1. Applying Formative Assessment Principles Astrid FossumMary Mooney Lee Ann PruskeBernard Rahming Laura MalyCynthia Rodriguez Mathematics Teaching Specialists, Milwaukee Public Schools www.mmp.uwm.edu The Milwaukee Mathematics Partnership (MMP) is supported by the National Science Foundation under Grant No. 0314898.

2. In this session participants will:  Examine how teacher teams utilize assessment for learning in order to improve teaching and learning in mathematics.  Consider implementation strategies for the principles of assessment for learning in classroom practice.

3. Distributed Leadership Student Learning ContinuumTeacher Learning Continuum Mathematics Framework

4. Comprehensive Mathematics Framework

5. MMP Learning Team Continuum Stage 1 Learning Targets Stage 2 Alignment of State Framework & Math Program Stage 3 Common Classroom Assessments 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. Tools Grade level lists of 9-11 big ideas per grade (the targets) Horizontal list of targets by content across grades Tools Target-descriptor alignment worksheets WKCE Depths of Knowledge Framework Curriculum Guides Tools Curriculum Guides District Model CABS Depths of Knowledge worksheet CABS Assessment Overview worksheet WKCE and Benchmarks student data Tools MMP Protocol for Analysis of Student Work DVD of MMP Protocol CABS Class Summary Report form School Educational Plan Tools Types of Feedback sheet Descriptive feedback worksheets CABS Class Feedback Summary worksheet

6. Assessment for learning Assessment for learning is about far more than testing more frequently or providing teachers with evidence so they can revise instruction, although these are part of it. Assessment for learning must actively involve students. Richard Stiggins

7. MMP Learning Team Continuum Aligned with Formative Assessment Principles (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 (CABS), and fits within the progression of student learning. (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. (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. 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 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.

8. “…children are more motivated and task oriented if they know the learning intention of the task, but they are also able to make better decisions about how to go about the task. “ Shirley Clark, 2001

9. Learning Intentions  Read pages 19 – 26 of Chapter 2, Sharing Learning Intentions, by Shirley Clarke.  Focused Reading.... √ Important idea ! New insight to ponder ? Question  Take turns, each person shares one thing that they marked and explains why.

11. Analyzing a Sample Lesson and Applying Formative Assessment Principles Analyze the lesson and background information to surface the big math ideas: Work in Groups of Three Read and study your lesson Identify the important mathematics in the lesson Translate this into a Student Friendly learning intention and success criteria, record on chart paper

12.  Post your chart paper with your learning intention and success criteria in student friendly language  Group discussion Share Your Thinking

13. Sharing Learning Intentions “Is only the first step in the processes of formative assessment, leading to pupil self-evaluation and teacher or peer feedback after the work is completed.” Shirley Clark, 2001

14. Forecast…

15. MMP Learning Team Continuum Aligned with Formative Assessment Principles (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 (CABS), and fits within the progression of student learning. (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. (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. 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 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.

16. The MPS Glossary Definition of CABS Classroom assessments aligned to the Milwaukee Public Schools’ Learning Targets; these assessments are developed, administered, and scored by teachers with the purpose of providing specific, meaningful, and timely feedback designed to improve student performance.

17. Research by: John Hattie “ The most powerful single modification that enhances achievement is feedback. The simplest prescription for improving education must be ‘dollops of feedback’.”

18. Type of Feedback  Goal is to make the learner feel good.  Feedback that is intended to encourage and support the learner.  It does not give guidance on how to improve the learner’s reasoning.  Since it is not intended to move students forward in the learning process, it can be given on summative assessments. Motivational

19.  Goal is to measure student achievement with a score or a grade.  Feedback that is intended to summarize student achievement.  It does not give guidance on how to improve the learner’s reasoning.  Since it is not intended to move students forward in the learning process, it can be given on summative assessments. Type of Feedback Evaluative ADCAADCA

20.  Goal is to improve student achievement by telling the learner how to move forward in the learning process.  Feedback that is intended to tell the learner what needs to be improved.  Feedback isn’t as effective in getting students to move forward in the learning process. Type of Feedback Descriptive

