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Milwaukee Mathematics Partnership

Year 6 Annual Report

2008 – 2009

DeAnn Huinker Principal Investigator

August 2009

Milwaukee Mathematics Partnership Year 6 Annual Report 2008–2009

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Year 6 Annual Report

2008 – 2009

DeAnn Huinker Principal Investigator

August 2009

Contributors

Pandora Bedford Darlene Boyle

Pam Buhr Cynthia Cuellar Kimberly Farley Astrid Fossum

Janis Freckmann Jacqueline Gosz

Carl Hanssen Sharonda Harris Melissa Hedges

Rosann Hollinger Heather Jones Henry Kepner

Eric Key

Henry Kranendonk Dan Lotesto Laura Maly

Kevin McLeod Mary Mooney

Lee Ann Pruske Alan Rank

Bernard Rahming David Ruszkiewicz

Beth Schefelker Alan Schnebly Sonya Sedivy

Meghan Steinmeyer Cindy Walker

This material is based upon work supported by the National Science Foundation under Grant No. 0314898.

Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation (NSF).


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Year 6 Annual Report 2008–2009

The Milwaukee Mathematics Partnership (MMP) has seen significant improvement in mathematics achievement for students in the Milwaukee Public Schools (MPS), with substantial gains in achievement and gap reductions on the most recent state tests. The University of Wisconsin-Milwaukee (UWM), Milwaukee Public Schools (MPS), and Milwaukee Area Technical College (MATC) have shared in the leadership for this student success as core partners to this unique collaboration among a large urban district, a four-year urban university, and a two-year technical college. The partners have remained steadfast and focused on their vision for challenging mathematics (shown below at right). Milwaukee Public Schools is the 30th largest district in the nation with enrollment for the 2008-09 school year at 85,369 and the racial profile at 89% non-white. Enrollment percentages are: American Indian (1%), African American (57%), Hispanic (23%), Asian (5%), White (12%), and other racial/ethnic groups (3%). Of these, 18.6% are identified with special education needs and 7.9% have limited English proficiency. Over 78% of all students qualify for free/reduced lunch. MPS is a District Identified for Improvement under NCLB. The MMP targeted 152 schools in Year 6. This included regular and instrumentality-charter schools: 113 elementary (e.g., K-5, K-8), 10 middle, and 29 high schools (15 large high schools, 14 small high schools). Some of the district affiliated non-instrumentality and alternative/partnership schools also participated. “Remarkable” and “Resolute” are the words chosen to characterize Year 6 of the MMP. The remarkable and noteworthy gains in student mathematics achievement reflected the steady and persistent improvement in the quality of mathematics instruction over these past several years. This improvement is clearly attributed to the resolute and tenacious work of the Math Teacher Leaders (MTL) and the Math Teaching Specialists (MTS). The MTLs, in their new release-time position this year, were remarkable in their accomplishments in persistently deepening the work of the MMP to impact more teachers, more classrooms, and more students. The discussion of Goal 1 highlights our focus on formative assessment principles and challenging mathematics (e.g., high school labs), and articulation of sound mathematics through Wisconsin Mathematics Standards Initiative. For Goal 2, we highlight our transition to a release-time model for our Math Teacher Leaders and the use of the MMP Learning Team Continuum as a tool to guide schools. For Goal 3, we summarize our content focus on algebraic reasoning, and provide updates on our work in the mathematical preparation and development of teachers. For Goal 4, we present the significant gains in students’ mathematics achievement and provide updates on work related to student transition to postsecondary education.


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Goal 1. Comprehensive Mathematics Framework Implement and utilize the comprehensive mathematics framework to lead a collective vision of deep learning and quality teaching of mathematics across the Milwaukee Partnership.

Focusing Instruction through Formative Assessment Through MTL professional development, I gained a deeper understanding of how to use formative assessment principles to guide my teaching and to better communicate with students. I was more focused on descriptive feedback, both oral and written. There was a lot more discussion with students on their progress, misconceptions were cleared up more readily, and students were able to deepen their understanding of the math. Students also seemed to have more purpose in their work. ---MTL This was a huge area of growth for me this year, beginning with watching a snippet of the Stiggin's video at one of our first MTL meetings this year. I showed the video to my staff, and we began a year-long journey studying assessments that could be used in the classroom and discussing the need for formative assessment to guide instruction. Teacher buy-in appears to have been significant. ---MTL

An emerging body of evidence suggests strongly that we need to be more intentional in our use of formative assessment practices. In fact, a seminal research review by Black and Wiliam (1998) found that improving formative assessment resulted in profound achievement gains for all students, with the largest gains for lowest achievers. The recently released report from the National Mathematics Advisory Panel (2008) provides further support. The Panel found that “teachers’ regular use of formative assessment improves their students’ learning, especially if teachers have additional guidance on using the assessment to design and to individualize instruction” (p. xxiii, Major Finding #25). The Panel noted that formative assessments in mathematics (1) lead to increased precision in how instructional time is used in class, (2) assist in identification of specific topics and instructional needs, and (3) should be an integral component of instructional practice in mathematics. One of their major recommendations is for teachers to make “regular use of formative assessment, particularly for students in the elementary grades” (p. 47). While it was not explicit in our original proposal for the MMP, formative assessment has become a pervasive and central thread in our work. This year seemed to be the year in which we “pulled it all together.” We had dabbled with learning targets, classroom assessments based on standards (CABS), constructed response items, and descriptive feedback. Yet, in many ways, they appeared as disparate pieces of a puzzle not yet put together.

THE TEN MMP PRINCIPLES OF FORMATIVE ASSESSMENT This year, we made explicit ten principles of formative assessment to fit together the pieces of the assessment puzzle and unpacked these principles in district-wide professional development and assisted teachers in linking them to classroom practice. The ten principles are listed in Figure 1 and draw heavily from the work of Rick Stiggins (Chappuis, Stiggins,


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Arter, & Chappuis, 2005; Stiggins, 2006; Stiggins, Arter, Chappuis, & Chappuis, 2004). With the articulation of these ten principles of formative assessment, our journey is now more focused on ways to link these principles to classroom practice. We are moving toward viewing assessment as something that is not done to students but rather with students.

Ten Principles of Formative Assessment

Teacher and Student Articulation of Math Learning Goals (1) Prior to teaching, teachers study and can articulate the math concepts students will be learning. (2) Teachers use student-friendly language to inform students about the math objective they are expected to learn during the lesson. (3) Students can describe what mathematical ideas they are learning in the lesson. (4) Teachers can articulate how the math lesson is aligned to district learning targets, state standards, and classroom assessments, and fits within the progression of student learning.

Teacher Focus on Using Assessment Information to Guide Teaching (5) Teachers use classroom assessments that yield accurate information about student learning of math concepts and skills and use of math processes. (6) Teachers use assessment information to focus and guide teaching and motivate student learning.

Student Focus on Using Assessment Information to Move Learning (7) Feedback given to a student is descriptive, frequent, and timely. It provides insight on a current strength and focuses on one facet of learning for revision linked directly to the intended math objective. (8) Students actively and regularly use descriptive feedback to improve the quality of their work. (9) Students study the criteria by which their work will be evaluated by analyzing samples of strong and weak work. (10) Students keep track of their own learning over time (e.g., journals, portfolios) and communicate with others about what they understand and what areas need improvement.

Figure 1. MMP Principles of Formative Assessment for Mathematics

WALT: MAKING TEACHING MORE INTENTIONAL The idea of WALT (learning intentions and success criteria) has strengthened my teaching in a profound way this year. I plan to make it a major focus for the whole staff next year. It is amazing to find that adding that small step at the beginning of a lesson makes a big impact on the entire lesson. Students are focused (as am I) on the lesson's goal ---MTL. I learned the importance of the first steps—finding the big idea, identifying targets, and stating learning intentions. I now use WALT for every lesson I teach, which allows me and my students to stay focused. ---MTL By using WALT in classrooms with students, I found myself teaching more focused lessons. Students were generally more engaged, and had a deeper personal investment because they not only knew the goal, but knew there was an accountability piece at the end of the lesson also. ---MTL

Over the years, we have noticed that a continual challenge is recognizing and articulating the important mathematics to develop in a way that makes it clear whether or not students are learning significant ideas. It is perplexing to consider how difficult this is for teachers. We can say that students are learning “multiplication” but what does this really mean and what does it look like? “Multiplication” might be the topic, but what is really the important mathematics that we want students to understand about multiplication and its connections to other mathematical ideas. Too often, the goal seems to be to get through the lesson or through the activity and the success criteria is merely whether or not the task was completed. We have made a major shift this year—it feels like we have finally gotten to the heart of instruction, to making instruction intentional and explicit in regards to the important


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mathematics students should be learning. We are shifting away from “how” to implement an activity to the critical conversations on the specific mathematical ideas students are to be learning and how we (teachers and students) will know whether it is being learned. At the December MTL seminar, the MTLs studied a reading by Shirley Clarke (2001) on “Sharing Learning Intentions.” Through this reading, the district was introduced to WALT, which stands for “We are learning to …,” and to the concept of success criteria. This clarified the purpose and provided examples of the first four assessment principles which focus on making the mathematics explicit to both teachers and students. Prior to teaching, teachers study the math concepts students are learning. The purpose is to revisit one’s own understanding of the mathematics, identify the essential ideas students are to learn, and examine how the mathematical ideas are developed across a sequence of lessons. Teachers use their own curricular materials and other resources to support their understanding of the math and the pedagogy they will use to teach the mathematics. Once the math concepts are clarified, teachers focus on articulating, in student-friendly language, the specific math goals for each lesson. Clarke (2001) stated, “It is important to post, in writing, the daily goal as a focus for the lesson and to engage the students in considering the objective.” This is WALT (We are learning to…), explicitly stating and posting in writing what it is that students will be learning. Along with the learning goals or intentions, Clarke emphasizes that success criteria for the lesson should also be stated and posted so students and teachers can better judge whether the mathematics has been learned. The MMP also developed a new tool, the “Lesson Planning with Formative Assessment Principles” template. It evolved over the fall semester through a few iterations and resulted in the version shown in Figure 2. This template became a tool leaders could use in their schools with teachers. The whole template was important, but the focal point of the tool this year was on Part 1 (i.e., WALT and success criteria).

Lesson Planning with Formative Assessment Principles Part 1: Selecting and Setting Up a

Mathematical Task Part 2: Supporting Student

Exploration of the Task Part 3: Summarizing the

Mathematics This part contains four critical components that need to be considered when selecting and setting up a mathematical task.

Construct three questions to develop the mathematics of the lesson. Consider the depth of knowledge required in the questions. Use these questions with students individually or in small groups.

Construct a question to orchestrate a whole class discussion of the task, and that uses different solution strategies produced by the students to highlight the mathematics being learned.

1. Important Mathematics to Develop:

2. Learning Target and Descriptors:

3. Lesson Objective in Student Friendly Language:

4. Success Criteria:

Q1. Access background knowledge: Q2. Develop understanding of the

mathematics by pushing student reasoning:

Q3. Summarize the important math in the lesson. This should tie back to the success criteria.

Summarize the important mathematics in the lesson as a whole class discussion and connect it back to the success criteria.

Figure 2. MMP Template for Lesson Planning

The Math Teaching Specialists often noted the focus on WALT and success criteria as they visited the schools. One noted, “To me the biggest highlight is the excitement that MTLs have when talking about WALT and Success Criteria (SC). It seems to have generated a real entry point for their work with teachers at their schools.” In one school the MTL began by modeling it in classrooms and then laminated posters for her staff that read: “We’re learning


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to…” and “We’ll know we’ve achieved this because…” The staff seemed to embrace WALT and were using it in content areas beyond mathematics. The MTL noted that even teachers who had previously been resistant to some of the initiatives became willing and comfortable in using WALT and success criteria. This focus has also created an entry point for the district math specialists to work more closely with teachers in their cohort schools. The specialist noted, “I think WALT/SC is very concrete. Teachers and students can visualize the outcomes of it. I also think most teachers had not thought about the success criteria before or about how students know when they are successful. This new focus has helped everyone better understand the purpose of a lesson or activity and how we will know if learning has occurred.” A challenge with this process is that some teachers are using WALT without always linking it to the success criteria. Our next steps will include further more emphasis on connecting these two components to focus instruction and learning.

