Supporting Rigorous Mathematics Teaching and Learning

© 2013 UNIVERSITY OF PITTSBURGH

Supporting Rigorous Mathematics Teaching and Learning

Using Academically Productive Talk Moves: Orchestrating a Focused Discussion

Tennessee Department of EducationMiddle School MathematicsGrade 6-8

Rationale

Mathematics reform calls for teachers to engage students in discussing, explaining, and justifying their ideas. Although teachers are asked to use students’ ideas as the basis for instruction, they must also keep in mind the mathematics that the class is expected to explore (Sherin, 2000, p. 125).

By engaging in a high-level task and reflecting on ways in which the facilitator structured and supported the discussion of mathematical ideas, teachers will learn that they are responsible for orchestrating discussions in ways that make it possible for students to own their learning, as well as for the teacher to assess and advance student understanding of knowledge and mathematical reasoning.


Session Goals

Participants will:

• learn about Accountable Talk® features and indicators and consider the benefit of all being present in a lesson;

• learn that there are specific moves related to each of the talk features that help to develop a discourse culture; and

• consider the importance of the four key moves of ensuring productive discussion (marking, recapping, challenging, and revoicing).

Accountable Talk® is a registered trademark of the University of Pittsburgh


Overview of Activities

Participants will:

• review the Accountable Talk features and indicators;

• identify and discuss Accountable Talk moves in a video; and

• zoom in for a more specific look at key moves for engaging in productive talk (marking, recapping, challenging, and revoicing).

TASKS

as they appear in curricular/ instructional materials

TASKS

as set up by the teachers

TASKS

as implemented by students

Student Learning

The Mathematical Tasks Framework

Stein, Smith, Henningsen, & Silver, 2000

Linking to Research/Literature: The QUASAR Project

Setting Goals Selecting TasksAnticipating Student Responses

Orchestrating Productive Discussion• Monitoring students as they work• Asking assessing and advancing questions• Selecting solution paths• Sequencing student responses• Connecting student responses via Accountable

Talk® discussionsAccountable Talk® is a registered trademark of the University of Pittsburgh


Accountable Talk Features and Indicators


Accountable Talk Discussion

• Study the Accountable Talk features and indicators.

• Turn and Talk with your partner about what you would expect teachers and students to be saying during an Accountable Talk discussion so that the discussion is accountable to:

− the learning community;− accurate, relevant knowledge; and− standards of rigorous thinking.


Accountable Talk Features and IndicatorsAccountability to the Learning Community

• Active participation in classroom talk.• Listen attentively.• Elaborate and build on each others’ ideas.• Work to clarify or expand a proposition.

Accountability to Knowledge• Specific and accurate knowledge.• Appropriate evidence for claims and arguments.• Commitment to getting it right.

Accountability to Rigorous Thinking• Synthesize several sources of information.• Construct explanations and test understanding of concepts.• Formulate conjectures and hypotheses.• Employ generally accepted standards of reasoning.• Challenge the quality of evidence and reasoning.


Solving and Discussing the Cognitive Demand of the

Light Bulb Task


The Structure and Routines of a Lesson

The Explore Phase/Private Work TimeGenerate Solutions

The Explore Phase/Small Group Problem Solving

1. Generate and Compare Solutions2. Assess and Advance Student Learning

Share, Discuss, and Analyze Phase of the Lesson1. Share and Model2. Compare Solutions3. Focus the Discussion on Key

Mathematical Ideas 4. Engage in a Quick Write

MONITOR: Teacher selects examples for the Share, Discuss,and Analyze Phase based on:• Different solution paths to the same task• Different representations• Errors • Misconceptions

SHARE: Students explain their methods, repeat others’ ideas, put ideas into their own words, add on to ideas and ask for clarification.REPEAT THE CYCLE FOR EACH

SOLUTION PATHCOMPARE: Students discuss similarities and difference between solution paths.FOCUS: Discuss the meaning of mathematical ideas in each representationREFLECT: Engage students in a Quick Write or a discussion of the process.

Set Up the TaskSet Up of the Task


Engaging in a Lesson: The Light Bulb Task

• Solve the task.

• Discuss your solutions with your peers.

• Attempt to engage in an Accountable Talk discussion when discussing the solutions. Assign one person in the group to be the observer. This person will be responsible for reporting some of the ways in which the group is accountable to:

− the learning community;− accurate, relevant knowledge; and − standards of rigorous thinking.


Engaging in a Lesson: The Light Bulb Task

Alazar Electric Company sells light bulbs to big box stores – the big chain stores that frequently buy large numbers of bulbs in one sale. They sample their bulbs for defects routinely. A sample of 96 light bulbs consisted of 4 defective ones. Assume that today’s batch of 6,000 light bulbs has the same proportion of defective bulbs as the sample. Determine the total number of defective bulbs made today. The big businesses they sell to accept no larger than a 4% rate of defective bulbs. Does today’s batch meet that expectation? Explain how you made your decision.