21.  Goal is to get student to internalize the effective feedback to use the suggested strategies independently on future work.  Feedback that is intended to be used by the learner to independently move their reasoning to the next level.  Criteria-based phrases are used to describe the strengths and weaknesses of the learner’s work.  Limits feedback to one or two traits/aspect of quality at a time.  Students should have an opportunity to “redo” their work based on the effective feedback. Type of Feedback Effective

22. 1.I agree with the pattern that you have identified in the table. I am not convinced that the rule you wrote works for all the values in the table. How could you prove this? Motivational 2.I like how you completed the assignment. Descriptive & Effective Examples of Feedback

23. 3.Your explanation of your work is the best that you have done. Nice use of sequence words in your explanation. Evaluative 4.You accurately found the number of students in 4th grade who said chocolate ice-cream was their favorite. You now need to divide this number by the total number of students to get the percent who said chocolate ice-cream was their favorite. Descriptive Examples of Feedback

24. What Does Effective Feedback Look Like? Effective Feedback Should:  Describe and inform, not judge  Be specific, not general  Be clear to students  Suggest what students should do to improve Adapted from Formative Assessment Strategies for Every Classroom, Susan M. Brookhart, ASCD

25. Type of Feedback Activity Motivational EvaluativeDescriptiveEffective Feedback is primarily motivational Feedback is primarily evaluative Descriptive feedback primarily tells the student how to correct their reasoning. Descriptive feedback asks the student what to do to move their reasoning to the next level. Purpose: to encourage and support the learner Purpose: to measure student achievement with a score or a grade Purpose: to improve learning by indicating to the student what needs to be improved Purpose: to improve learning, by moving student reasoning to the next level MoreSummativeMoreFormative

26. Mathematics Grade 4 Classroom Assessment Based on Standards Power CABS Identifier: “Babysitting” Shaquisha babysits for her auntie’s children. She made this table. If she works nine hours, how much money will she earn? Using mathematical vocabulary, explain how you figured out how much she would earn working nine hours. Hours Worked Money Earned 2$8 4$16 7$28 9?

27. Mathematics Grade 4 Classroom Assessment Based on Standards Power CABS Identifier: “Babysitting” MPS Learning Target: Algebraic Relationships MPS Learning Target #9: Represent and extend patterns and describe rules for functional relationships. MPS Learning Target #10: Use symbols to represent problem situations and use properties and order of operations to solve equations involving all operations.

28. Wisconsin Sub-skill Descriptors (Beginning of Grade 5) Sub-skill F.a: Patterns, relations and functions 1) Recognize, extend, describe, create and replicate a variety of patterns including attribute, numeric, and geometric patterns. 2) Represent patterns and relationship with pictures, tables, and charts. 3) Describe a rule that explains a functional relationship or pattern using addition, subtraction, or multiplication rules. 4) Determine a future event in a pattern up to the eighth item when given the first five. Sub-skill F.b: Expressions, equations and inequalities 5) Solve simple one-step open sentences involving all operations in context. 6) Demonstrate a basic understanding of equality and inequality using symbol (, =) with all operations. 7) Solve simple, one-step open sentences including missing factor in problems with and without context e.g., “box” or letter variable and whole number coefficients. 8) Represent problem situations with one-step equations involving multiplication and division with simple open sentences. 9) Represent problem situations with one-step equations or expressions using one of the four operations. Sub-skill F.c: Properties 10) Use the commutative property of multiplication with positive single digits. 11) Use the inverse relationship of division and multiplication with single-digit, whole numbers. 12) Demonstrate understanding of order of operations by solving two-step open sentences involving all operations.

29. Mathematics Grade 4 Classroom Assessment Based on Standards Power CABS Identifier: “Number Pattern” Wisconsin Assessment Framework for Mathematics Objective: A. Mathematical Processes Descriptors: Use reasoning and logic to perceive patterns, identify relationships, formulate questions, pose problems, make conjectures, justify strategies, and test reasonableness of results Communicate mathematical ideas and reasoning using the vocabulary of mathematics 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.