Grades 8–9 Assessment Summits

While the MMP has maintained a focus on the transition of students from grade 8 to grade 9 over the years, the structure for this work has evolved and changed. The goal of this work has continued to be to find ways to bridge the gaps across these two critical years. Initially, a committee of teachers of these grades met after school in occasional meetings. By last year, it had evolved into six day long meetings that we called “Assessment Summits.” The summits were continued this year but with an increased expectation of the participants and their schools. The participants were referred to as teacher leaders and were to support and lead activities with other staff members back in their schools. The policy statement for the release-time K-8 MTL is that she or he must attend either the K-7 MTL seminar or the Grade 8-9 summits. All K-8 schools are strongly encouraged to identify a second person to attend the other series of meetings; if no second person can be found, we recommend that the MTL attend the K-7 MTL seminars. The policy for the high school release-time MTL is that she or he must attend the 8-9 summit meetings. If the school can manage the substitute coverage, a second, ninth grade MTL may attend the summits. High schools without a release-time MTL were strongly encouraged to identify a ninth grade math teacher to participate in the monthly summits. Of the 71 schools in the district that have grade 8 students, 51 schools identified a grade 8 teacher who participated in at least one summit with 19 of these teachers considered “active” participants (attending 4 of the 6 summits). At the high school level, 25 targeted high schools with grade 9 students had a math teacher who participated in at least one summit with 20 of those teachers considered active participants. In addition, several non-targeted schools also send representatives to the summits (e.g., partnership, non-instrumentality charter, or alternative schools). The six day-long summits supported the goals of the MMP—the comprehensive math framework, the teacher learning continuum, distributed leadership, and the student learning continuum. All summits had core components of formative assessment, content (algebraic reasoning), and leadership. The biggest change in the meetings was the inclusion of a leadership strand similar to and almost the same as the leadership sessions at the K-7 MTL


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seminars. This pointed to the increased role of the participants as leaders in their schools. Table 1 provides a snapshot of each summit. Table 1. Grades 8-9 Assessment Summits Summit Formative Assessment Content Leadership Sept Use “Assessing the Assessment” to

analyze new grade 9 CABS; Analyze constructed response items and student work on district benchmarks

Recursion and linearity using the Shoelace Problem

NCSM PRIME framework, Leadership of Self; What are the expectations of you as an MTL?

Oct MMP protocol for analyzing and learning from student work; Analyze Toothpick Hexagons

Big ideas of linearity (Shoelace Problem posters)

Stiggins’ video, “Inside the Black Box,” MMP Continuum principles of assessment for learning

Dec Examine The Umbrella Problem and Toothpick Hexagons problem

Exponential growth and decay

Formative assessment systems, Carl Hanssen’s Year 5 Findings, connections to leadership of self.

Feb Giving feedback on descriptive feedback samples; Examine Unidel CABS; Scoring constructed response items Grade 8 and 9

Finding areas and relationships, the Pythagorean Theorem with understanding

Linking Stiggins' first four principles to classroom practice; complete a lesson plan with formative assessment principles

Mar Write descriptive feedback statements for groups of students, Examine Mary’s Dots

Quadratic relationships and representations

Lesson Planning with WALT

May Using a Portfolio Protocol, Examining Sally’s Doorbell Problem

Linear and non-linear functions

Align principles of formative assessments and leadership journey

While the summits provided a venue to continue discussions of student expectations from grade 8 to grade 9 and provided strong professional learning for individuals, they did not seem to meet the needs of participants in their varied roles. For the most part the grade 8 teachers used the information to improve their own instructional practices and shared ideas and information with other grade 8 teachers. In these schools, the K-7 MTL, for the most part, was the math leader at their school, with the grade 8 individual in a support role. However, in regards to the high school teachers at the summit, many of these individuals were the released MTL and had a different role at their schools and thus had different needs. It was difficult to meet the needs of both of these groups of individuals. Next year, our plan is to hold K-12 MTL meetings thus addressing all participants as “leaders” for mathematics in their schools. This should allow us to more directly meet their needs as leaders. We will also continue some grade 8-9 networking sessions as critical transition topics and issues are identified and begin Grade 7-8 labs to continue teacher learning of mathematics content.

High School Algebra and Geometry Labs: Mathematics Related to the New Curricula

The labs provide instructional strategies for the classroom. Every time I’ve returned to school with new ideas to try in the classroom. ---HS math teacher I really liked the stress on not only investigation but the importance of big ideas and conceptual knowledge. ---HS math teacher The geometry labs have been a great source of ideas for my own geometry classes. So much of what we do gets applied directly to my students. The labs give me a chance to preview lessons and see how they work, what difficulties students may have, and what the big mathematical ideas are and how they connect to other ideas. ---HS math teacher

Last year, the MMP intensified its work with high school teachers by running a series of Algebra Learning Labs designed to provide opportunities for high school mathematics


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teachers to deepen their mathematics content knowledge and to improve their instruction of algebra. During Spring 2008, a committee of MPS teachers selected new textbooks for grade 9 algebra and grade 10 geometry. Unusual for MPS, the result was a single district-wide selection for each course: Discovering Algebra and Discovering Geometry from Key Curriculum Press. This choice presented us with both the challenge of ensuring the successful implementation of text programs which were very different in style from those previously used in the district, and the opportunity of using the labs to focus teachers’ attention on the mathematical ideas as they are presented in the text programs. We ran two series of labs during the year, Algebra and Geometry; each series met three times per semester, for a total of 12 labs during the year. This was an intensive schedule, and we built two teams of facilitators in an attempt to spread the workload. Kevin McLeod (UWM), Mary Mooney, and Laura Maly (high school teaching specialists) were involved in both series of labs. Gary Luck (UWM) played a lead role in the Geometry series. Marta Magiera (Marquette) and Bill Mandella (UWM) were heavily involved in the Algebra labs. We were particularly pleased to deepen our connections with Marquette university this year, with the involvement of Dr. Magiera with algebra labs, and Dr. Jack Moyer in the grade 8-9 summits. The title and topic of each lab are shown in Table 2. Each lab lasted approximately 4 hours; teachers were released using substitute teachers funded by the MMP. Approximately 20 high school teachers attended each session. This was a slight increase over the attendance at last year’s labs. The overall goals of the labs were: (1) To familiarize teachers with the approach to mathematical content and pedagogy in Discovering Algebra or Discovering Geometry, (2) To provide a forum for teacher discussion around students’ understandings, preconceptions, and misconceptions, and (3) To build a community of classroom teachers of algebra and enhance collaboration amongst teachers focused around teaching and learning. Table 2. Titles and Topics of Algebra and Geometry Labs

Month Algebra Title and Topic Geometry Title and Topic Oct How Do I Solve These? Let Me Count the Ways

Solving equations by undoing and balancing How Do I Know What I Know? Inductive versus deductive knowledge; van Hiele Levels of Geometric Thought

Nov On the Road Again Linear relationships

Prove It! Moving from experiment (induction) to conjecture to proof

Dec What's My Line? Fitting a line to real-life data.

Rotations, Translations, Reflections, Oh My! Rigid motions and congruence

Feb Function, Function, What's Your Function? Examples, definition and properties of functions

Cutting the Pythagorean Knot Different approaches to and proofs of the Pythagorean theorem and its connections

Mar Do You Know Where It’s Going To? Equivalent forms & uses for quadratic functions

Do We Look Alike? Similarity and similarity transformations

May Looking Back to the Future Review of the year, and discussion of ways to start the new year in September.

From Play to Proof Review of the year, and discussion of how the text program builds to formal proof

Most labs began with looking at student work using the protocol developed through the MMP. Working in small groups, teachers had time to share their teaching experiences on replicating the lessons with their students. This included how they had to adapt the lesson for their particular classrooms, student misconceptions, student background knowledge needed for the activity, and how it was received by students. A new lesson composed of content and pedagogy was then modeled for the participants, who were actively engaged in the lesson. At the conclusion of the lab, the teachers were given an assessment for their classroom, based on


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the content of the lesson and learning expectations for their students. The expectation was that they would administer the assessment when they taught the lesson themselves, and return to the next lab with samples of student work for discussion. The new textbooks met with some resistance from some teachers, but participants in the labs have uniformly indicated that the labs have been helpful to them in understanding the content and pedagogy in the texts, and have reported that their own students are showing an increased interest in and engagement with the mathematics they are learning. The teachers also indicated that they appreciated having the time to think and talk collaboratively about their classes. An unexpected outcome from the labs was that many participants facilitated evening sessions of their own to other MPS teachers during the year, on some aspect of the textbook, strengthening the district-wide community of teacher learners. Based on these outcomes, we consider the labs to have been highly successful in meeting their goals, and are hoping to expand them next year. The Algebra and Geometry labs will continue, but will be expanded to full-day sessions. This is partly for logistical reasons—it is inconvenient for teachers to be released from their schools for half days—but we plan to use the extra time to have the teachers work collaboratively on developing lesson plans. In addition, we hope to introduce two new lab series: an Algebra II/Pre-calculus lab, following this year’s district selection of Discovering Advanced Algebra (from Key Curriculum Press) as the text for Algebra II; and a grade 7-8 lab, responding to the district need for higher-level mathematics instruction at middle school level.

MMP Involvement in Wisconsin Mathematics Standards Initiative

Several representatives of the MMP and the IHE Network have been deeply involved this year with a state-wide initiative to rewrite Wisconsin’s model academic standards for mathematics. The initiative actually began in the Summer of 2007, when Wisconsin joined the American Diploma Project (ADP) and the Partnership for 21st Century Skills (P21). Over 10 months, a committee of mathematicians (including MMP Co-PI Kevin McLeod), mathematics educators, and high school teachers carried out an alignment study of the current Wisconsin high school standards with the ADP high school benchmarks and the P21 framework. This work concluded with a recommendation to the State superintendent that the high school standards should be revised to align with national initiatives, but that this should not be done in isolation. If the high school standards were to be revised, it would be necessary to look at the elementary and middle grade standards also. In Fall 2008, the state Department of Public Instruction (DPI) brought together another group of educators with the charge of rewriting the standards to bring them into alignment with ADP and P21. Four grade-band subcommittees were formed (PreK-2, 3-5, 6-8 and 9-12), and the MMP was represented on each of these subcommittees. DeAnn Huinker was a co-leader for the PreK-2 and 3-5 groups; Beth Schefelker (MTS) was a member of the 3-5 group. Astrid Fossum (MTS) was a member of the 6-8 group, and Henry Kranendonk was a co-leader of the High School group. Kevin McLeod was a member of the High School group, but was also one of three committee members who had oversight of the whole project. A


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draft document was ready for public comment in June 2009, and made available on a DPI web page: http://www.dpi.wi.gov/cal/math-intro.html. Partly as a result of the heavy involvement of the MMP, the new document is aligned not only with national initiatives, but also with those of the MMP, including the Comprehensive Mathematics Framework, though it should also be stressed that the MMP itself is strongly aligned with the beliefs of other mathematics education leaders across the state. Parallel to the DPI standards initiative, institutes of higher education across the state are working on a “Common Competencies” project to determine the mathematics needed by incoming students if they are to be successful in their college work, and to verify alignment of these competencies and the new Wisconsin standards. The Common Competencies committee is composed of four members each from the University of Wisconsin System, the Wisconsin Technical College System, the Wisconsin Association of Independent Colleges and Universities, and the K-12 system. Kevin McLeod and David Ruszkiewicz (MATC) are amongst the representatives from the university and technical college systems, respectively. The original timeline for these projects would have resulted in final revision of the standards this Summer with implementation with the 2009-2010 school year. As we were working on the project, however, Wisconsin joined the national Common Core standards initiative, and it became apparent that we could not release final versions of the new standards until we could determine their alignment with the (as yet unreleased) Common Core. The public comment period has therefore been extended, and the current plan is to finalize the state documents as the Common Core is released, with implementation in fall 2010.

