Applying Formative Assessment Principles

Astrid Fossum Mary MooneyLee Ann Pruske Bernard RahmingLaura Maly Cynthia 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.

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.

Distributed Leadership

Student Learning Continuum

Teacher Learning Continuum

Mathematics Framework

Comprehensive Mathematics Framework

MMP Learning Team ContinuumStage 1

Learning TargetsStage 2

Alignment of State Framework & Math Program

Stage 3Common

Classroom Assessments

Stage 4Student Work

on CABS

Stage 5Descriptive Feedbackon 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

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

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 whatmathematical ideas they are learning in the lesson.

(4) Teachers canarticulate how the math lesson is aligned to district learning targets, state standards, and classroom assessments(CABS), and fits withinthe progression ofstudent learning.

(5) Teachers useClassroom 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 1Learning Targets

Stage 2Align State Framework and

Math Program

Stage 3Common CABS

Stage 4Student Work on CABS

Stage 5Descriptive Feedback on

CABSUnderstand 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.

“…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

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.

Lesson Planning with Formative Assessment Principles Date: ______________ Grade: ______________ Lesson: ______________

Part 1: Selecting and Setting Up a Mathematical Task This part contains four critical components that need to be considered when selecting and setting up a mathematical task.

Part 2: Supporting Student Exploration of the Task In this section, construct three questions that will develop the mathematics of the lesson. Be sure to consider the Depth of Knowledge to develop the questions. These questions could be used with students individually or in small groups.

Part 3: Summarizing the Mathematics In this section, construct a question that focuses on orchestrating a whole group discussion of the task that uses different solution strategies produced by the students that highlight the mathematics of the lesson.

1. Important Mathematics to Develop: 2. Learning Target & Descriptors: 3. Lesson Objective in Student Friendly Language: We are learning to… 4. Success Criteria: We know we are successful when…

Q1. Access background knowledge: Q2. Develop understanding of the mathematics by pushing student reasoning: Q3. Summarize the important mathematics in the lesson. This should tie back to the success criteria.

Q. Summarize the important mathematics in the lesson as a whole class discussion. This should tie back to the success criteria.

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

Post your chart paper with your learning intention and success criteria in student friendly language

Group discussion

Share Your Thinking

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

Forecast…

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 whatmathematical ideas they are learning in the lesson.

(4) Teachers canarticulate how the math lesson is aligned to district learning targets, state standards, and classroom assessments(CABS), and fits withinthe progression ofstudent learning.

(5) Teachers useClassroom 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 1Learning Targets

Stage 2Align State Framework

and Math Program

Stage 3Common CABS

Stage 4Student Work on CABS

Stage 5Descriptive Feedback

on CABSUnderstand 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.

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.

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’.”

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

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 FeedbackEvaluative

A

D

C

A

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 FeedbackDescriptive

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 FeedbackEffective

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?

Motivational2. I like how you completed the assignment.

Descriptive & Effective

Examples of Feedback

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

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 ActivityMotivational 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 More Formative

Mathematics Grade 4Classroom 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.

HoursWorked

MoneyEarned

2 $8

4 $16

7 $28

9 ?

Mathematics Grade 4Classroom 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.

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.

Mathematics Grade 4Classroom Assessment Based on Standards

Power CABS Identifier: “Number Pattern”Wisconsin Assessment Framework for Mathematics

Objective: A. Mathematical ProcessesDescriptors:• 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?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 Understandingo Reasoningo Computingo Engagemento Problem-solving

o Understandingo Reasoningo Computingo Engagemento Problem-solving

Identify misconceptions identified after analyzing student work:

o Understandingo Reasoningo Computingo Engagemento Problem-solving

Analyzing Student Work Samples

ThinkOn your own, think about what type of feedback is represented by each statement.

PairTurn to a partner and share your thoughts. Come to agreement on the type of feedback represented.

ShareShare with the whole group some of your thoughts and discussions.

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.

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:

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.”

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. . .

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.

Stage 1Learning Targets

Stage 2Alignment of

State Framework & Math Program

Stage 3Common Classroom

Assessments

Stage 4Student Work

on CABS

Stage 5Descriptive 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

Stage 1. Learning TargetsUnderstand importance of identifying and articulating big ideas in mathematics to bring consistency to a school’s math program.

1Weak

Teachers have not yet or barely started to

study or use learning targets.

2Emerging

Teachers are beginning to unpack and consider value and use of targets.

3Moving Forward

Teachers can articulate learning goals for their

students.

4Strong

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

Continuum Stage

What percent of the staff is at each stage?

Plan for School Professional WorkPlan to Document Evidence of

Impact on Classroom Practice or Teacher Instructional GrowthWeak 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

Learning Team Continuum of Work for Mathematics

Next steps…

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.

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

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