30. What Mathematics Am I Assessing? Description of Assessment: School: Grade Level: CABS Assessment Overview After working through the assessment, reflect on what you expect students to do. Complete the following table before developing your descriptive feedback. Identify appropriate Key Mathematics Features students may develop as a response to this assessment : Connections to the Comprehensive Mathematics Framework Identify misconceptions you anticipate students will demonstrate : o Understanding o Reasoning o Computing o Engagement o Problem-solving o Understanding o Reasoning o Computing o Engagement o Problem-solving Identify misconceptions identified after analyzing student work: o Understanding o Reasoning o Computing o Engagement o Problem-solving

31. Analyzing Student Work Samples Think On your own, think about what type of feedback is represented by each statement. Pair Turn to a partner and share your thoughts. Come to agreement on the type of feedback represented. Share Share with the whole group some of your thoughts and discussions.

32. Writing Feedback With your shoulder partner: Modify a feedback statement to make it a descriptive or an effective feedback statement. OR Write your own descriptive or effective feedback statement for a work sample.

33. School: Teacher: Date: Grade Level: _______Sp.Ed _______Reg.Ed MPS Learning Target(s): State Descriptor(s): Expectations: (What do you expect to see on student’s paper to demonstrate understanding?) Students’ Successes:Students’ Challenges: Next Steps: CABS Class Summary Report Description of Assessment :

34. Research by: Richard Stiggins “Achievement gains are maximized in context where educators increase the accuracy of classroom assessments, provide students with frequent informative feedback (versus infrequent judgmental feedback), and involve students deeply in the classroom assessment, record keeping, and communication process. In short, these gains are maximized where teachers apply the principles of assessment for learning.”

35. Personal Reflections An idea that squares with my beliefs... A question or concern going around in my head... A point I would like to make...

36. Looking Back and Looking Forward  In school teams, share one point from your personal reflections.  Discuss the structures you have in place to begin implementing Formative Assessment Principles.

37. Stage 1 Learning Targets Stage 2 Alignment of State Framework & Math Program Stage 3 Common Classroom Assessments 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. 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. School Professional Work 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. School Professional 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. School Professional Work 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. Tools Grade level lists of 9-11 big ideas per grade (the targets) Horizontal list of targets by content across grades Tools Target-descriptor alignment worksheets WKCE Depths of Knowledge Framework Curriculum Guides Tools Curriculum Guides District Model CABS Depths of Knowledge worksheet CABS Assessment Overview worksheet WKCE and Benchmarks student data Tools MMP Protocol for Analysis of Student Work DVD of MMP Protocol CABS Class Summary Report form School Educational Plan Tools Types of Feedback sheet Descriptive feedback worksheets CABS Class Feedback Summary worksheet

38. 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. Stage 1 Learning Targets

39. Continuum 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 WeakEmergingMovingStrong 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 Learning Team Continuum of Work for Mathematics

40. Next steps…

41. In this session participants will:  Examine how teacher teams utilize assessment for learning in order to improve teaching and learning in mathematics.  Consider implementation strategies for the principles of assessment for learning in classroom practice.

42. Resources  Black, P., & Wiliam, D. (1998). Inside the black box: Raising standards through assessment. Phi Delta Kappan, 80(2), 139-148.  Brookhart, S.M., (2007). Feedback that fits. Educational Leadership, 65(4), 54-59.  Clarke, S. (2001). Unlocking formative assessment: Practical strategies for enhancing pupils’ learning in the primary classroom. Abingdon, UK: Bookpoint LTD.  Stiggins, R.J., Arter, J., Chappuis, J., & Chappuis, S. (2005). Assessment for learning: An action guide for school leaders. Portland, OR: Assessment Training Institute.  Wiggins, G., & McTighe, J. (1998). Understanding by design. Alexandria, VA: Association for Supervision and Curriculum Development. The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding from the National Science Foundation

43. The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding from the National Science Foundation. www.mmp.uwm.edu