learn. Proficiency 2.3: Candidate creates and implements instruction that embodies multiple cultures and a rich, diverse curriculum. [NCTM 7.1, 8.7] Proficiency 2.4 Candidate creates effective, well-managed and active learning environments. [NCTM 7.2] Proficiency 2.5: Candidate creates environments that reflect high expectations


for student achievement.

Proficiency 2.6: Candidate designs effective instruction. [NCTM 8.5] Proficiency 2.7: Candidate implements effective instruction that positively impacts the learning of all students. [NCTM 7.3] Proficiency 2.8: Candidate uses a variety of methods, materials, and technologies. [NCTM 6.1, 8.2, 8.9] Proficiency 2.9: Candidate utilizes a variety of strategies to assess student learning. [NCTM 3.4, 7.5, 8.3,16.3] Proficiency 2.10: Candidate uses the results of assessments to improve the quality of instruction. [NCTM 16.3] OUTCOME 3: COLLABORATIVE PROFESSIONALS

Proficiency 3.1: Candidate communicates effectively orally and in writing Proficiency 3.2: Candidate reflects upon and improves professional performance. Proficiency 3.3: Candidate builds collaborative and respectful relationships with colleagues, supervisors, students, parents and community members. Proficiency 3.4: Candidate displays professional and ethical behavior.

Assessment #7 1

Assessment #7: MATH 3495 Problem Analysis (PA) Project

7a) Description of the assessment In the Advanced Perspective of School Mathematics course (MATH 3495) each candidate completes a problem analysis (PA). The PA provides the candidate with the opportunity to demonstrate deep understanding of school mathematics, and engage in communicating about mathematics, reasoning, problem solving, exploring problems with technology, experimenting with multiple representations, and making connections. The candidate chooses a problem from topics in the 6-12 mathematics curriculum and then explores the problem and associated concepts in depth. The PA is composed of 7 sections: approaches, generalization, analysis, extension, concepts, connections, and history. Each candidate selects one problem to solve using 5 different approaches (including an approach using technology, algebra, and an incorrect approach that the candidate must explain). The problem is then generalized, allowing all inputs to vary, with a discussion of the conditions under which the problem has a unique solution. The generalization is analyzed using what the student knows about the characteristics of different types of functions. An extension of the problem is written, demonstrating how the problem connects with a more advanced topic. The mathematical concepts underlying the original problem are then listed, and one of the concepts is explored in depth, detailing associated properties, connections to other areas of mathematics and real world applications. Finally, candidates give a very brief history of the concept.

7b) Alignment of NCTM Standards and Indicators with the PA Project

NCTM Standards/Indicators Assessment Alignment with NCTM Standards/Indicators

Standard 1: Knowledge of Mathematical Problem Solving [ NCTM 1.1, 1.2, 1.3, 1.4]

In the problem analysis assessment, candidates describe different ways of solving or representing the problem, including ways involving diagrams or pictures, technology, algebra, guess and check, arithmetic approach.

Standard 3: Knowledge of Mathematical Communication [NCTM 3.1, 3.2, 3.3, 3.4]

During the problem analysis assessment, candidates explain in writing their thinking.

Standard 4: Knowledge of Mathematical Connections [NCTM 4.1, 4.2, 4.3]

During the problem analysis assessment, candidates are required to demonstrate a deep understanding of the connections between the problem, the concept, and other problems and concepts in the curriculum.

Standard 5: Knowledge of Mathematical Representations [NCTM 5.1, 5.2, 5.3]

During the assessment, candidates choose a mathematical problem and solve it using at least 5 approaches (multiple representations). They often use guess and check or make a table which allows for organization and recording.

Standard 6: Knowledge of Technology [NCTM 6.1]

Candidates find at least 5 approaches to solve a mathematical problem in which they often use technology (spreadsheets, graphing calculators, computer algebra systems).

Standard 8: Knowledge of Mathematics Pedagogy

In order to complete the concepts and connections section of the assessment, candidates explore activities, problems, and articles in

Assessment #7 2

[NCTM8.5] professional mathematics journals.