Goal 2. Distributed Leadership Institute a distributed mathematics leadership model that engages all partners and is centered on school-based professional learning communities.

Release-time Model for Math Teacher Leaders The biggest impact the MMP has had in our school has been the released MTL position. It allowed me the time to focus the school’s collective efforts on learning about and implementing strategies that are moving my school along the MMP Continuum. I have had time to design and facilitate professional development and to work closely with teachers in their classrooms….What an awesome gift! ---MTL Being able to be a released MTL has given me the opportunity to help teachers more effectively. I am able to model lessons, help with interventions, and provide textbook support. The teachers in the school have been focused on improving the teaching and learning of mathematics. When problems arise they know that there is someone in the building who can support them in their efforts, and in my opinion that is what is making an impact in our building. ---MTL

Essential to improving student math achievement is improving the quality of math teaching in each school. School-based learning teams were established the year prior to the MMP and had focused their work on literacy initiatives. The MMP expanded this structure for mathematics as shown in the diagram to the right by initiating the Math Teacher Leader (MTL) position which began in the second semester of the 2003-04


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school year. The MTL was a full-time classroom teacher who agreed to take on additional school leadership responsibilities for mathematics. These individuals became members of their school learning teams and began attending monthly professional development seminars. During this time, the district literacy coach model was a fully released-time position. It was often raised in discussions whether the MTL should be a full or partial release-time position. A few schools had already moved to a release-time model by reallocating funds from their school budgets. As a result of discussions between Superintendent Andrekopoulos and Governor Doyle, the Governor included a special allocation of $10 million to support the Milwaukee Mathematics Partnership. In particular, these funds were to be used to establish a release-time MTL position in the district. The transition for about 100 MTLs began in spring 2008 at the start of the second semester with district funds. This year, the MMP implemented a partial-release (80%) model for 113 Math Teacher Leaders with the allocation from the Wisconsin Office of the Governor. In addition, this money provided funds to support some professional development for teachers and teacher leaders. The Governor has again included a request for funds in the State budget to continue this support for the MMP. The release-time MTLs include 99 positions at the K-8 level and 14 at the high school level. It should be noted that we have 152 targeted MMP schools. Thus we also have another 38 schools with non-released MTLs. Only one small high school did not have an identified MTL this year. The MMP release-time position model ensures that the district’s most expert teachers remain engaged as instructors of mathematics for at least 20% of their day. For the remaining 80% of their day, they remain in schools to assist all staff members in improving mathematics instruction. We believe that this model promotes teacher leadership by providing teachers with a district “teacher” position that allows them to take advantage of their expertise yet maintains critical classroom credibility. We feel strongly that MTLs must maintain direct and regular contact with students and be responsible for student learning of mathematics, thus practicing “Leadership of Self” while becoming skilled in “Leadership of Others.” The introduction of the release-time model for the Math Teacher Leaders presents challenges and opportunities for the teacher leaders. Their role shifted from classroom teacher to school leader in mathematics. This shift in responsibility from instructing students in their own classrooms to supporting mathematics instruction in classrooms outside of their own grade level background, forces MTLs to broaden their own understanding of the depth and breadth of the world of mathematics. Many MTLs had stark realizations. “I need to get a better understanding of what is going on at a different grade level…I don’t know anything about Kindergarten…how am I supposed to help the teachers understand what is happening?” Or as another MTL said, “I was asked to help out in an eighth grade classroom…I was scared to death! But, I took the lesson home and studied it and did the best I could. I realized that I can get eighth grade students to think effectively and showed the teacher how to manage it with eighth graders.” With the shift in the role of the MTL, comes a corresponding need to adjust the work of the MMP. This year changes have included more accountability for the work of the Learning Teams and MTLs in the schools and have involved adjustments in the work of the Math Teaching Specialists. These two areas are discussed in the next sections.


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MMP Learning Team Continuum for Mathematics: A Journey for School Reform A teacher said to me yesterday that, although she was never good at math, she now looks forward to teaching it. She said, “Now I love teaching math!” Teachers now talk about math on their own in the halls, in their carpools, and after school. We have a common structure in place that allows that to happen. We have tools (MTL, pacing guides, Targets, math texts, administrators, peers) to support those who are insecure about the content. We know what was taught in previous grades, so we know how to get students to recall those past experiences. The system is starting to take shape! ---MTL

For five years (2003-2008), the Math Teacher Leader (MTL), supported by the school Learning Team and the district Math Teaching Specialists, has focused the work of mathematics at that school. The Learning Team “Continuum of Work for Mathematics” (see Table 3) brought order to this effort. The continuum is a cohesive framework used at the school level to guide and monitor formative assessment practices and used at the district level to focus professional development of teacher leaders and learning teams. The MMP learned that a developmental continuum such as this is a powerful tool for guiding reform. It allows teachers and schools access and entry at various stages. It also clearly delineates a pathway for making incremental progress that supports student learning and classroom instruction. Table 3. MMP Learning Team Continuum of Work for Mathematics

Stage 1: Learning Targets

Stage 2: Align State

Framework and Math Program

Stage 3: Common Classroom Assessments (CABS)

Stage 4: Student Work on

CABS

Stage 5: Descriptive Feedback

on CABS

Understand importance of identifying and articulating big ideas in mathematics to bring consistency to a school’s math program.

Develop meaning for math embedded in targets and alignment to state standards and descriptors and to school’s math program.

Provide a measure of consistency of student learning based on standards/descriptors and targets.

Examine student work to monitor achievement and progress toward the targets and descriptors.

Use student work to inform instructional decisions, and to provide students with appropriate descriptive feedback.

We developed a school self-assessment tool and rubric based on the Continuum (included in Appendix F). The tool provided greater detail, as shown in Table 4, on the school professional work associated with each stage and the MMP tools developed to support teacher learning and work at that stage. Each school with a released MTL was required to complete the school self-assessment at the beginning and end of the school year. This self-reflection and analysis was to be completed by the school’s Learning Team (e.g., principal and math committee). The initial self-assessment was titled the “Continuum Entry Point Assessment” and the second self-assessment was titled the “Continuum Progress Update.” Accountability for the released position was high due to its visibility and direct support in the Governor’s Office. The funds were housed centrally, not at the school level. To monitor the MTL position, the district hired Sharonda Harris full-time as the “MMP Accountability Monitor.” She, along with Henry Kranendonk, conducted monitoring conferences with all schools in the fall and in the spring using the continuum tool to focus the meetings. The fall conference included the principal, the MTL, and a district math supervisor. The Math Teaching Specialists were also invited to attend the spring monitoring conferences for their cohort schools. Some of the non-released MTLs also completed the tool and requested conferences as they found it to be a valuable tool for the work in their schools as well.


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Table 4. Types of Expected School Professional Work and MMP Tools School Professional Work Tools

Stage 1 Learning Targets

• Teachers develop an awareness of district learning targets for each mathematics strand.

• Teachers discuss what each learning target means and can articulate the math learning goals students are to reach.

• Teachers examine the development of mathematical ideas across grade levels.

• Grade level lists of 9-11 big ideas per grade

• Horizontal list of targets by content across grades

Stage 2 Align

Targets to State

Framework

• Teachers examine alignment of state descriptors to targets. • Teachers identify the depth of knowledge in the descriptors. • Teachers study how the mathematical ideas in the descriptors are

developed in the school’s math program. • For each lesson, teachers inform students of the math learning

goals in terms that students understand.

• Target-descriptor alignment worksheets

• WKCE Depths of Knowledge

• Curriculum pacing guides

Stage 3 Classroom

Assessments

• Teachers select and study common CABS that will be used within a grade level.

• Teachers identify math expectations of students assessed through the CABS.

• Teachers identify potential student misconceptions revealed through the CABS.

• Learning Team and teachers examine student WKCE and Benchmark Assessment data to identify areas of strengths and weaknesses for focusing teaching and learning.

• Curriculum Pacing Guides

• District Model CABS • Depths of Knowledge • CABS Assessment

Overview worksheet • WKCE and Benchmark

Assessments student data

Stage 4 Student Work

• Teachers collaborate in grade-level meetings to discuss student work and implications for classroom practice.

• Teachers meet in cross grade-level meetings to discuss common expectations of student math learning and implications for school practice.

• Learning Team monitors and discusses student learning on CABS results from across the school, shares observations with staff, and uses data for Educational Plan.

• MMP Protocol for Analysis of Student Work

• DVD of MMP Protocol • CABS Class Summary

Report form • School Educational Plan

Stage 5 Descriptive Feedback

• Teachers collaborate to write students descriptive feedback on Benchmark Assessments and on common CABS from the curriculum guides.

• Students use descriptive feedback to revise their work and improve learning.

• Teachers use descriptive feedback to continuously adjust and differentiate instruction.

• Learning Team monitors the successes and challenges of writing descriptive feedback and identifies professional learning needs of teachers.

• Types of Feedback sheet

• Descriptive feedback worksheets

• CABS Class Feedback Summary worksheet

In April, we asked all Math Teacher Leaders to reflect on the work within their schools along this continuum. They were asked to indicate the placement of their schools at the end of the 2007-08 school year, and current placement, towards the end of 2008–2009 school year. The results for the K-8 schools is shown in Table 5 and for the high schools in Table 6. A progression can clearly be seen across the six years of our work with more K-8 schools each year moving further along on the continuum. Almost all of these schools are now using some common classroom assessments for mathematics and more schools are collaboratively examining the student work on the CABS and providing students with descriptive feedback.


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Table 5. Learning Teams Continuum of Work, Percent of K–8 Schools at Each Stage of Continuum

n

Stage 1. Learning Targets

Stage 2. Align State

Framework & Math Program

Stage 3. Common Class

Assessments (CABS)

Stage 4. Student Work

on CABS

Stage 5. Descriptive

Feedback on CABS

Year 1, 2003-04 101 38% 53% 9% 0% 1% Year 2, 2004-05 97 18% 34% 38% 5% 4% Year 3, 2005-06 89 13% 26% 41% 18% 2% Year 4, 2006-07 109 11% 26% 39% 18% 6% Year 5, 2007-08 113 20% 32% 32% 14% 2% Year 6, 2008-09 113 3% 8% 39% 30% 20%

The high school MTLs have only been asked to reflect on and report on the work within their schools along this continuum for three years. A progression can be seen with more high schools further along on the continuum each year. This year has been particularly encouraging at the high school levels in that more of the staff in these schools are beginning to consider and use common classroom assessments and some have even begun to put more emphasis on collaboratively examining the student work on the CABS and even writing descriptive feedback. We attribute this movement largely to having a release-time MTL in some of the high schools more ready to provide leadership for this work. Table 6. Learning Teams Continuum of Work, Percent of High Schools at Each Stage of Continuum

n

Stage 1. Learning Targets

Stage 2. Align State

Framework & Math Program

Stage 3. Common Class

Assessments (CABS)

Stage 4. Student Work

on CABS

Stage 5. Descriptive

Feedback on CABS

Year 4, 2006-07 20 50% 25% 25% 0% 0% Year 5, 2007-08 22 26% 32% 21% 16% 5% Year 6, 2008-09 22 0% 5% 56% 26% 16%

Math Teaching Specialists: Driving District Mathematics Efforts

I really, really enjoyed this year and think it had the “most movement” in the six years I’ve been an MTS, and it is mostly due to the role of the “released MTL.” ---District MTS

Prior to the MMP, a single individual was responsible for oversight of mathematics throughout the school district, namely the district’s K12 Mathematics Curriculum Specialist. The MMP initiated the Math Teaching Specialist position to provide district-wide teacher leadership for mathematics. The MMP began with a cadre of six Math Teaching Specialists, which has now expanded to ten. Each Math Teaching Specialist works directly with a cohort of 15 to 25 school-based math teacher leaders. They facilitate critical professional development, assist with school educational plans and action plans in mathematics, work with schools to analyze student work, disaggregate achievement data, and study math learning targets and performance assessments. The transition to a new release-time Math Teacher Leader (MTL) model has presented the MMP, and especially the district Math Teaching Specialists (MTS), with both new opportunities and new challenges. The opportunities arise primarily from the fact that the school-based teacher leaders now have more time to plan professional development and work with their staffs, and are requesting MTS assistance in doing so. The challenges include time management by the math specialists and, in a small number of schools, lack of understanding of the new MTL model by the principal, staff, or MTL.


