Descriptive Feedback: Moving to the Next Level . . . The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding from the National Science Foundation under Grant No. EHR-0314898. 1

Presented by: The Milwaukee Math Partnership Cynthia Cuellar Milwaukee Public Schools Math Teaching Specialist Karen Corlyn Teacher-in-Residence, UW-Milwaukee Milwaukee Public Schools Carmen Reyes Teacher, Wedgewood International Middle School Milwaukee Public Schools

Learning Teams Continuum of Work for Mathematics School Self-Assessment and Guide Learning Teams Continuum of Work for Mathematics Stage 1: Learning Targets Stage 2: Unpack & Align Targets with State Framework Stage 3: CABS Level 1: Select/Design CABS Stage 4: CABS Level 2 Student work Stage 5: CABS Level 3 Formative Feedback 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 the alignment to state standards/descriptors school’s math program. Provide a measure of consistency around student achievement based on the targets. Examine student work to monitor achievement and progress toward the targets. Use student work for instructional decisions, and appropriate. continuous, feedback to students. Tools • Grade level lists of 9-11 big ideas per grade • Horizontal list of targets by content across grades • Target-descriptor alignment worksheets • WKCE Depths of Knowledge Framework • Pacing Guides • WKCE data on student achievement Assessing the Assessment Guide • District Model CABS • MMP Protocol for analysis of student work • DVD of the MMP protocol in use • Descriptive Feedback • Class and Student Feedback Summary • CABS Class Summary Report

Stage 4. Level 2 CABS—Student Work Goal: To collaboratively examine student work from CABS in order to monitor student achievement and progress toward Learning Targets. Do grade level teachers regularly (e.g., monthly) examine students’ mathematics work and identify strengths and weaknesses of individual students, of a class of students, or a grade level? Have teachers used the district protocol for collaboratively looking at student’s mathematics work from CABS? Do teachers have opportunities to share student work from CABS across grade levels? Do grade level groups have opportunities to discuss with the Learning Team both summaries of student achievement on CABS and a range of student work samples (e.g., low, middle, and high benchmark papers)? How does the Learning Team monitor students’ progress toward meeting the Learning Targets and report this to the school staff? Do teachers use the “Descriptive Feedback (Everyday) Rubric” in classroom practice and when examining student work samples?

Stage 5. Level 3 CABS—Formative Feedback Goal: To use student work from common classroom assessments (CABS) to drive instructional decisions on “what do we do next” in the classroom and to provide appropriate and continuous feedback to students. Can teachers give a specific example of a way they have used results from CABS to inform and modify classroom practice? How do teachers use the “CABS Class Summary Report” to share the successes, challenges, and next steps for student learning? How do teachers give students descriptive feedback that prompts them to self-reflect on ways to improve their work? How do teachers use the “Class Student Feedback Summary” to make instructional decisions based on descriptive feedback to students?

Purpose: Participants will . . . Examine what research says about the effects of feedback. Deepen their understanding of different types of feedback. Analyze student work in mathematics while writing effective feedback. Discuss ways to use feedback in the classroom to guide student learning of mathematics. . .

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.”

Research by: John Hattie 1992 “The most powerful single modification that enhances achievement is feedback. The simplest prescription for improving education must be ‘dollops of feedback’.”

Type of Feedback: Motivational 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. 9

Type of Feedback: Evaluative 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. 10

Type of Feedback: Descriptive 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. 11

Type of Feedback: Effective 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. 12

Examples of Feedback Descriptive & Effective Motivational A. 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? Descriptive & Effective Motivational B. I like how you completed the assignment. C. 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 D. Your explanation of your work is the best that you have done. Nice use of sequence words in your explanation. Evaluative 13

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

Type of Feedback Activity Motivational Evaluative Descriptive Effective 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 More Summative Formative

CABS: Number Patterns Study this sequence: 5, 7, 2, 4, -1, 1, -4 . . . 5, 7, 2, 4, -1, 1, -4 . . . What is the 10th term in this sequence? Answer: ______ How did you determine what this number is?

Mathematics Grade 8 Classroom Assessment Based on Standards Power CABS Identifier: “Number Pattern” MPS Learning Target: Algebraic Relationships • MPS Learning Target #6: Analyze, describe, and generalize mathematical and real-world patterns of change and functional relationships with emphasis on the role of variable quantities. • MPS Learning Target #7: Model, justify, and solve linear equations and relationships using translations among tables, graphs/grids, and symbolic forms. • MPS Learning Target #8: Explain use of properties (e.g., commutative, associative, distributive) to evaluate expressions and solve linear equations.

Mathematics Grade 8 Classroom Assessment Based on Standards Power CABS Identifier: “Number Pattern” Wisconsin Assessment Framework for Mathematics Objective: F. Algebraic Relationships Subskill: Patterns, Relations, and Functions Descriptor: Analyze, generalize and represent patterns of change, e.g. direct and inverse variations, including numerical sequences,, patterns to a given term, algebraic expressions and equations. 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.

What Mathematics Am I Assessing? 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. Description of Assessment: School: Grade Level: 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: Understanding Reasoning Computing Engagement Problem-solving Identify misconceptions identified after analyzing student work:

How to Manage the Use of Feedback in the Classroom When should I use feedback? A success story. The Gail Burrill Strategy

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.”

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

A Guide to Formative Assessment Forecast A Guide to Formative Assessment 23

Thank you. www.mmp.uwm.edu This material was developed by the Milwaukee Mathematics Partnership (MMP) with support 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 Foundation.