7c) Analysis of the data findings Rubric results are displayed in Data Table A7.1 for two assessment applications (fall 2009 and spring 2010). Results are combined for all candidates evaluated each term and delineated for each assessment criterion and rating. Thirty-two candidates completed the assessment over two assessment periods. The data table depicts the percentage of candidates as well as the number of candidates scoring at each rubric level for each Problem Analysis assignment rubric element/criterion. Level 1 (L1): the candidate’s performance offers little or no evidence of achieving the element/criterion has been met. Level 2 (L2): the candidate’s performance provides limited evidence that the element/criterion has been met. Level 3 (L3): the candidate’s performance provides evidence that the element/criterion has been met. Level 4 (L4): the candidate’s performance provides consistent and convincing evidence that the element/criterion has been met. The minimum acceptable rating for each rubric criterion is L-2. Looking at combined scores, the data shows that at least of candidates scored at L2 or above for rubric criteria. One candidate scored at L1 for generalizations and extensions and two scores occur at L1 for analysis of generalizations. 7d) An interpretation of how the data provides evidence for meeting standards These data indicate that most of our candidates are successful in demonstrating deep understanding of school mathematics. The data also indicate that our candidates engage in communicating about mathematics, reasoning, problem solving, exploring problems with technology, experimenting with multiple representations, and making connections. As the chart in 7b) demonstrates, the problem-analysis project is nicely aligned with the NCTM standards. The mathematics education faculty members continue to discuss ways in which interrater reliability can be enhanced. In the fall 2010, faculty who teach this course will begin evaluating the Problem Analysis projects together as a group in order to improve/enhance consistency in grading.

Assessment #7 3

7e) Assessment #7 documentation

The Problem Analysis

This text deals in great detail with Polya’s “looking back” phase of the problem solving process. As described in the preface, the approach used in this text to the “looking back” phase was inspired by the problem and concept analyses suggested by Usiskin et al (2003) in Mathematics for High School Teachers: An Advanced Perspective. Given any problem, the solver must first understand the problem, devise a plan, and carry out the plan. Depending on the problem, these first three phases could take minutes, hours, or years. You will be considering problems from the middle grades and secondary curriculum that usually require minutes or hours to solve. Our goal is to have you spend a great deal of time on looking back at the problem as specified below:

Approaches In this section of a problem analysis, different ways of solving or representing the problem are described and explained, including ways involving diagrams or pictures, technology, algebra, guess and check, or some purely arithmetic or reasoning approach. In developing these different techniques you are encouraged to ask others to solve the problem, and seek to understand and characterize others’ reasoning. Being able to solve problems in different ways and examine others’ reasoning are skills that are particularly important for future teachers; as stated in the NCATE/NCTM Program Standards, future teachers should be able to “apply and adapt a variety of appropriate strategies to solve problems” and “build new mathematical knowledge through problem solving.” As you develop your problem analysis, you might want to consider incorrect approaches, as well as correct ones, and explain why the approach is attractive but incorrect. Through examination of books or in discussion with others, you’ll learn new ways of approaching old problems. Questions that you should ask include: Does the solution make sense? Why is each approach correct? Generalization The solution is generalized by deriving a formula for the solution of the problem regardless of the inputs. The solution of any one problem should inform the method of solving a whole class of problems. In addition, this section requires you to engage in significant algebraic manipulation, which is also fundamental to doing mathematics. According to the CBMS recommendations, future teachers should: “Understand and be able to work with algebra as a symbolic language, as a problem solving tool, as generalized arithmetic, as generalized quantitative reasoning, as a study of functions, relations, and variation, and as a way of modeling physical situations.” (CBMS, 2001, p. 31) You will use algebra to generalize a solution and describe how the original inputs must be limited. Questions you should ask include: Under what conditions is there no solution? Under what conditions is the solution unique? Under what conditions does the problem have multiple solutions?

Assessment #7 4

Analysis of Generalization using Functions In this section, you’ll do a lot of playing with the generalization, exploring how the generalized solution depends on different values of the input. You’ll explore how pairs of inputs vary to produce the same solution. This analysis requires the use of functions, characteristics of functions, and their graphs. The importance of future teachers being comfortable in exploring and manipulating functions with and without technology cannot be overemphasized. According to the CBMS: “The concept of function is one of the central ideas of pure and applied mathematics. For nearly a century, recommendations for school curricula have urged reorganization of school mathematics so that a study of functions is a central theme.” (CBMS, 2001, p. 42).