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The math specialists reported spending an average of two days per week in their cohort schools. The amount of time spent in schools was remarkably consistent across the 10 specialists, and was in addition to time spent consulting with the teacher leaders on the phone or beyond the school day. It was considerably more time than they had spent in schools in previous years. Some of the support activities reported by the math specialists included working in classrooms, delivering or assisting the MTL with in-school professional development sessions on content or assessment, and working with the MTL and principal on the school’s education plan for mathematics. As the teacher leaders prepared professional development sessions for their school staffs, or worked with teachers in their classrooms, many of them asked the math specialists for guidance and assistance in carrying out, what were for many of them, new responsibilities. One math specialist described a typical interaction: “[The MTL] asked me for input or my perspective often this year, whether it was via numerous, lengthy e-mails, phone conversations, or visits. Once she pinpointed her teachers’ lack of content knowledge, it became a major avenue for her work. She would plan a lesson, have me review it, and then asked me to observe the lesson, along with the classroom teacher. She and I debriefed; then she would debrief with the teacher.” The math specialists showed strong consensus that the time and work they put in on school sites was extremely valuable, and helped them to build their relationships with school staffs. As one math specialist put it, “As I reflect on my successes this year, I think it’s about relationships. I was able to build a stronger relationship with the MTLs and because of this, I was allowed to enter their school culture and climate.” The challenge for the math specialists was (and is) that the additional time spent in schools was not compensated by a comparable decrease in their other responsibilities. A math specialist noted, “The biggest challenge that came with this increased involvement in schools was just the sheer number of requests. With about 20 schools to juggle, there are simply too many requests to be in all the different places at the same time. I have a hard time saying no, but I had to….These schedule conflicts were particularly bad the weeks of MTL meetings…and days when we had other district training.” Over the year, the math specialists came to understand that the ultimate solution had to involve the MMP goal of distributed leadership—their priority must be to build the capacity of the MTL as a largely independent school-level leader of math teaching and learning. The success stories reported by the math specialists for the year reflected this understanding. One specialist described an MTL who had initially been unsure of her ability to perform her new duties, “As much as [she] talks about me being her role model, she became my role model! She worked really hard to learn about her teachers as individuals. She found out what they needed, how talk to them, and how to listen. She made herself available to their every need and in return they respected her enough not to let her down!... She is a true example of the effectiveness of distributed leadership!” Another specialist reported, “Too many MTLs have


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become dependent on me for resources, designing and facilitating professional development, and starting initiatives in their schools. I want the ideas to come from them.” Additional challenges concern the new MTL role. In some schools the MTL has not yet grasped or taken hold of the leadership role which might be due to resistance or suspicion from other teachers who do not understand how the release-time MTL fills his or her workday. In a small number of schools there is also resistance from the administration. An extreme case is the statement from a principal (in a struggling SIFI school) who told the math specialist at the end of the year, “I can’t believe elementary teachers need help teaching math. What’s the big deal? They have a book, what more do they need?” More often, a misunderstanding of the MTL role led a principal to overburden an MTL with administrative tasks; such misunderstandings were usually resolved through MMP monitoring. It is also easy to forget that not all MTLs are released. Several math specialists remarked on the challenges this produces as they consider how they (and the MMP in general) should differentiate the expectations and support for non-released versus released MTLs.

Math Teacher Leaders: The PRIME Framework and Formative Assessment My ability to be a reflective leader was a significant area of growth this year. I learned to recognize needs of staff that were not verbalized and to read more of the hidden messages or unspoken needs of staff members. I became more reflective and purposeful in my interactions with staff. --MTL The session on the different levels of change really helped me understand my staff more, which in turned helped me grow as a leader. I was able to look at each teacher, recognize what level each person was at, and meet them at that level to assist them. For example, one teacher would make comments about how she wasn’t going to be able to implement CABS in her classroom. After the session, I was able to recognize that for her it was a management issue. So while working with her I was able to model and give her information about how to manage the use of CABS in her classroom. She is now using CABS regularly and even sharing her ideas and experiences with others. ---MTL

The National Council of Supervisors of Mathematics (NCSM) released its PRIME Leadership Framework in 2008. PRIME is the acronym for “Principles and Indicators for Mathematics Education Leaders.” We used this framework as a focus for the leadership development of the teacher leaders. Its essential questions are: “What does an effective mathematics education leader need to know?” and “What does an accomplished leader do?” The stages of leadership action are shown in Figure 3. These stages became part of our language this year as we first emphasized and the MTLs embraced the challenge of the first stage, “Leadership of self.” In other words, it is essential that the leader be respected for his or her own teaching and learning skills, which requires the leader to be knowledgeable and to model the specific strategies being developed. Then the MTLs considered “Leadership of Others.” The PRIME framework also sets out four leadership principles with a set of indicators for each. This year we chose to focus on the “Assessment Principle” which emphasizes high levels of learning for every student by using formative assessment practices to inform teacher practice and student learning.

Figure 3. Stages of Leadership Action

Stage 1: Know & Model

Leadership of Self

Stage 3: Advocate & Systematize Leadership in the

Extended Community

Stage 2: Collaborate & Implement

Leadership of Others


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The MTLs assessed their own growth as a leader during the school year. This entailed the question, What is my progress on the PRIME indicators for Assessment Leadership? The results are show in Table 7. Every MTL reported growth in understanding and using formative assessment practices based on participating in the MTL seminars this year and in the the work in their schools. In September, 78% of the MTLs reported that they had a basic understanding of assessment leadership and by the end of the year 45% reported that they had a deep understanding and 50% said they were using their understanding to take action and model assessment practices for others. Table 7. MTL Understanding of PRIME indicators for Assessment Leadership

I have no understanding and

have taken no action

I have a basic understanding.

I have deep understanding

I use my understanding to take action and model for others.

Sept 14% 78% 7% 0% May 0% 5% 45% 50%

We developed eight leadership sessions. A summary of these sessions is shown in Table 8. Planning for these meetings was always comprehensive. We continually analyzed the skills and knowledge set of the Math Teacher Leaders to determine what supports were needed to enable them to be effective leaders in their schools and across the district. Throughout the planning process, we kept in mind the following goals: (1) To develop knowledge of systems thinking—formative assessment and systemic change, (2) To increase ability to recognize and address adults working through a change process on the topic of assessment, and (3) To provide resources for MTLs to use to facilitate similar types of learning opportunities with their school staffs. Table 8. Overview of Topics and Tasks for MTL Leadership Development Month Topic Key Tasks

Aug PRIME Framework: Stages of Action

Reflection on quotes from the PRIME document; Stages of leadership action, Set goals for Leadership of Self and Leadership of Others.

Sept PRIME Framework: Assessment Principle

Assessment Principle; Discussion of assessment indicators and actions of each indicator at stage 1 of the leadership cycle.

Oct Our Assessment Future: Comparing Assessment of and for Learning

What is Formative Assessment? Does research support formative assessment practices? What is needed to support formative assessment practices? What are formative assessment classroom strategies ?

Dec Leadership of self within a system of assessment

Understand assessment practices as a system; Link formative assessment principles to the Learning Team Continuum.

Jan Guidelines to Implement an Assessment System

Understand the nature of systems thinking; Discuss article, “Leading Through Systems Thinking” by Jerry L. Anderson.

Mar Understanding Change: Concerns Based Adoption Model

Assumptions of the Concerns Based Adoption Model (CBAM) and Stages of Concern; Examine where individual change fits into the concept of systemic change (a system of change).

Apr What is Effective Dissemination?

Understand dissemination strategies and ways to overcome obstacles when disseminating new practices.

May Our Leadership Journey Understand the connections in our “leadership” sessions, and reflect on the leadership journey and the connections to the PRIME document.

We knew the MTLs were familiar with the strategies of summative assessment but needed to understand the research from Richard Stiggins on formative assessment strategies. They needed to learn how this work aligned to the MMP Learning Team Continuum. Once the leaders understood and used the formative assessment strategies in their own teaching, they had to think hard about the topic of change and change strategies. Math Teacher Leaders


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worked with the CBAM (concerns-based adoption model) to understand ways of working with adults in their buildings. The materials for the sessions are available on the MMP Web Site: www4.uwm.edu/Org/mmp/_resources/MTLpage.html. A hurdle most of the MTLs had to climb this year was the sense of urgency they felt as they took on the role of a release-time Math Teacher Leader. They knew they needed skills to work with adults and content knowledge of formative assessment strategies and they wanted everything all at once. Each month in their training sessions, we helped them understand that this was a journey for them too. They needed to implement and understand formative assessment strategies and how it impacts student learning before they could lead others. Each month the leaders learned and reflected on assessment strategies and discussed ways they could begin to work with teachers in their buildings. Some steps for next year include: • Continuation of study of formative assessment principles and how to support staff

members as they begin implementing them more consistently in their math classrooms. • Strengthening understanding of working with and leading among peers. • Study of coaching practices to enhance communication around formative assessment and

the teaching and learning of mathematics.

Learning Teams and Math Action Plans: The Big 5 Strategies

The Learning Team in each school continued to provide leadership for mathematics. Teams were provided with the opportunity to obtain MMP funds for Math Action Plans to support their work focused on the “Big 5 Strategies.” These include: 1. Teachers will know how the mathematics curriculum aligns with the Learning Targets

and Wisconsin State Assessment Framework and use the alignment to focus teaching. 2. Common CABS and other formative assessments will be consistently administered at

each of the grade levels (“smaller” and “more frequent” assessment strategies). 3. Teachers and other instructional staff will develop (and learn) more descriptive feedback

techniques to assess students’ work and to engage students in using the feedback to revise work and improve learning, particularly regarding CABS and the constructed response items on the Benchmark Assessments.

4. Math teachers and leaders will analyze data from the Benchmark Assessments and constructed response problems and use it to inform school and classroom practice.

5. The school will develop a portfolio system for teachers to use to analyze student learning over time and to document progress toward attainment of targets/descriptors.

