1. EVOLUTION OF A CONTINUUM OF MATHEMATICS LEADERSHIP
Charting the Course to Formative Assessment Practices in a Large Urban District
DeAnn Huinker, University of Wisconsin-Milwaukee
Henry Kranendonk, Milwaukee Public Schools
National Council of Supervisors of Mathematics
San Diego, California
April 19, 2010

2. Student Achievement in Mathematics
STEADY
STAY THE COURSE

3. Session Goals
Examine the roadmap used by a large urban district to chart a course to student learning gains in mathematics, the Continuum of Work for Mathematics.
Consider change as a developmental process for individuals, schools, and districts.

4. Milwaukee Mathematics Partnership (MMP)
Fall 2003
Awarded a 5-year Comprehensive Mathematics and Science Partnership grant through the National Science Foundation

5. Mathematics Framework
Distributed Leadership
Teacher Learning Continuum
Student Learning Continuum

6. Milwaukee Public Schools
• Summer 2003
Approximately 100,000 students (pre-K to 12)
Approximately 200 schools
• Fall 2009
Approximately 85,000 students
Approximately 190 schools
Approximately 5700 classroom teachers

7. Prior to the MMP (Before 2003)
Inconsistency across and within schools for math
De-centralization issues
schools operated independently of central office
principal as primary leader in setting direction for school’s implementation of mathematics
Lack of sustained professional development
Pedagogy more an “emotional state of mind” than based on sound instructional practices.

8. Early Years of the MMP (2003–2004)
District
Vision of
Mathematics
Grade Level Learning Targets in Mathematics

9. District Mathematics Leadership Mathematics & Math Education
Early Years of the MMP (2003–2004)
School Learning Team
District Mathematics Leadership
IHE Faculty
Mathematics & Math Education
New school leadership position, the Math Teacher Leader (MTL)
Literacy Coach
Principal
Math Teacher Leader
Other Key Teachers
Established district leadership team, new position, Math Teaching Specialists (MTS)

10. Early Years of the MMP (2004 – 2005)
Developed common “Classroom Assessments Based on Standards” (CABS)
Established monthly MTL professional development
MTL emerged as an accepted leader of math within schools for teachers and principals

11. MMP Continuum Years (Spring 2005 – Present)
Principles of formative assessment as key to MTL leadership
Three MMP “pillars” for MTL development
Mathematics Content
Formative Assessment
Leadership
Evolvement of the “MMP Learning Team Continuum of Work for Mathematics” as a roadmap for implementing the MMP

12. MMP Continuum of Work for Mathematics
Stage 1. Learning Targets
Understand importance of identifying and articulating big ideas in mathematics to bring consistency to a school’s math program.
Stage 2. Align State Framework & Math Program
Develop meaning for the math embedded in the targets and alignment to state standards and descriptors and to the school’s math program.
Stage 3. Common Classroom Assessments (CABS)
Provide a measure of consistency of student learning based on standards/descriptors and targets.
Stage 4. Student Work on CABS
Examine student work to monitor achievement and progress toward the targets and descriptors.
Stage 5. Descriptive Feedback on CABS
Use student work to inform instructional decisions, and to provide students with appropriate descriptive feedback.

13. Stage 1
Learning Targets
Stage 2
Alignment of State Framework & 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 the math embedded in the targets and alignment to state standards and descriptors and to the 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.
School Professional Work
• 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.
• 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.
• 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.
• 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.
• 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.

14. School Self-Assessment Report
Stage
What percent of the staff is at each stage?
Plan for School Professional Work
Plan to Document Evidence of Impact on Classroom Practice or Teacher Instructional Growth
Weak
Emerging
Moving
Strong
Stage 1.
Learning Targets
Stage 2.
Align State Framework and Math Program
Stage 3.
Common CABS
Stage 4.
Student Work
on CABS
Stage 5.
Descriptive Feedback on CABS

16. Stage 1: Learning Targets
Understand importance of identifying and articulating big ideas in mathematics to bring consistency to a school’s math program.
Learning Targets are statements of mathematics for focused study at a grade level.
Aligned to State standards.
Grade 6
Apply, explain, and evaluate strategies to estimate, compare, and compute fractions, decimals, and percents using a variety of methods (e.g., mental computation, technology, manipulatives) with and without context.

