All Teachers Reaching All Students

Math Teaching Specialists

Banking Day

March 14, 2011

Pattern Time

What is Size 7? On your own, think about how you would

approach this problem. With a partner

Share your strategies Determine the Size 7 Communicate clearly how you arrived at your solution

As a table group, everyone shares their strategy Record all strategies Be prepared to share out whole group

Logistics

IntroductionsAnnouncementsNormsAgendaParking Lot

Learning Intention We are learning to understand the connections

between the Principles of Formative Assessment and math instructional practices.

Success CriteriaWe will know we are successful when we can… articulate the connections between the Principles of

Formative Assessment and math instructional practices.

develop a plan of action to embed formative assessment principles into our math instructional practices.

Comprehensive Mathematics Framework

Common Core State Standards

Standards for Mathematical Practice

K – 8 Grade level standardsHigh School standards

“conceptual categories”

Standards for Mathematical Practice3. Construct viable arguments and critique the reasoning of others.Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Linking the Mathematical Practice Standard to the Classroom What would this practice look like in a

classroom?

Students would be…

Teachers would be…

What is Formative Assessment?

ThinkOn your own, think about what formative assessment means to you….

PairTurn to a partner and share your thoughts. Discuss similarities and differences…

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

Instructional CycleInformed by Assessment

Assessment

Plan InstructionContent/process/

product

Model

Guided practiceReadiness/interest/

Learning Inventory

PracticeAnd

Application

Know your students

Rick DuVall

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

What Are the Purposes of Assessment for the TEACHER?

Assessment for Learning

Formative assessment

Supports learning by providing information about what a child knows, understands, and is able to do. where the learners are in their learning and how to

achieve learning goals.

Assists teacher in making instructional decisions for the individual child and the whole class.

What Are the Purposes of Assessment for the STUDENT?

Assessment for Learning

Formative assessmentSupports learning by providing information about

what a child knows, understands, and is able to do. where the learners are in their learning and how to

achieve learning goals.

Encourages child to identify their areas of weakness or strength so they can focus on their efforts more precisely.

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.”

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.

What does a Math Block Look Like?

Problem-centered teaching opens the mathematics classroom to exploring, conjecturing, reasoning, and communicating.

Lappan, Fey, et al., 2006

Building with Toothpicks

Learning Intention We are learning to describe a symbolic rule

for a given pattern.

Success CriteriaWe will know we are successful when we can

communicate clearly our thought process in developing a symbolic rule.

“…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

Formative Assessment Strategies Learning Intentions

Help students make better decisions about how to go about a task. Emphasizes what the students will learn rather than what they will do. “What is the Big Math Idea?”

What do I want students to know…? What do I want students to understand…?

...as a result of the learning and teaching activities.

Success Criteria Criteria for assessment. Helps teachers and students decide whether the learning intention has

been achieved Helps teachers and students determine next steps for learning

Principles of Assessment for Learning Learning Intentions and Success Criteria support which Principles?

Building with Toothpicks On your own, think about how you would approach this

problem

Use a pattern from the shapes above to determine the perimeter of the fifth shape in the sequence.

With a partner Share your strategies. Work together to determine the perimeter of the fifth shape. Discuss how you arrived at your solution.

“Sharing of learning intentions is only the first step in the process of formative assessment, leading to pupil self-evaluation and teacher or peer feedback after the work is completed.”

Shirley Clark, 2001

Formative Assessment Strategy Strategic use of questioning

Not only a pedagogical tool but a deliberate way for teachers to find out what students know, understand and are able to do.

Provides teachers with the opportunity to identify and correct misconceptions and gaps in knowledge.

Also identifies the need for extension work for those children whose knowledge and skills base demand it.

Informs the teacher’s planning and selection of teaching strategies to move students from where they are in relationship to the learning target and where they need to go.

Principles of Assessment for Learning Strategic use of questioning supports which Principles?

Strategic Use of Questioning Think about the questions you or your

group were asked. At your table, discuss what questions we

used to find out what “students” know, understand, and are able to do.

What questions would you ask students?With a partner, write questions for Building

with Toothpicks that would: access background knowledge push student reasoning summarize math learning

More Building with Toothpicks

On your own write a formula that you could use to find the perimeter of any Shape n.

Working with your partner Explain how you each found your formulaOn blank piece of paper, record your formulas

and explanations of how you arrived at your solutions

Be prepared to share your solutions

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

Motivational Goal is to make the learner feel good.

Evaluative Goal is to measure student achievement with a score or a

grade.

Descriptive Goal is to improve student achievement by telling the learner

how to move forward in the learning process.

Effective Goal is to get student to internalize the effective feedback to use

the suggested strategies independently on future work.

A

D

C

A

Formative Assessment Strategy

Effective teacher feedback Focuses on Success Criteria and tells children what

they have achieved, where they need to improve. Provides specific suggestions of how that

improvement might be achieved.

Principles of Assessment for Learning Effective teacher feedback supports which Principles?

Formative Assessment Strategy Peer feedback

Children offer each other advice about their work which references

what is done well in relation to the Success Criteria. what still needs to be done in order to achieve the

Success Criteria or learning target. specific suggestions on how the improvement might

be achieved.

Principles of Assessment for LearningPeer feedback supports which Principles?

Peer Feedback Strategies

Plus, minus and what’s next? Two stars and a wish

Thinking Hats

Traffic lights

Trying Peer Feedback With your partner, decide which peer

feedback strategy you would like to try. Find another partner pair to try out your

strategy. As a group of 4

Share your work on Building with ToothpicksGive feedback Make adjustments to your work as needed

Formative Assessment Strategy Using models or exemplars

Teachers demonstrate for students how they can match the work of a peer to an exemplar which most closely resembles its qualities.