Schools were eligible to receive compensation for 25-100 hours of professional development, depending upon the number of math teachers in the school. These small grants of approximately $1000 to $3500 per school continue to be of great value in supporting the MTL. The plan gives the MTL leverage because then teachers can be paid in accordance with the union contract to meet before or after school or to hire substitute teachers to release teachers in the building to engage in professional development. In Year 6, approximately


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$150,000 was used for action plans. The funds came from three sources showing movement toward the district sustaining support: $78,000 NSF funds, $20,000 district funds, $50,000 Governor’s Math Initiative. Of 152 targeted K-12 schools, 117 (77%) submitted plans and accessed these funds; 89% (110/123) of K–8 schools and 47% (7/15) of large high schools. For many schools this money enabled them to influence important conversations among teachers, particularly grade level meetings, to examine strategies for improving mathematics teaching and learning. It was apparent that most schools were implementing the Big 5 strategies on a regular basis. It was so rewarding to see the district finally developing a common vision and focus regarding the teaching and learning of mathematics. This collective focus is especially strong at the elementary level where it is often embedded throughout the school and across most staff members while there is a great need for more high schools to study and implement the Big 5 strategies and engage more teachers. Of particular note in Year 6 was the amount of in-kind hours devoted to mathematics in relation to MMP hours built into the math action plans. The in-kind hours consist of using existing school-based meetings, such as staff meetings, bank days, and collaborative planning sessions that do not require additional funds as they are built into the teacher contract, or use of Title I funds. The number of in-kind hours has been increasing over the years and this year it was estimated to be twice that of the hours paid for by the MMP, district, or Governor’s initiative. This provides evidence of greater focus and commitment to improving mathematics as MMP strategies are being embedded into the regular workday of the schools.

Goal 3. Teacher Learning Continuum Build and sustain the capacity of teachers, from initial preparation through induction and professional growth, to deeply understand mathematics and use that knowledge to improve student achievement.

Teacher Leaders Study Algebraic Reasoning

My understanding of math content grew by the sessions devoted to algebraic reasoning across the grade levels. This became one of the hallmarks of my conversations with teachers and it also led to an emphasis on cross-grade level sharing of math concepts. ---MTL As I develop my understanding of math content, especially the knowledge that reflects the focus of our MMP trainings, I find I am better able to field questions, provide strategies, and move my staff in a direction that reflects the core ideas and goals of the MMP. ---MTL

Each year of the MMP, a content area is selected for study. The content strand for this year was algebraic reasoning, with a focus on the foundations of number knowledge for learning algebra. We developed nine content sessions (see Table 9) with each session lasting approximately two hours. Planning for each session included mathematics educators, a mathematician, and two Math Teaching Specialists. A central theme throughout the year was considering the difference between algebra and algebraic reasoning, being able to describe examples of algebraic reasoning, and identifying what teachers need to know about algebraic reasoning in order to support the development of it in their students.


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Table 9. Algebraic Reasoning Content Sessions in 2008-09 Month Topic Key Tasks or Mathematical Ideas Aug Recursive Relationships The same yet smaller—recursive triangles. Sept Relational versus Computational Thinking Double compare and double digit compare; True and

false statements Oct Relational Thinking and Operation Sense Equality; Peter’s method for subtracting five. Dec. Operation Sense: Analyzing Student

Thinking Solving One Step Problems Decisions students make when deciding how to solve word problems, sorting word problems by operation

Jan Operation Sense: Exploring Quantitative Analysis with Multi-Step Problems

Quantitative analysis with contextual situations, quantity versus value, Dieter’s problem

Feb Patterns: Structural Analysis of Geometric Patterns (Recursive Thinking)

How does the “C” pattern continue? Staircase towers

Mar Patterns: Moving From Recursive Thinking To Functional Thinking

Repeating and growing patterns and their underlying functional relationships; Investigating an AB pattern

April Mathematical Properties: Distributive Property

Rectangular arrays to solve 36 x 49; thinking strategies for basic multiplication facts

June Connecting Ideas of Algebraic Reasoning to Textbook Programs

Finding implicit and explicit use of the distributive property in texts and how the idea is introduced

The year began by exploring the question, “At what age do students begin to think algebraically?” This question started a year long conversation as MTLs explored ideas that are fundamental in developing algebraic reasoning. The MTLs readily identified the fact that our middle grades students find algebra hard to learn. Purposefully building algebraic reasoning skills at the elementary level seemed logical, though many MTLs were unsure as to how that might look in the classroom. Increasing awareness that the foundation of algebra has its roots in good knowledge of number properties and basic operations was a primary focus for all content sessions. This meant supporting MTLs to know how to strategically and purposefully move computational lessons into the realm of algebraic reasoning. An equally important focus included understanding how that knowledge can be extended to facilitate students’ transition into algebra at the middle grades. For that reason, content sessions consistently highlighted two big ideas: (1) the language of arithmetic focuses on computing answers, and (2) the language of algebra focuses on relationships. By grounding our work in those essential differences, the MTLs began to understand that algebraic reasoning at the elementary level meant that number knowledge must go far beyond arithmetic calculations and basic skills. MTLs discovered that important relationships and generalizations can surface by building deep understanding of general properties both of numbers and of operations. Moreover, by using large numbers, fractions, and decimals, the MTLs were able to recognize when a general relationship or rule applies to the whole range of numbers. It was eye-opening how these discoveries about how numbers work form the building blocks of generalized number knowledge, which are developed and expressed in later years as algebra. Looking back over the year, there were three areas that seemed to have made a big impact on Math Teacher Leaders. Through conversations after the session, email requests for the content slides, or requests to come to a school to deliver a content session, MTLs began to see the need for their teachers to engage in specific, meaningful, content sessions in order to see an effect on classroom instruction. The sessions that will be highlighted are: (1) Relational Thinking versus Computational Thinking, (2) Operation Sense and Quantitative Analysis, and (3) Distributive Property.


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RELATIONAL THINKING VERSUS COMPUTATIONAL THINKING I have spent a good bit of time discussing and practicing the idea of relational versus computational thinking with both the faculty and my students. I have been surprised by the number of teachers who have never really considered relational thinking to be of any value, or to be of only secondary importance to computational thinking. --MTL

As an MTL began her released position, she was asked a question from the first grade teachers. Spending most of her time in seventh grade, the MTL made a panicked phone call to her math specialist. It was then that we realized how important it was to provide MTLs with experiences in each content session that supported their new responsibilities for working with teachers at all grade levels. This episode was the impetus for an activity in our first content session for the year. The MTLs were presented with the task in Figure 4.

One of the teachers in your building comes to you and wants to know why this CABS was developed for first grade. How would you explain the mathematics presented in the CABS and support the reason for using it?

True and False Number Sentences For each number sentence, tell whether it is true or false. a. 9 = 5 + 4 True or False b. 9 = 9 True or False c. 5 + 4 = 4 + 5 True or False d. 5 + 4 = 5 + 3 True or False e. 5 + 4 = 6 + 3 True or False For the letter “e” above, explain how you know whether it is true or false?

Figure 4. MTL Task on Relational Thinking

MTLs then engaged in a series of relational thinking activities, such as “Double Compare” (deciding which of two single-digit numbers is greater) and “Double-digit Double Compare” (comparing two double-digits numbers). This demonstrated the variety of strategies that could be used to compare number combinations in order to find a total without computing. For example, 24 + 37 is larger than 25 + 35 because 25 is only one more than 24 whereas 37 is two more than 35. These activities affirmed that important mathematical conversations can take place at all grade levels even in Kindergarten. Although we explored the idea behind relational and computational thinking a few years ago, it worked well to begin our study of algebraic reasoning with this topic. The interest and conversation that sparked from this session was the catalyst we needed to help MTLs establish credibility during their first staff content session and to acknowledge the important mathematical ideas developed at all grade level. As One MTL wrote in an email to her MTS, “I used the September algebra session (Double Compare and Double-digit Double Compare) with my staff yesterday, it was a huge success! I had several teachers give me feedback on the activity using the CMF(Comprehensive Mathematics Framework) and then I had teachers request materials to use with their students. Just wanted to let you know it was an overall success! Thank you all!”

OPERATION SENSE AND QUANTITATIVE ANALYSIS I presented the quantitative analysis of word problems in almost every classroom. It really worked well and it helped the students to better comprehend story problems. I do believe that I need to continue working with the quantitative analysis more in the school. It was very helpful and was one of my favorite ideas that I introduced and shared with the teachers and the students. --MTL


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These sessions highlighted the importance of students abilities to select operations to solve single-step and multi-step word problem. After studying some sixth grade student work samples, it came as no surprise to our MTLs that many of our middle grades students do not know how to begin making sense of word problems. We used this launch to build understanding that operation sense is a critical aspect of algebraic reasoning. We used a process called Quantitative Analysis (adapted from Clement & Bernhard, 2005) to study the structure of word problems. In essence, this process entails surfacing the quantities in a word problem situation, attaching known values (or numbers) to each quantity, and identifying which quantities had unknown values. Then the appropriate operations could be determined based upon the relationships among the quantities. MTLs were pleasantly surprised as the necessary operations surfaced very naturally through the course of their conversations as they quantitatively analyzed multi-step problems. Through the sessions, they discovered the power of identifying the quantities in the problem and separating them from the value assigned. This explicit analysis of the structure of a word problem helped to surface the operations needed to meaningfully represent and solve the problem regardless of the specific numbers in the problem. We also highlighted how this critical aspect of number knowledge was essential for algebra learning – recognizing operations in order to model problem situations with symbols.

DISTRIBUTIVE PROPERTY During the April content session, the MTLs were encouraged to try this experiment. “Calculate the answer to 39 x 46 using the U.S. standard algorithm. Keep detailed notes of each step you take.” Many MTLs found themselves saying “6 time 9 is 54, put down the 6 carry the 5…” As MTLs discovered, this approach provides opportunity for procedural practice, but actually works against students’ conceptual understanding of multiplication. Additionally, as many teachers find, the U.S. standard algorithm is error prone and students naturally lose sight of the quantities they are multiplying. As the session progressed MTLs found themselves asking, is there a better way? One method that fits with students’ thinking and aligns directly with algebraic reasoning employs the distributive property and is often called the “partial product method.” In this method, students partition the factors using expanded notation, multiply to get partial products, and then added the products together. We explored this approach with an array model and studied how it supports and develops a deep understanding of place value, number relationships, and the impact of multiplication on large numbers. Many MTLs found the idea of arrays to be a meaningful, and very visual way, to approach the distributive property. They were surprised by the direct connection of this method to algebra, in particular to the multiplication of binomials (e.g., (3x + 9)(4x + 6)).

Assessment of Teacher Knowledge of Statistics and Probability Statistics, probability, and data analysis has always been an area of weakness for me, but the content sessions have really allowed me to expand my knowledge. They have also given me the opportunity to see a continuum of thinking across grade levels that I didn't have before. –MTL Because some of the content presented in these meetings was challenging for me at the K–5 level, it helped me reach beyond what I might have done in the past with my students, giving me the enrichment I needed as a teacher to thoroughly teach concepts at deeper levels. --MTL


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During the 2007-2008 school year, the MTLs studied statistics and probability as the content strand for the year using the GAISE framework (American Statistical Association, 2005). The annual report last year presented a summary of the content development sessions. The data from the teacher assessments was analyzed last fall and is presented here. The GAISE framework presents a three stage model of how knowledge of statistics and probability develops across the grades in each of the four framework components: (1) Formulate Questions, (2) Collect Data, (3) Analyze Data, and (4) Interpret Results. The developmental nature of the framework allowed teachers at all grade levels to consider implications of the content sessions for their work with students. • We had grade level discussions about formulating good questions and the implications of

teachers always giving students the questions rather than having students develop them. • I have seen teachers applying this idea of formulating questions in several different subject areas.

For example, the kindergarten teachers were having students ask questions that they thought they might be able to answer from data they were planning to graph.

The framework emphasizes the need to focus on the nature of variability as statistics is and should be considered the study of variability in our world. GAISE also emphasizes the critical role of context in the study of statistics. MTLs commented: • I have a better understanding of variability. I realize that statistics is centered more on the main

term “variability” than it is on mean, median, and mode. Usually when statistics is mentioned, someone automatically talks about mean, median, and mode. Now I understand that these “m” terms are used to help describe variability.

• I found that I could push my students to make some statements that were more precise than saying "pink has more than yellow.” They were able to connect their representations back to their questions and the context, and say "more children in our class like pink than yellow. It's just a small step, but it's the kind of tweaking that could make our students more successful.