17. Stage 1: Learning Targets
Understand importance of identifying and articulating big ideas in mathematics to bring consistency to a school’s math program.
School Professional Work
Teachers develop an awareness of district learning targets for each mathematics strand.
Teachers discuss what each target means and can articulate math learning goals students are to reach.
Teachers examine the development of mathematical ideas across grade levels.

18. Examples: Stage 1 Learning Targets

19. Stage 2: Align State Framework & Math Program
Develop meaning for the math embedded in the targets and alignment to State standards and descriptors and to the school’s math program.
District Math Learning Targets
State Standards & Assessment Descriptors
School Math Program

20. Stage 2: Align State Framework & Math Program
Develop meaning for the math embedded in the targets and alignment to State standards and descriptors and to the school’s math program.
School Professional Work
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.

21. Examples: Stage 2 Alignment

22. School Self-Assessment Guide
Stage 1. Learning Targets
Understand importance of identifying and articulating big ideas in mathematics to bring consistency to a school’s math program. 1
Weak
Teachers have not yet or barely started to study or use learning targets. 2
Emerging
Teachers are beginning to unpack and consider value and use of targets. 3
Moving Forward
Teachers can articulate learning goals for their students. 4
Strong
Teachers can articulate learning goals for students and growth across grades.
Estimate the percent of teachers of mathematics (regular and special education) that are at each position.
Stage Descriptors
Summary Statements and Planning Ideas
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.

23. Where are You, Your School, or District?
Estimate percent of teachers at each position.
Stage 1
Learning Targets 1
Weak 2
Emerging 3
Moving Forward 4
Strong
Stage 2
Align State & Math Program
Make notes on each stage descriptor.
THEN share and discuss as a small group.

24. Stage 3: Common Classroom Assessments (CABS)
Provide a measure of consistency of student learning based on standards/descriptors and targets.
CABS
Classroom Assessments Based on Standards
Selected/developed/adapted by teams of teachers and IHE mathematics faculty.
Aligned to district targets and state standards and descriptors.
Aligned to district pacing guides for adopted math programs.

25. CABS Example: Paxolai’s Purchase
Paxolai purchases a video game that costs $ She uses two coupons when she buys the video game. The first coupon gives 25% off of the regular price. The second coupon is for $5.00 off the price of any video game. When the clerk rings up Paxolai’s purchase, he takes the $5.00 off first and then applies the 25% discount. How much does Paxolai pay for the video game?
Would the price that Paxolai paid for the video game have increased, decreased, or stayed the same if the clerk had taken the 25% discount first and then taken off the $5.00 coupon?
Grade 7

26. Grade 7 Learning Target: Number & Operations
Explain comparisons and operations on real numbers and use proportional reasoning (including ratios and percents) to solve problems with and without contexts.
Wisconsin Assessment Framework: Descriptors
Number & Operations: Concepts
Analyze and solve problems using percents.
Mathematical Processes
Communicate mathematical ideas and reasoning in a variety of ways (e.g. using words, numbers, symbols, pictures, charts, tables, diagrams, graphs, and models).
Solve and analyze routine and non-routine problems.

27. Connections to the Comprehensive Mathematics Framework
CABS Assessment Overview
After working through the assessment, reflect on what you expect students to do.
Description of Assessment:
School:
Grade Level:
Identify appropriate Key Mathematics Features students may develop and use as a response to this assessment:
Connections to the Comprehensive Mathematics Framework
Identify misconceptions you anticipate students will demonstrate:
Understanding
Reasoning
Computing
Engagement
Problem-solving
Identify misconceptions identified after analyzing student work:
This is where you get your language from your feedback.

28. Stage 3: Common Classroom Assessments (CABS)
Provide a measure of consistency of student learning based on standards/descriptors and targets.
School Professional Work
Teachers select and study common CABS to use at a grade level.
Teachers identify math expectations assessed through CABS.
Teachers identify potential student misconceptions.
Learning Team and teachers examine student WKCE and Benchmark Assessment/CABS data to identify areas of strengths and weaknesses for focusing teaching and learning.