Extension The original problem is extended by creating and solving a new problem that requires application of the methods used to solve the original problem and/or additional mathematics that builds on the methods used to solve the original problem. The NCATE/NCTM Program Standards call for future teachers to be able to “demonstrate how mathematical ideas interconnect and build on one another.” The extension is not a problem that requires the same mathematical approach in a different context, but a problem that requires more sophisticated mathematics. You will have what may be a new experience – designing your own problem from scratch! Concepts Key concepts underlying the problem and its solution are identified. You’ll choose one particular concept to examine in depth by investigating how the concept is defined, how it is represented, its important properties, applications, connections to other mathematical concepts, and appearance in the curriculum. Connections What other problems or types of problems are similar structurally to the problem under analysis? For example, in an article from Mathematics Teacher entitled “Choices and Challenges,” the author states that “We need to change our practice so that students see and understand mathematical connections. How many double-dip ice-cream cones can you make with ten flavors of ice cream? If ten people are at a gathering and each person shakes hands with every other person, how many hand-shakes will occur? Among ten cities, how many routes are possible if each city is connected to every other city? What are the triangular numbers? UNDER CERTAIN ASSUMPTIONS, these problems are basically the same – and students should come to recognize why.”

Assessment #7 5

In this section of the problem analysis, you should make connections between the problem under analysis and other problems in the K-12 curriculum or problems that you encountered in your college career. History One particular aspect of the history of the concept and/or problem is explored. The NCATE/NCTM Program Standards require that prospective teachers demonstrate a wide knowledge of the history of mathematics. In this section, you will explore in depth one particular historical aspect. You’ll have plenty of opportunity to practice the phases of “looking back” in the rest of the text. In the next section, we’ll first practice a set of useful problem solving strategies.

Assessment #7 6


Grading of Problem Analysis

(Please note that your specific problem may lend itself to a more detailed treatment in one area than another. I will take this into consideration when assigning points. For example, if your problem lends itself to a wealth of different solutions, but a very simple, straightforward generalization. . . that’s OK! )

1. Approaches: Describe different ways of solving or representing the problem, including ways

involving diagrams or pictures, technology, algebra, guess and check, arithmetic approach … Always explain your reasoning and reflect on differences or similarities between approaches. (20 -25 points) 0 Section is missing. Approaches are incomplete and/or incorrect and/or inconsistent. (L1) 5 Only a few correct approaches are provided. Little discussion is provided. (L1) 10 At least three correct approaches are provided (including approaches involving technology

and algebra); however, there is little discussion (explanation, comparison, reflection) of the approaches and/or some interesting approaches were omitted. (L2)

15 At least four correct approaches are provided (including approaches involving technology and algebra) and discussed to some extent, but it is not clear that the student understood the problem deeply and can appreciate different approaches. The student provides procedural solutions but it is not clear that the student understood the procedures conceptually. (L3)

20-25 At least four correct approaches as well as at least one wrong approach are provided (including approaches involving technology and algebra) and discussed thoroughly. It is clear that the student deeply understands the problem and the conceptual underpinnings of each approach. The student demonstrates an understanding of how solutions and representations are connected. Any algorithms used are explained conceptually. (L4)

2. Generalization: Generalize the problem and its solution. Describe the characteristics of the solution

set. (15 points) 0 No generalization is provided or the generalization is incorrect, inappropriate, or contains

major conceptual errors. (L1) 5 Generalization has some procedural errors and/or is not well stated, clearly not well

understood. (L2) 10 Generalization is correct but not well stated and/or characteristics of solution set are not

explored. (L3) 15 Generalization is correct and well stated and characteristics of the solution set are explored.