The K-7 and Grade 8-9 teacher leaders completed a pretest in September 2007 and a posttest in June 2008 on statistics and probability using the Diagnostic Mathematics Assessments for Middle School Teachers developed at the University of Louisville. In the past we had used items from the University of Michigan, but no items on statistics and probability were available. We contacted Bill Bush at the University of Louisville to obtain pretest and posttest instruments on statistics and probability and to arrange for them to score the results. Each instrument was composed of 10 selected response items and 10 constructed response items (total of 40 points). The assessments measure four types of knowledge in the domain of statistics and probability. The four types of knowledge are: (1) declarative knowledge, (2) conceptual understanding, (3) problem solving and reasoning, and (4) mathematical knowledge for teaching or pedagogical content knowledge. Each of these is described in more detail in Table 10.


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Table 10. Types of Knowledge Measured on Diagnostics Mathematics Assessments Type Description of Knowledge

Type 1. Declarative knowledge

This mathematics knowledge is rotely learned and employs memorization. It includes memorized knowledge of definitions, procedures, or rules. Teachers with this knowledge can rotely perform skills, apply rules, and give definitions.

Type 2. Conceptual knowledge

This mathematics knowledge is conceptual in nature. It includes a deep understanding of mathematical concepts, procedures, laws, principles, and rules. It is knowledge of connections and relationships among concepts. It is often associated with meaning. Teachers with this knowledge can give examples/non-examples and identify properties/ characteristics of mathematical concepts. They can compare and contrast and represent mathematical concepts and generalizations in multiple ways. They can explain and create mathematical procedures and represent them in multiple ways.

Type 3. Problem solving and reasoning

This mathematics knowledge is higher order in nature. It includes applying knowledge to solve problems and real-world applications. Teacher with this knowledge can reason informally and formally, conjecture, validate, analyze, and justify. They can use deductive, inductive, proportional, and spatial reasoning to solve problems.

Type 4. Mathematics knowledge for teaching

This mathematics knowledge is unique to teaching mathematics. It represents the mathematics knowledge that teachers use in the act of teaching. It includes knowledge of the most regularly taught topics in mathematics, the most useful forms of representation of those ideas, the most powerful analogies, illustrations, examples, explanations, and demonstrations. Teachers with this knowledge can identify student misconceptions about mathematics and provide strategies to correct them. Teachers can derive activities that promote understanding, reasoning, and proficiency. They can provide examples, analogies, models, or representations to help students understand mathematical concepts or procedures.

Source: Louisville.edu/education/research/centers/crmstd/math_assess_middle.html

The K-7 MTLs (n=62) and the Grade 8-9 summit leaders (n=32) each group completed the pretest and posttest. Figure 5 shows that both groups made similar gains for the domain of statistics (maximum score = 20) and for the domain of probability (maximum score = 20), as well as for the total score (maximum = 40). All gains were highly statistically significant (p<0.000). The similarity in performance of the two groups was surprising. Given that the Grade 8-9 group included high school teachers and teachers of grade 8, one would expect their scores to be higher than teachers of grades K-7. However, this was not the case. This supports a finding noted in the MET (CBMS, 2001) report, “Of all the mathematical topics now appearing in the middle grades curricula, teachers are least prepared to teach statistics and probability” (p. 114). Our experiences also reflect that many teachers have had either no or limited college course work in statistics and probability, including high school teachers.

Figure 5. Results on Statistics and Probability for Math Teacher Leaders (MTL)

0

5

10

15

20

25

30

K-‐7 MTL 8-‐9 MTL K-‐7 MTL 8-‐9 MTL K-‐7 MTL 8-‐9 MTL

Statistics Probability Total

Pretest Posttest


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The design of the Louisville Assessments allow for more detailed analysis of teachers’ level of knowledge. The pretest and posttest results for each of the four types of knowledge are shown in Figure 6; each area has a maximum score of 10. (The blue lines are the K-7 group and the orange lines are the Grade 8-9 group). Both groups made statistically significant gains in each of the four areas (p<0.000). The highest pretest and posttest mean scores for both groups was on declarative knowledge which was not surprising. The lowest pretest scores for both groups was on mathematical knowledge for teaching (MKT) and of most interest here, is that the K-7 group actually higher MKT scores than the 8-9 group on both tests. MKT is also the area in which both groups made the greatest gains. In contrast, the 8-9 group demonstrated greater knowledge in problem solving and reasoning in this domain, with both groups improving at similar rates. Another surprising result is the interaction that occurred in regards to conceptual knowledge. The Grade 8-9 group began with a lower score but ended with a higher score. Perhaps this results implies that the teachers in the 8-9 group were more ready to deepen their understanding of statistics and probability.

Figure 6. Results by Types of Knowledge for Statistics and Probability

Topics of Emphasis in School-Based Professional Learning

The professional learning at school sites flows directly from the training of the Math Teacher Leaders during their monthly meetings. Each MTL was asked to indicate, “Of the topics emphasized this year, which have become a focus of work in your school?” The results are shown in Table 11 for K-8 schools and in Table 12 for high schools. The results show strong alignment of school-based learning in the K-8 schools to the topics emphasized in the MTL seminars, showing that MTLs took their learning back to their schools and engaged their staff. Of greatest emphasis across schools was use of common

0

5

10

Pretest Posttest

Type I. Declarative Knowledge

0

5

Pretest Posttest

Type II. Conceptual Knowledge

0

2

4

6

8

Pretest Posttest

Type III. Problem Solving and Reasoning

0

2

4

6

8

Pretest Posttest

Type IV. Mathematics Knowledge for Teaching


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math CABS among teachers at a grade level (mean=3.53) and use of district model CABS in math (3.46) which is the third stage on the MMP continuum. This speaks to the increased efforts of the MTLs to engage teachers in moving toward greater consistency in student expectations for math learning by having them decide on common assessments for students and then set the stage for looking at the student responses together. The next topics of greatest emphasis were implementation of district-adopted mathematics textbook program (3.38) and use of the district mathematics curriculum pacing guides (3.33). Also given emphasis was teachers collaboratively examining student performance on district benchmark assessments (3.12) and other assessments (3.05), giving descriptive feedback on assessments (3.01), and lesson planning with formative assessment principles (2.90). Table 11. School-based Professional Development in K-8 Schools, 2008-2009 (Percent of schools)

Topic n Mean Rating

(1) Not Yet

(2) Beginning

Conversations

(3) Some

Emphasis

(4) Major

Emphasis

Emphasis previous

years

Lesson Planning with formative assessment 113 2.90 5.3% 23.9% 44.2% 24.8% 1.8% State and post lesson objectives n student friendly language (WALT) 113 2.54 12.4% 38.1% 21.9% 16.8% 0.9%

State and post success criteria for lessons 113 2.12 24.8% 42.5% 25.7% 5.3% 1.8% Framework of six types of questions to support math learning goals 112 1.78 44.6% 33.9% 14.3% 4.5% 2.7%

Portfolios of student math learning 113 2.71 17.7% 18.6% 29.2% 27.4% 7.1% Implementation of district-adopted mathematics textbook programs 112 3.38 8.0% 1.8% 13.4% 42.9% 33.9%

Use of the district math curriculum guides 109 3.33 6.4% 6.4% 22.9% 46.8% 17.4% Use of district model CABS in math 112 3.46 0.9% 9.8% 25.0% 51.8% 12.5% Use of common math CABS at a grade level 112 3.53 1.8% 2.7% 31.3% 52.7% 11.6% Teachers collaboratively examining student work from math assessments 113 3.05 3.5% 19.5% 40.7% 31.0% 5.3% Teachers give written/verbal descriptive feedback on math assessments 113 3.01 3.5% 21.2% 44.2% 29.2% 1.8% Teachers collaboratively examine student performance on Benchmarks 113 3.12 4.4% 17.7% 36.3% 38.1% 3.5% Deepening teacher understanding of math content related to teaching 113 2.59 13.3% 29.2% 38.9% 15.9% 2.7%

At the high school level, results also show strong alignment of school-based learning in the to the topics emphasized in the 8-9 summits and the high school release-time MTL meetings. Of greatest emphasis across schools was use of district model CABS in math (3.55) and implementation of district-adopted mathematics textbook program (3.43). This supports movement toward great consistency in mathematics teaching and student expectations. Also given emphasis was deepening teachers content knowledge (3.09), use of common CABS (3.05), and giving descriptive feedback (3.00). At both the K-8 and high school levels, the new topics of emphasis this year—lesson planning, WALT, success criteria, questioning, and portfolios—received less emphasis than our more well-established topics. This is understandable as the MTLs must first develop more ownership of these topics themselves and then support colleagues in their schools in these areas. Even with the newness of these topics, we were encouraged at the amount of emphasis each was given across the district. This sets the stage for building on the awareness established this year and moving toward stronger implementation of these topics next year.


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Table 12. School-based Professional Development in High Schools, 2008-2009 (Percent of schools)

Topic n Mean Rating

(1) Not Yet

(2) Beginning

Conversations

(3) Some

Emphasis

(4) Major

Emphasis

Emphasis previous

years Lesson Planning with formative assessment 22 2.82 0.0% 31.8% 54.5% 13.6% 0.0% State and post lesson objectives n student friendly language (WALT) 22 2.81 4.5% 31.8% 36.4% 22.7% 4.5%

State and post success criteria for lessons 22 2.23 18.2% 50.0% 22.7% 9.1% 0.0% Framework of six types of questions to support math learning goals 22 1.73 54.5% 22.7% 18.2% 4.5% 0.0%

Portfolios of student math learning 22 2.45 22.7% 31.8% 22.7% 22.7% 0.0% Implementation of district-adopted mathematics textbook programs 22 3.43 9.1% 9.1% 9.1% 68.2% 4.5%

Use of the district math curriculum guides 22 2.86 13.6% 13.6% 45.5% 27.3% 0.0% Use of district model CABS in math 22 3.55 0.0% 4.5% 36.4% 59.1% 0.0% Use of common math CABS at a grade level 22 3.05 4.5% 22.7% 36.4% 36.4% 0.0% Teachers collaboratively examining student work from math assessments 22 2.47 9.5% 33.3% 42.9% 4.8% 9.5% Teachers give written/verbal descriptive feedback on math assessments 22 3.00 4.5% 13.6% 59.1% 22.7% 0.0% Teachers collaboratively examine student performance on Benchmarks 22 2.59 13.6% 22.7% 54.5% 9.1% 0.0% Deepening teacher understanding of math content related to teaching 22 3.09 9.1% 18.2% 27.3% 45.5% 0.0%

UWM-MMP Courses for Teachers

The MMP continued to offer professional development courses for MPS teachers and administrators. During Year 6, the MMP offered 15 course sections with approximately 450 participations from over 80 different schools (see Tables 13 and 14). During the academic year, there were approximately $58,000 in tuition waivers, and in the summer we estimate approximately $75,000 in tuition waivers. Table 13. UWM-MMP Professional Development Courses, 2008–2009

Course or MMP district event Number of Participants

Number of Schools

Lenses on Learning: Instructional Leadership in Mathematics (579-101) Sp'09 15 12 Number & Computation Development: Addition & Subtraction (560-105, 106) Sp'09 51 38 Number & Computation Development: Multiplication & Division (560-102) Sp'09 26 16 Number & Computation Development: Special Education Focus (560-103) Sp'09 27 21 Standards-based Mathematics: Early Number Relationships (560-104) Sp'09 32 21 Standards-based Mathematics: Instructional Strategies (560-101) F'08 30 20 Total Participations 181 128 Number of Distinct Schools across Courses 80

Table 14. UWM-MMP Professional Development Courses, Summer 2009

MMP Courses Number of Participants

Number of Schools

Developing Mathematical Ideas: Working with Data (560-176) 29 22 Making Sense of Statistical Studies (560-168) 21 18 Number & Computation Development: Addition & Subtraction (560-184, 195) 43 34 Number & Computation Development: Multiplication & Division (560-153) 27 23 Standards-based Mathematics: Exploring Early Number Relationships (560-152) 25 19 Standards-based Mathematics: Instructional Strategies (560-199) 33 24 Teaching Fraction Concepts and Computation (560-197) 29 23 Total Participations 207 163


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The interest in the MMP courses was overwhelming this year. Every course section was full and had waiting lists. Of particular note, we had more enrollments in the courses from schools that previously had low participation. We see this as an indication of increased focus on improving mathematics teaching and learning in these schools. In addition, we obtained Wisconsin ESEA Title IIA funding to support programs in collaboration with the MMP. Beginning in summer 2008, the three-semester “Developing Geometric Knowledge for Teachers” project directed by Dr. DeAnn Huinker had 33 participants from 22 different schools. Dr. Kevin McLeod also has Title IIA funding to support a three-year Math Fellows program that began in summer 2008, in which K-8 teachers can add a mathematics minor onto their teaching license. This year, 29 participants completed a course in problem solving and critical thinking in fall 2008, 29 participants completed algebraic structures in spring 2009, and 27 participants completed a foundations course in geometry and statistics in summer 2009.