29. Examples: Stage 3 Common CABS

30. Stage 4: Student Work on CABS
Examine student work to monitor achievement and progress toward the targets and descriptors.
Name a fraction that is between 1/2 and 2/3 in size.
Justify how you know your fraction is between 1/2 and 2/3.

32. Stage 4: Student Work on CABS
Examine student work to monitor achievement and progress toward the targets and descriptors.
School Professional Work
Teachers collaborate in grade-level meetings to discuss student work and implications for classroom practice.
Teachers meet in cross-grade meetings to discuss common expectations of student learning & 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.

33. Examples: Stage 4 Student Work on CABS

34. Where are You, Your School, or District?
Estimate percent of teachers at each position.
Stage 3
Common CABS 1
Weak 2
Emerging 3
Moving Forward 4
Strong
Stage 4
Student Work on CABS
Make notes on each stage descriptor.
THEN share and discuss as a small group.

35. Stage 5: Descriptive Feedback on CABS
Use student work to inform instructional decisions, and to provide students with appropriate descriptive feedback.

36. Motivational/Evaluative Feedback Examples
Very nice diagrams. You developed representations of the fractions to make your selection of 7/12 as a fraction between 1/2 and 2/3.
Your answer of 7/12 is correct. You receive full credit for your work.

37. Descriptive Feedback Examples
Explain your decision of dividing the rectangles into equal sections of 6ths and then 12ths.  
I’m impressed with your representations of 1/2 and 2/3 to help you. Your rectangles appear to grow in size. Do the 6 shaded sections and the 8 shaded sections in your last rectangle still represent the same fractions? Draw the next representation you would use to represent the fractions. How are you deciding the number of sections to create in the rectangles?

38. Stage 5: Descriptive Feedback on CABS
Use student work to inform instructional decisions, and to provide students with appropriate descriptive feedback.
School Professional Work
Teachers collaborate to write students descriptive feedback on Benchmarks and on common CABS from the curriculum guides.
Students use feedback to revise work and improve learning.
Teachers use feedback to adjust and differentiate instruction.
Learning Team monitors successes and challenges of writing descriptive feedback, and identifies professional learning needs of teachers.

39. Examples: Stage 5 Descriptive Feedback CABS

40. Discuss Stage 5 as a Small Group
In ways do you use descriptive feedback or how might you begin to use more descriptive feedback with students?
What might be some benefits of providing students with opportunities to use descriptive feedback to revise their work?

41. Alignment State & Program
Impact
K-8 Schools at Each Stage n
Stage 1
Learning Targets
Stage 2
Alignment State & Program
Stage 3
Common
CABS
Stage 4
Student Work
Stage 5
Descriptive Feedback
Year
101
38%
53% 9% 0% 1%
Year 97
18%
34%
38% 5% 4%
Year 89
13%
26%
41%
18% 2%
Year
109
11%
26%
39%
18% 6%
Year
113
20%
32%
14% 2%
Year
113 3% 8%
39%
30%
20%

42. Impact High Schools at Each Stage 50% 25% 0% 26% 32% 21% 16% 5% 56% 20n
Stage 1
Learning Targets
Stage 2
Alignment
State & Program
Stage 3
Common
CABS
Stage 4
Student Work
Stage 5
Descriptive Feedback
Year 20
50%
25% 0%
Year 22
26%
32%
21%
16% 5%
Year
56%

43. Student Proficiency on WKCE Mathematics

44. Align State Framework & Math Program Common Classroom Assessments
MMP Continuum
Stage 1
Learning Targets
Stage 2
Align State Framework & 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 the math embedded in the targets and alignment to state standards and descriptors and to the 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.

45. Building the capacity of schools stage by stage along the “MMP Continuum” for continuous improvement toward student success with challenging mathematics.

46. MMP website DeAnn Huinker Henry Kranendonk Thank you. www.mmp.uwm.edu
Henry Kranendonk
This material is based upon work supported by the National Science Foundation Grant No