(L4)

3. Analysis of Generalization using Functions: Using your generalization, analyze the relationships between quantities in the problem. (20 - 25 points) 0 Section is missing or substantially incorrect. (L1) 5 Some analysis is provided but major parts of the analysis are missing and/or incorrect, and/or

the student clearly cannot express or does not understand the properties of the functions involved or the relationships among the inputs of the problem and its solution. (L1)

10 Most of the appropriate functions are provided but pieces of the analysis are incorrect and/or incomplete, and/or the student clearly cannot express or does not understand the properties of

Assessment #7 7

the functions involved or the relationships among the inputs of the problem and its solution. (L2)

15 Most of the appropriate functions are provided and analyzed and/or minor errors are made and/or descriptions of the functions do not include some important properties of the function, and/or the student lacks a deep understanding of the relationships among the inputs of the problem and its solution. (L3)

20-25 Appropriate functions are provided, graphed correctly, analyzed thoroughly, and the analysis reveals a deep conceptual understanding of the relationships among the inputs of the problem and its solution. (L4)

4. Extension: Extend the problem and create a new problem so that a deeper understanding or more mathematics is required to solve the problem. (20 points) 0 No extension is provided. (L1) 5 An extension is provided and solved but does not include significant new mathematics and/or

does not build on the original problem. (L1) 10 An appropriate extension is provided and solved, but there are significant conceptual errors

in the problem statement or solution. (L2) 15 An appropriate extension is provided and solved, but there are minor procedural errors in the

problem statement or solution. (L3) 20 An appropriate extension is provided, solved correctly, and represented appropriately. (L4)

5. Concepts. General overview of concepts underlying the problem and then in-depth focus on one particular concept including exploration of the definitions of the concept, properties, representations. Here the student should explore tests and articles from Mathematics Teacher and Mathematics Teaching in the Middle School (25 points). 0 Section missing. (L1) 5 Brief, general listing of concepts and definitions. Little or no discussion and/or major

misconceptions revealed in discussion. (L1) 10 General, shallow discussion of concept. Student deomonstrates a shallow understanding of

the concept underlying the problem and/or makes significant mathematical errors. (L2) 15 Student provides an adequate discussion of the concept but overlooks some major properties

of the concept and/or makes significant mistakes in the discussion. L3) 20 Student provides a thorough discussion of the concept and demonstrates a deep

understanding, but overlooks some properties of the concept or makes some mistakes in the discussion.

25 Student provides a thorough discussion of the concept and demonstrates a deep understanding of all important aspects of the concept. (L4)

6. Connections. Discussion of connections with other problems in the curriculum, including

applications, extensions, etc. In-depth exploration of one particular connection. Again, student should explore middle grades and secondary texts, the Frameworks for the Georgia Performance Standards, Intermath, and articles from Mathematics Teacher and Mathematics Teaching in the Middle School. (25 points) 0 Section missing (L1) 5 Brief, general listing of problems. Little or no discussion. (L1)

Assessment #7 8

10 General, shallow discussion of connections. Student demonstrates a shallow understanding of the connections between the problem, relevant concepts, and other problems and concepts and/or makes significant mathematical errors. (L2)

15 Student provides an extensive discussion of connections and demonstrates some understanding of the connections between the problem, the concept, and other problems and concepts in the curriculum. Student may overlook some major related concepts and/or applications and/or make significant errors in the discussion. (L3)

20 Student provides an extensive discussion of connections and demonstrates an understanding of connections between the problem, concept, and other problems and concepts in the curriculum. Student may overlook some related concepts and/or applications and/or make some minor errors in the discussion. (L4)

25 Student demonstrates a deep understanding of the connections between the problem, the concept, and other problems and concepts in the mathematics curriculum. (L4)

7. History. One particular aspect of the history of the concept and/or problem is explored. (15 points) 0 Section is missing. (L1) 5 The historical vignette is not related to the mathematics involved in the problem but to

personalities only. (Where’s the math?) (L2) 10 Historical vignette is not well-stated and/or it is not clear that student understands the

mathematics. (L3) 15 Historical vignette is well-stated, appropriate, and it is clear that the student understands the

mathematics involved. (L4)

Total: 150 points

Assessment #7 9

7g) Candidate data derived from Assessment #7: Math 3495 Problem Analysis Project