Mathematical Preparation of Teachers

The MMP has been working to improve the mathematical preparation of teachers through development of new courses and revision of existing courses. We now have three long-term Academic Staff and two key tenured faculty members that constitute the Department’s Mathematics Education Unit and meet on a regular basis to discuss education issues within the Department. Since many issues involve liaison with MATC, David Ruszkiewicz, is also a member of this group. Henry Kepner and DeAnn Huinker from the School of Education are also frequent contributors to the discussions.

MCEA (GRADES 1–8) MATHEMATICS FOCUS AREA COURSES The UWM Department of Mathematical Sciences continued the institutionalization of the four specialized courses developed for the Middle Childhood/Early Adolescence (MCEA) mathematics focus area minor. These are, in the order in which they were developed: (1) Problem Solving and Critical Thinking (MATH 275), (2) Geometry (MATH 277), (3) Discrete Probability and Statistics (MATH 278), and (4) Algebraic Structures (MATH 276). While minor changes will continue to be made in response to student needs and feedback, development of all four courses is complete and each set of course materials has been sent out for external review. As each course was developed, it was added to the Department’s course rotation and offered once per year; the Department is now experimenting with additional offerings of MATH 275 and MATH 277. In the 2007-2008 academic year, MATH 277 was offered in both the Fall and Spring semesters last year; the experiment was considered successful and the course was offered again twice last year. MATH 275 was offered in Summer 2009, the first time that one of the focus courses has been offered in Summer. We plan to offer these courses in both Fall and Spring semesters next year. MATH 278 will continue to be offered in the Fall, and MATH 276 in the Spring. The increased number of offerings necessarily means that the instructional pool will have to expand. The Summer section of MATH 275 was taught by Professor Jay Beder (a previous winner of a UWM distinguished teaching award); this is the first time he has taught one of the focus courses. In addition, Gabriella Pinter who has often taught the Problem Solving course, taught MATH 278 for the first time last year.


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CAPSTONE COURSE FOR PRESERVICE HIGH SCHOOL TEACHERS The Capstone course has been taught each spring since 2006. This year was the fourth offering of the course, and as with the MCEA focus courses, the course may be considered as essentially fully developed. Topics vary slightly from year to year, depending on the instructor’s perception of student needs, but the emphasis is always on making connections: between different strands of advanced mathematics the students have studied in college, and between those advanced topics and mathematics in the high school classroom. As in most previous years, the course was taught by Kevin McLeod. Topics covered this year were • Number systems, including the Peano Axioms and induction; • The function concept and its historical development; • Descartes’ “Big Idea” that geometry and algebra are intimately connected; • Sequences and series; • Essential Trigonometry, and connections between trigonometry and calculus. An interesting twist to this year’s class was that MPS had chosen new textbooks for grade 9 Algebra and grade 10 Geometry. As this was a district-wide adoption, it was possible to link many of the topics in the Capstone course to particular chapters or units in these books.

Goal 4. Student Learning Continuum Ensure that all students from PK-16 have access to, are prepared and supported for, and succeed in, challenging mathematics.

MPS Student Learning: Significant Increase in Achievement

The most exciting news to convey in this year’s annual report is the remarkable increase in MPS student mathematics achievement on the Wisconsin Knowledge and Concepts Examination (WKCE). We now have four time points of comparable data. Because testing occurs in November, the results discussed here are reflective of MMP impact through Year 5 (2007-08). Figure 7 shows the increase in proficiency in mathematics from 2005 to 2008, a 9.5 percentage point increase. In 2005, about 40% of the students were proficient on the state test. In 2008, approximately 50% of the students are proficient. With five years of intense work by the MMP, it is very rewarding to see a significant increase in achievement. In addition, a noteworthy decrease occurred in the achievement gap between the district and the state. The gap narrowed from 33.2 percentage points in 2005 to 27.6 percentage points in 2008, a gap decrease of 5.6 percentage points.

Figure 7. WKCE Math Achievement in MPS


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Figure 8 displays a comparison of district and state WKCE grade-level results from 2005 through 2008. Of particular note are the gains revealed on the 2008 test in comparison to 2007. The percentage of students scoring at or above the proficient level in mathematics increased in all seven grades tested (grades 3, 4, 5, 6, 7, 8, and 10) in 2008 compared to the prior year. This is an average increase of more than five percentage points across all grades. Grade 4 and 8 students posted the largest increases at nine and 10 points respectively. The state assessment results also show that the district has reduced the achievement gap with the state in all seven grades in 2008 compared to the prior year, with an average decrease of more than three percentage points. An analysis of changes in proficiency of individual schools in the district revealed that 70% of all MPS schools showed a jump in mathematics proficiency from 2007 to 2008.

Figure 8. WKCE Results for MPS by Grade Level, 2005 to 2008

In addition to a decrease in the achievement gap between the state and the district, the gaps have also narrowed for all major subgroups within the district except with the special education cohort. Although the special education students have improved in the percent of students scoring proficient or advanced, their improvement is still lagging behind the achievement of students without learning disabilities. Figure 9 shows how achievement has increased for all race/ethnic groups in MPS from 2005 to 2008. Table 15 gives more detail to this analysis. Since 2005, African American students have made a 9.4 percentage point increase and Hispanic students have made a 9.3 percentage point increase in proficiency, compared to a 7.2 percentage point increase by White students. Clearly much work still

43 46 48 51 44

52 50 59

40 46 48

53

73 74 74 75 73 78 77 81

72 75 76 79

0 10 20 30 40 50 60 70 80 90

2005 2006 2007 2008 2005 2006 2007 2008 2005 2006 2007 2008

Grade 3 Grade 4 Grade 5

MPS Wisconsin

38 40 43 46 37

44 40 46

37 40 38 48

21 29 27 28

72 76 76 77 73 78 77 78

73 74 75 78 70 70 69 69

0 10 20 30 40 50 60 70 80 90

2005 2006 2007 2008 2005 2006 2007 2008 2005 2006 2007 2008 2005 2006 2007 2008

Grade 6 Grade 7 Grade 8 Grade 10


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needs to be done, but the analysis of this data provides evidence of the Milwaukee Mathematics Partnership’s impact in two critical areas, increasing student mathematics achievement and decreasing achievement gaps for subgroups of students.

Figure 9. WKCE Results for MPS by Grade Level, 2005 to 2008

Table 15. Proficiency Trends on the WKCE Mathematics by Race and Ethnicity Milwaukee Public Schools

Enrolled in Tested Grades

Advanced + Proficient Total

Percentage Point Change from Previous Year

Percentage Point Increase from 2005 to 2008

Nov 2005 Asian/Pacific Is. 1,798 58.7%

+8.6 Nov 2006 Asian/Pacific Is. 1,752 61.8% +3.1 Nov 2007 Asian/Pacific Is. 1,739 62.8% +1.0 Nov 2008 Asian/Pacific Is. 1,675 67.3% +4.5 Nov 2005 African Am. 24,070 29.7%

+9.3 Nov 2006 African Am. 22,995 33.3% +3.6 Nov 2007 African Am. 21,588 33.5% +0.2 Nov 2008 African Am. 19,779 39.0% +5.5 Nov 2005 Hispanic 8,230 45.7%

+9.4 Nov 2006 Hispanic 8,281 49.5% +3.8 Nov 2007 Hispanic 8,260 48.5% -1.0 Nov 2008 Hispanic 8,284 55.1% +6.6 Nov 2005 White 6,361 63.6%

+7.2 Nov 2006 White 6,033 67.7% +4.1 Nov 2007 White 5,735 67.8% +0.1 Nov 2008 White 5,507 70.8% +3.0

Mathematics Readiness Exam in Grades 10-12

During the third year of the MMP (2005-2006), the MMP produced a “post-secondary mathematics readiness test,” based on the UW System placement test and the Accuplacer used at MATC. (Along with the Readiness Test itself, the committee also produced practice tests and answer keys for those practice tests.) The ultimate goal was to have all students in grades 10, 11, and 12 in MPS take the test each year, and to use the results for advising individual students and for planning school schedules and curricula. The test was piloted at seven high schools in January 2007. Based on the results of the pilot, the MPS Research


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Office hired an outside company to administer the test developed by the MMP to all students in grades 10 to 12. This eased the logistical issues of the test and increased timely reporting of the results to schools. As we did had done for the Benchmark Assessments in grades 3–9, we also added a constructed response item to the readiness test to expand its usefulness to inform instruction. Thus, students in grades 3–12 across the district were required to complete common constructed response items at their grade level. The first district-wide administration of the readiness test occurred in January 2008; the second was in January 2009. Scoring sessions were held in February of each year, as part of the High School Math Learning Team Seminar. These successful events brought together high school teachers who focused on student work that cut across grades and courses. Teachers discussed expectations for student work, scored anchor papers, scored their own students’ papers, and then discussed potential next steps for their schools. Results for two schools are listed in Table 16 to provide a snapshot of initial findings. With only two years of data, it is too early to draw firm conclusions, but some points do stand out. First, it must be acknowledged that the overall scores are poor, especially in the Algebra portion of the test. However, in both schools, the students who were in grade 10 in 2008 made notable improvement in both Basic Skills and Geometry when they retook the test in grade 11 in 2009. At School 2, there was also improvement in all areas between grades 11 and 12; this was less marked at School 1. We plan to continue administering the readiness test in future years, to analyze data from a larger sample of schools, and to study the effects of the test on counseling and instruction in individual schools. Table 16. Percent of Students Passing Each Section of the Readiness Test

Number of Students Basic Skills Algebra Geometry Grade 10 11 12 10 11 12 10 11 12 10 11 12

School 1, 2008 209 204 194 12.4 21.1 27.3 0.0 2.0 1.0 5.3 5.4 6.7 School 1, 2009 210 228 164 10.5 33.8 22.6 0.0 4.4 1.2 2.9 15.4 2.4 School 2, 2008 42 41 41 14.3 24.4 26.8 0.0 2.4 4.9 7.1 12.2 12.2 School 2, 2009 49 46 39 30.6 28.3 48.7 0.0 0.0 5.1 26.5 10.9 17.9 All students, 2009 10,402 17.8 3.5 7.8

Mathematics Placement at UWM and MATC

The MMP has studied the transition of MPS high school graduates to the University of Wisconsin-Milwaukee (UWM) and the Milwaukee Area Technical College (MATC). Our goal remains to increase the number of freshman placed into mathematics credit courses at the postsecondary level, thus reducing the number of students in remedial math courses. Table 17 shows a comparison of MPS to non-MPS graduates on math placement levels of new freshmen over four years. In fall 2008, 68% of MPS graduates entering UWM placed into remedial mathematics courses as compared to 39% of non-MPS graduates. At MATC, 93% of potential freshman from MPS schools placed into remedial mathematics courses as compared to 64% of non-MPS graduates. Although substantially higher proportions of MPS graduates require remedial math courses compared with non-MPS graduates, a substantial proportion of the latter also require remediation. The four-year trend does show a closing of the achievement gap between 2005 and 2008 (from 46.4 to 28.3 percentage points at UWM, and from 45 to 29 percentage points at MATC), but this decline appears to be due more to an increased need for remediation of non-MPS students than to improved placement of MPS graduates. There is a clear need for further work and study in this area.