Students explain to the peer why they have selected this particular exemplar and, using other exemplars, explain what the peer needs to do in order to improve.

Exemplars of various products can be displayed in the classroom for use both by individuals to self-assess and also by peers to provide feedback. Students use the exemplars to help them articulate what changes they need to make to their own work in order to achieve the success criteria.

Set learning targets based on what they still need to learn.

Principles of Assessment for Learning Using models or exemplars supports which Principles?

Learning Intention We are learning to understand the connections

between the Principles of Formative Assessment and math instructional practices.

Success CriteriaWe will know we are successful when we can… articulate the connections between the Principles of

Formative Assessment and math instructional practices.

develop a plan of action to embed formative assessment principles into our math instructional practices.

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. . .

Lunch Time

What are the Sources of Evidence for Assessment?

“… Whatever conclusions we may make about children’s thinking must be based on observations [and] or products.”

Bell, et al., 2007

Wrapping It Up

With your group of four, prepare your final presentation of Building with Toothpicks

Be sure to includeYour work around “What is the perimeter for

the fifth shape?”Your work around “Write a formula that you

could use to find the perimeter of any Shape n.”

Carousel Each table group passes their poster clockwise

to the next table group when the facilitator calls “switch”.

Each person takes individual notes about each poster around these ideas

What question do you have about the strategy they used to build the formula and the written formula?

What “aha” did you have about their strategy or written formula?

How was their strategy or written formula similar to or different from yours?

What other comments or questions do you have for the group about their poster?

What Did We Learn? What question do you have about the strategy

they used to build the formula and the written formula?

What “aha” did you have about their strategy or written formula?

How was their strategy or written formula similar to or different from yours?

What other comments or questions do you have for the group about their poster?

Formative Assessment Strategy Student self-assessment

Understand the Learning Intention and Success Criteria Use the Success Criteria to evaluate their learning and what

they still need to learn Act on feedback received from teacher and peers Set learning targets based on what they still need to learn Engage in oral reflections. Whole class or small group

reflections are often more useful than written reflections.

Principles of Assessment for Learning Student self-assessment supports which Principles?

Student Self-Assessment Strategies

Traffic Lighting ‘I can explain this aspect to someone else.’ (green light) ‘I think I understand this aspect but I’d have difficulty explaining it

to someone else.’ (yellow light) ‘I don’t understand this aspect.’ (red light)

Reflective & Growth activities What have you learned? What did you find easy about learning to …? How would you do things differently next time? What did you find difficult while you were learning to …? What helped you when something got tricky …? How would you change this activity for another group/class who

were learning to…?

Self Assessment

What helped you when something got tricky as you worked on the task or critiqued the reasoning of others?

Building with Toothpicks Learning Intention

We are learning to describe a symbolic rule for a given pattern.

Success CriteriaWe will know we are successful when we can

communicate clearly our thought process in developing a symbolic rule.

Formative Assessment Strategies Identifying the big math idea

Unpacking the standardsCCSS Grade Level Standards

CCSS 6-8 Domain Progression Expressions and Equations

Principles of Assessment for Learning Identifying the big math ideas and unpacking the

standards support which Principles?

Content StandardsK-8 Structure Domain: Expressions and Equations (6.EE)

Cluster: Apply and extend previous understandings of arithmetic to algebraic expressions.

Standard 1: Write and evaluate numerical expressions involving whole-number exponents. (6.EE.1)

Middle Grades Domains

Ratio-Proportional Relationships6-7

The Number System 6-8

Expressions & Equations 6-8

Functions 8

Geometry 6-8

Statistics & Probability 6-8

Unpacking the Content Standard

What is the big math idea in the activity?

What standards did we address? Individually read Grades 6-8 Domain

Progression for Expressions and EquationsWith your group, discuss questions and

highlight key ideas in this standard.Whole group discussion

“Asking a student to understand something means asking a teacher to assess whether the student has understood it. But what does mathematical understanding look like? One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from.”

Introduction to Common Core State Standards, 2010

District DefinitionDifferentiated Instruction is a concept that makes it possible to maximize learning for ALL students. It is a collection of instructionally intelligent strategies based on student-centered, best practices that make it possible for teachers to meaningfully respond to the needs of diverse learners. It is made possible by modifying the content, process and/or product of instruction of a particular student or small group of students (typically to scaffold and extend learning), rather than the more typical pattern of teaching the class as though all individuals in it were basically the same.  Differentiated instruction is an approach to ensuring all children achieve to the same high standards; instructional approaches are varied, not the expectations or the standards.

Next steps…

Planning Time

Decide which formative assessment principles you want to embed into your math instructional practices this month.

Develop your plan of action

Tools of the Trade Comprehensive Mathematics Framework Standards for Mathematical Practice Common Core State Standards Developing Effective Questions Types of Feedback Peer Feedback Student Self-Assessment

Lesson Planning with Formative Assessment

Planning Time

Decide which formative assessment principles you want to embed into your math instructional practices this month.

Develop your plan of action When and how will you implement your strategy? What additional information do you need? How can your MTL support you? How can your MTS support you? Plan a lesson embedding your strategy

Learning Intention We are learning to understand the connections

between the Principles of Formative Assessment and math instructional practices.

Success CriteriaWe will know we are successful when we can… articulate the connections between the Principles of

Formative Assessment and math instructional practices.

develop a plan of action to embed formative assessment principles into our math instructional practices.

3-2-1 Take AwaySchool:

3 ideas you are walking away with from this session are…

2 ideas you will take back to your school to share with other grade level teachers are…

1 idea you will take back to your classroom to try with your students is…

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