Assessment #7 Data Table A7.1 Fall 2009 and Spring 2010

Fall 2009 and

Spring 2010

L1 Little or

No Evidence

L2 Limited Evidence

L3 Clear

Evidence

L4 Clear,

Consistent, and

Convincing Evidence

Total % scoring at L2 or above

% scoring at L1

Elements/ Criteria

% N % N % N % N % N % %

Approaches

Generalization Analysis of Generalization using Functions Extension

Concepts Connections

History

Assessment #8: Historical Development Assignment 1

Assessment #8: MAED 3475 Historical Development Assignment 8a) Description of the assessment In this assessment students research and present the chronological development (timeline) of specific content areas (Number & Operation, Algebra & Trig, Geometry & Measurement, Data Analysis, Statistics & Probability, Discrete Mathematics, Calculus) in the field of mathematics emphasizing significant highlights and diverse cultures/mathematicians contributing to each field. The purpose of this assignment is for students to select and describe what they consider to be three significant steps/events/contributions in the historical development of each of the above content areas. This assessment specifically addresses the candidate’s knowledge of the historical development of the mathematical content areas as well as cultural contributions.

8b) Alignment of NCTM Standards and Indicators with MAED 3475 Historical

Development Assignment

NCTM Standards/Indicators


Standard 9: Knowledge of Number and Operation [NCTM 9.5, 9.10]

The candidate is expected to provide a thorough and accurate description and understanding of the event(s) in the development of number & operation including contributions from diverse cultures as well as the impact on the mathematics of the time and historical significance.

Standard 10: Knowledge of Different Perspectives on Algebra [NCTM 10.6]

The candidate is expected to provide a thorough and accurate description and understanding of the event(s) in the development of algebra including contributions from diverse cultures as well as the impact on the mathematics of the time and historical significance.

Standard 11: Knowledge of Geometries [NCTM 11.8]

The candidate is expected to provide a thorough and accurate description and understanding of the event(s) in the development of geometry including contributions from diverse cultures as well as the impact on the mathematics of the time and historical significance.

Standard 12: Knowledge of Calculus [NCTM 12.5]

The candidate is expected to provide a thorough and accurate description and understanding of the event(s) in the development of calculus including contributions from diverse cultures as well as the impact on the mathematics of the time and historical significance.

Standard 13: Knowledge of Discrete Mathematics [NCTM 13.4]

The candidate is expected to provide a thorough and accurate description and understanding of the event(s) in the development of discrete mathematics including contributions from diverse cultures as well as the impact on the mathematics of the time and historical significance.

Standard 14: Knowledge of Data Analysis, Statistics, and Probability

The candidate is expected to provide a thorough and accurate description and understanding of the event(s) in the development of data analysis, statistics, and probability including contributions from diverse cultures as well as the impact on the mathematics of


[NCTM 14.8] the time and historical significance. Standard 15: Knowledge of Measurement [NCTM 15.4]

The candidate is expected to provide a thorough and accurate description and understanding of the event(s) in the development of measurement including contributions from diverse cultures as well as the impact on the mathematics of the time and historical significance.

8c) Analysis of the Data Findings

Rubric results are displayed in Table A-8 for the assessment administered during spring 2010. The content assignment and rubric were redesigned spring 2009 and first piloted in summer 2009. The previous rubric was vague and did not appropriately align with the NCTM standards. Results of the summer 2009 pilot indicated that students needed more specific instructions as well as a structured format to complete the assignment. Spring 2010 was the first application of the current rubric. The results in data Table A-8 depict percentages as well as the number of candidates scoring at each rubric level for each rubric criterion. The analysis of data is based on the results displayed in the Table A-8. The minimum acceptable rating for each criterion is L3, indicating that the candidate’s performance is coherent, complete, consistent and accurate and provides evidence that the rubric criterion has been met. Looking at the scores on relevant rubric criteria shows all ratings at L3 or above.

8d) An Interpretation of how the data provides evidence for meeting standards Results from the assessment show that of our candidates demonstrate competency in the rubric criterion relevant to NCTM standards 9 through 15 listed above. All candidates clearly and accurately demonstrated they are able to describe their understanding of historical events in the development of number and operation, algebraic perspectives, geometry, data analysis and probability, discrete mathematics, and calculus.