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Table 17. Mathematics Placement of MPS Graduates at UWM and MATC in Remedial Math Courses Placement Fall 2005 Fall 2006 Fall 2007 Fall 2008 MPS Non-MPS MPS Non-MPS MPS Non-MPS MPS Non-MPS UWM Total 309 3465 269 3729 330 4180 299 3751 Basic Mathematics 52% 11% 46.8% 11.0% 42.4% 11.3% 40.1% 10.2% Essentials of Algebra 20% 14% 22.3% 19.0% 30.6% 24.8% 27.4% 29.1% Percent Remedial UWM 71.8% 25.4% 69.1% 30.0% 73.0% 36.1% 67.6% 39.3% MATC Total 798 528 709 594 690 658 721 637 Basic Mathematics 72% 26% 74% 29% 75% 25% 73% 27% Essentials of Algebra 20% 21% 20% 24% 19% 41% 20% 37% Percent Remedial MATC 92% 47% 94% 53% 94% 66% 93% 64%

UWM Transition Support

At UWM, the MMP continued to expand its summer mathematics bridge program and to collaborate with the university in offering accelerated versions of remedial courses. Our work in this area was led by Professor Eric Key of the Department of Mathematical Sciences.

ACCELERATION PROGRAM: MOVING FROM REMEDIAL TO CREDIT COURSES The Math Pilot initiative, offered as part of UWM’s Access to Success program gives students the opportunity to work at their own pace using the computer-adaptive learning software ALEKS, potentially completing two courses in one semester. In past years, there have been two versions of the accelerated Math Pilot courses: combined MATH 090/095 and combined MATH 095/105. MATH 090 and 095 are remedial courses. From its first offering in Fall 2005, the intervention has been a success, with over 90% of participants completing both courses during a semester. This year the university institutionalized the MATH 090/095 combined course as MATH 094. Table 18 compares the cohort in the Math Pilot in Fall 2007 to non-participants. The Pilot participants had a higher success rate (i.e., maintaining a C average) in Spring 2008 and a higher enrollment rate in subsequent semesters than non-participants with most differences statistically significant. As shown, 70.6% of pilot participants compared to 69.0% of non-participants maintained satisfactory grades in Spring 2008, and 78.4% of pilot participants compared to 68.1% non-participants re-enrolled at UWM in Fall 2008. The results for targeted minorities are particularly encouraging with 85.2% in the pilot re-enrolling compared to 59.3% of those not in the pilot. The higher re-enrollment rate bodes well for continued institutionalization of the program. Table 18. Effects of Math Acceleration Pilot for Fall 2007 Participants

Math Pilot Participants Math Pilot Non-Participants N Satisfactory

Spring 2008 Enrolled Fall 2008 N Satisfactory

Spring 2008 Enrolled Fall 2008

All students 102 70.6% 78.4% * 4433 69.0% 68.1% All students with any remedial placement 102 70.6% * 78.4% ** 1860 59.5% 62.7%

All students with MATH 090 placement 47 70.2% 83.0% ** 563 56.7% 61.8%

Targeted minorities total 27 66.7% 85.2% ** 621 51.2% 59.3% Targeted minorities with any remedial placement 27 66.7% * 85.2% ** 407 44.7% 54.3%

Targeted minorities with MATH 090 placement 15 66.7% * 80.0% ** 174 39.1% 50.0%


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MMP SUMMER BRIDGE PROGRAM The MMP Summer Bridge program provides an opportunity for students to study mathematics with the goal of placing into higher-level course upon entering college—usually placing out of remedial mathematics courses. The Summer Bridge program has been held over four weeks in July and August each year since 2006, with 2-hour sessions in both mornings and afternoons, five days per week. Through the Summer of 2008, the program was led by Professor Eric Key, with assistance from UWM mathematics lecturers and MPS high school teachers. With help and guidance from the instructors, students work with ALEKS, a computer program, to improve their skills in arithmetic and algebra. For summer 2008, we attempted to increase enrollment by opening the bridge program to MPS students entering grades 11 and 12, as well as recent high school graduates. We also sent out information about the program earlier in the year, and made a conscious effort to reach students through their high school teachers. We had responses from 35 students, of whom 27 actually participated in the program with 15 being high school graduates and the remainder equally divided between prospective juniors and seniors. Results for the 15 graduates (14 of whom enrolled at UWM in the Fall) were mixed; 4 of these students increased their placement by at least 2 levels, 3 students increased their placement by one level, and 7 showed no change. Of those who increased placement by two levels, 3 students moved from a placement score of 0 (the lowest level) to placing into credit-bearing courses, and one of these completed her mathematics graduation requirement in the Fall. The fourth student in this group obtained placement in first-semester calculus, and subsequently earned a grade of B- in that course. Of the students who increased their placement by one level, one deferred admission to UWM and the other two achieved grades of A in MATH 095 (a non-credit course) during the year. The results summarized above are broadly in line with previous years. We can show evidence that the bridge program produces results for approximately half of the participants, but enrollment is never as large as we would like, and we have not been able to determine criteria which would allow us to predict beforehand which students will benefit from the program. Nevertheless, the university has felt that our results are sufficiently positive to justify institutionalizing the program, and have taken on the responsibility of supporting it, starting with Summer 2009. The intention is to offer the program only to incoming UWM students who have MATH 090 or MATH 095 placement, and to do so mainly online. At the time of writing we do not have data on student enrollment or results under the new system.

Closing Comments During its sixth year, coincidentally the 40th anniversary of the Apollo 11 moon landing, the Milwaukee Mathematics Partnership (MMP) took a “giant leap“ towards its mission of improving student performance in mathematics in the Milwaukee Public Schools. This was a year in which several of our initiatives and activities really came together, especially for the Math Teacher Leaders (MTL) and classroom teachers. It was also the year in which we saw the greatest increase in student performance, and narrowing of achievement gaps, on the Wisconsin state mathematics assessment. The support for release-time MTL positions from the Office of the Governor in the state of Wisconsin is evidence of the value placed on the work of the MMP, and ensures that work


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will continue beyond the expiration of NSF funding. The transition to the new MTL model was challenging in some respects, but was smoothed by the district allocating funds (to the tune of $5 million) to begin the transition process in Spring 2008. This action was a strong indicator of the value placed by district leadership on the goals and strategies of the MMP, and meant that we were able to start the 2008–2009 academic year with our new cohort of MTLs largely in place. The support from the Office of the Governor is still strong, even in these difficult economic times, and he has again included a request for funds to support the MMP in its biennium budget. The district submitted a proposal in July 2009 to continue the state support through the 2009-2010 school year, committing $2.1 million of district funds in the process, with anticipation of additional state funds for the 2010-2011 school year. A major focus of our work in Year 6 was to prepare the MTLs for their expanded leadership roles. Over the years, we have developed many tools for MTLs to use with their school staffs. We revised and oversaw a revised textbook adoption process for K–8 that involved many more teachers in studying text materials for alignment to district learning targets, state standards, and the Comprehensive Math Framework. We developed, modified, and revised model classroom assessments based on standards (CABS) at all grade levels. We produced a several report forms (e.g., CABS Assessment Overview, Classroom Summary Report, and Student Feedback Summary) that teachers can use as a guide in analyzing CABS and writing descriptive feedback. We also developed, what perhaps is our most important tool, the MMP Learning Team Continuum of Work to guide the developmental progress of schools in movement toward formative assessment practices. This year, we further developed our school self-assessment tool and rubric based on the Learning Team Continuum. All schools with release-time MTLs were required to complete this self-assessment at the beginning and end of the school year, and many with non-released

MTLs did so also and found it to be a valuable reflective activity. The self-assessment tool serves as a summary of many of our initiatives over the years, and focuses a school’s discussion on the teaching and learning of challenging mathematics according to MMP principles. For schools with a released-time MTL, the self-assessment and monitoring conferences also introduced a level of accountability unusual in the district. This was also a year in which we made significant progress in reaching high

schools—traditionally our greatest challenge. Last year we began the grade 8-9 summits and the algebra labs which exposed many high school teachers to the work of the MMP for the


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first time. This year the summits were continued with an expanded focus on leadership. We also continued the algebra labs and began geometry labs focused to support implementation of the new textbook adoptions for these areas in grades 9 and 10. These summits and labs engaged many high school teachers more deeply in the work of the MMP. This was strongly supported by the release-time MTL positions at the high school level. All but one of the large high schools in the district received a release-time MTL position, and these MTLs were required to attend the grade 8-9 summits, which in some cases provided us with our first real chance to work with these schools with more intensity. Similarly, the release-time position allowed the MTLs to work more intensely with staff in their schools and to provide more math leadership aligned with the goals of the MMP. Of course, more work remains to be done. Despite the impressive gains this year, the achievement gap between MPS students and their peers in the rest of the state continues to be too large. The MMP external evaluation continues to indicate, however, that the goals and objectives of the partnership are contributing to the increases in student achievement scores, and that MPS schools that perform well with regard to MMP-related metrics—such as time spent on professional development, in-school network density, and teacher scores on content knowledge assessments— have higher student achievement levels. In particular, the expanded role of the Math Teacher Leaders is producing an increased focus on mathematics that is clearly reaching into the classrooms. Over the next year, we will continue to build this momentum by expanding our intentional emphasis on formative assessment practices (including WALT), by connecting our content work more explicitly to MKT and ensuring that MTLs and teachers can find the important mathematical ideas in their curriculum materials, and by strengthening the leadership and coaching skills of our MTLs. We have every expectation that if we, and they, remain resolute, the remarkable strides we have made this year will be repeated in our seventh year.


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References American Statistical Association. (2005). Guidelines for assessment and instruction in statistics

education (GAISE) report: A Pre-K-12 curriculum framework. Alexandria, VA: Author. Black, P., & Wiliam, D. (1998). Inside the black box: Raising standards through classroom assessment.

Phi Delta Kappan, 80(2), 139-148. Chappuis, S., Stiggins, R., Arter, J., & Chappuis, J. (2005). Assessment for learning: An action

guide for school leaders (2nd ed). Portland, OR: Assessment Training Institute. Clarke, S. (2001). Unlocking formative assessment: Practical strategies for enhancing pupils’

learning in the primary classroom. London: Hodder and Stoughton. Clement, L. & Bernhard, J. (2005). A problem-solving alternative to using key words.

Mathematics Teaching in the Middle School. 10(7) pp.360-365. Conference Board of the Mathematical Sciences. (2001). The mathematical education of

teachers. Providence, RI: American Mathematical Society and Mathematical Association of America.

National Council of Supervisors of Mathematics (2008) Principles and indicators for mathematics education leaders. Denver, CO: Author.

National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education. (Report available at: www.ed.gov/mathpanel)

Stiggins, R. (2006). Assessment for learning: A key to motivation and achievement. Edge, 2(2), 3-19. (www.assessmentinst.com/forms/KappanEdgeArticle.pdf)

Stiggins, R., Arter, J. A., Chappuis, J., & Chappuis, S. (2004). Classroom assessment for student learning: Doing it right—using it well. Portland, OR: Assessment Training Institute.

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