8e) Assessment #8 Documentation

Historical Development Assignment A major objective of MAED 3475 is for prospective teachers to understand the development of mathematical thought and major historical accomplishments in the content areas of (1) Number & Operation (2) Algebra & Trig (3) Geometry & Measurement (4) Data Analysis, Statistics & Probability (5) Discrete Mathematics (6) Calculus. Two of the Learning Outcomes for the course are:

*Students will understand the chronology of mathematics, beginning with the origin of mathematics in the civilizations of antiquity and continuing until the present day. *Students will gain knowledge of the major accomplishments of mathematics (including discoveries and proofs) as well as knowledge of the people who made the accomplishments and the conditions under which they did so.

The purpose of this assignment is for you to select and describe what you consider to be three significant steps/events/contributions in the historical development of each of the above content areas. For each of the three significant steps/events/contributions you are to include the following: 1. What? (Description of the step/event/contribution) 2. Who? (Specific individuals or cultures involved in the development) 3. Where? (Location(s)) 4. When? 5. How did this affect/improve/change the mathematics of the time? 6. Why do you consider this to be one of the most significant steps in the development of this content area?

The following template should be used for this assignment: Content Area: (Algebra, Geometry, etc)

Description of step/event/contribution

Who? (Culture/Individual)

Where? When?

Effect/change in

mathematics?

Why significant

?

1.

2.

3.


8f) Scoring guide for Assessment #8: MAED 3475 Historical Development Project

L1 L2 L3 L4 Score

Nu

mb

er &

Op

erat

ion

What/who/ where/when Description

0 points Not

included

1 point Weak or inaccurate description of the event(s) that was missing much of the

pertinent information

2-3 points Partial description of the event(s) that

included most of the pertinent information

4 points Thorough and accurate description of the

event(s) that included all pertinent information, including contributions from

diverse cultures

Effect on mathematics

of the time

0 points Not

included

1 points Your response indicated a weak

understanding of the event(s) and how it impacted the mathematics of the time.

2 points Your response indicated a partial

understanding of the event(s) and how it impacted the mathematics of the time

3 points Your response indicated that you fully

understood the event(s) and how it impacted the mathematics of the time

Why significant?

0 points Not

included

1 point Your response indicated a weak understanding of the historical

significance of the event


understanding of the significance of the event in the historical development of

mathematics


understood the significance of the event in the historical development of mathematics

Alg

ebra


0 points Not

included







diverse cultures


of the time

0 points Not

included







Why significant?

0 points Not

included





mathematics



Geo

met

ry &

Mea

sure

men

t


0 points Not

included







diverse cultures


of the time

0 points Not

included







Why significant?

0 points Not

included





mathematics




Dat

a A

naly

sis

& P

rob

abili

ty


0 points Not

included






event(s) that included all pertinent information, including contributions from diverse cultures

Effect on mathematics of the time

0 points Not

included







Why significant?

0 points Not

included





mathematics



Dis

cret

e M

ath

emat

ics


0 points Not

included








0 points Not

included







Why significant?

0 points Not

included





mathematics



Cal

culu

s

What/who /where/when Description

0 points Not

Included








0 points Not

Included







Why significant?

0 points Not

Included





mathematics



Candidate Name:

Total Points Earned (out of 60)


8g) Candidate data derived from Assessment #8: MAED 3475: Historical Development Assignment

Assessment #8 Table A-8

Spring 2010

Spring 2010

L-1 L-2 L-3 L-4 Total

Percent scoring

at L3/L4

Percent scoring

at L1/L2

Little or No Evidence

Limited Evidence

Clear Evidence

Clear, Consistent, and

Convincing Evidence

Elements/ Criteria % N % N % N % N % N % %

Number & Operation [NCTM 9.5, 9.10] Algebra [NCTM 10.6]

Geometry & Measurement [NCTM 11.8, 15.4] Data Analysis & Probability [NCTM 14.8]

Discrete Mathematics [NCTM 13.4] Calculus [NCTM 12.5]

program report for the preparation of secondary mathematics … · 2012-03-05 · scores (a minimum...

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