Reflecting on Our Engagement in the Lesson

The observer should share some observations about the group’s engagement in an Accountable Talk discussion.


Reflecting on Our Engagement in the Lesson

• In what ways did small groups engage in an Accountable Talk discussion?

• In what ways did we engage in an Accountable Talk discussion during the group discussion of the solutions?


Determining the Cognitive Demand of the Task:The Light Bulb Task


Determining the Cognitive Demandof the Task

Refer to the Mathematical Task Analysis Guide.Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A., 2000. Implementing standards-based mathematics

instruction: A casebook for professional development, p. 16. New York: Teachers College Press.

How would you characterize the Light Bulb Task in terms of its cognitive demand? (Refer to the indicators on the Task Analysis Guide.)

The Mathematical Task Analysis Guide

Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2000) Implementing standards-based mathematics instruction:

A casebook for professional development, p. 16. New York: Teachers College Press.


Accountable Talk Moves


Accountable Talk Moves

Examine the ways in which the moves are grouped based on how they:

• support accountability to the learning community; • support accountability to knowledge; and • support accountability to rigorous thinking.

Consider:In what ways are the Accountable Talk categories similar? Different?

Why do you think we need a category called “To Ensure Purposeful, Coherent, and Productive Group Discussion”?


Accountable Talk: Features and IndicatorsAccountability to the Learning Community

• Active participation in classroom talk.• Listen attentively.

• Elaborate and build on each others’ ideas.

• Work to clarify or expand a proposition.

Accountability to Knowledge• Specific and accurate knowledge.• Appropriate evidence for claims and arguments.

• Commitment to getting it right.

Accountability to Rigorous Thinking• Synthesize several sources of information.• Construct explanations and test understanding of concepts.

• Formulate conjectures and hypotheses.

• Employ generally accepted standards of reasoning.

• Challenge the quality of evidence and reasoning.

Accountable Talk MovesTalk Move Function Example

To Ensure Purposeful, Coherent, and Productive Group Discussion

Marking Direct attention to the value and importance of a student’s contribution.

That’s an important point.

Challenging Redirect a question back to the students, or use students’ contributions as a source for further challenge or query.

Let me challenge you: Is that always true?

Revoicing Align a student’s explanation with content or connect two or more contributions with the goal of advancing the discussion of the content.

S: 4 + 4 + 4.

You said three groups of four.

Recapping Make public in a concise, coherent form, the group’s achievement at creating a shared understanding of the phenomenon under discussion.

Let me put these ideas all together.What have we discovered?

To Support Accountability to CommunityKeeping the Channels Open

Ensure that students can hear each other, and remind them that they must hear what others have said.

Say that again and louder.Can someone repeat what was just said?

Keeping Everyone Together

Ensure that everyone not only heard, but also understood, what a speaker said.

Can someone add on to what was said?Did everyone hear that?

Linking Contributions

Make explicit the relationship between a new contribution and what has gone before.

Does anyone have a similar idea?Do you agree or disagree with what was said?Your idea sounds similar to his idea.

Verifying and Clarifying

Revoice a student’s contribution, thereby helping both speakers and listeners to engage more profitably in the conversation.

So are you saying..?Can you say more? Who understood what was said?


To Support Accountability to Knowledge

Pressing for Accuracy

Hold students accountable for the accuracy, credibility, and clarity of their contributions.

Why does that happen?Someone give me the term for that.

Building on Prior Knowledge

Tie a current contribution back to knowledge accumulated by the class at a previous time.

What have we learned in the past that links with this?

To Support Accountability toRigorous Thinking

Pressing for Reasoning

Elicit evidence to establish what contribution a student’s utterance is intended to make within the group’s larger enterprise.

Say why this works.What does this mean?Who can make a claim and then tell us what their claim means?

Expanding Reasoning

Open up extra time and space in the conversation for student reasoning.

Does the idea work if I change the context? Use bigger numbers?

Accountable Talk Moves (continued)


Reflecting on Talk Moves

What comes to mind when anaylzing the following Accountable Talk moves:

• marking;• recapping;• challenging; and• revoicing?

Why are these moves important in lessons?


Application to Practice

• What will you keep in mind when attempting to use Accountable Talk moves during a lesson? What role does talk play?

• What does it take to maintain the demands of a cognitively demanding task during the lesson so that you have a rigorous mathematics lesson?


Bridge To Practice

• Audio or video record yourself teaching a lesson.

• Analyze the lesson for Accountable Talk Moves. Journal as you reflect about the lesson and determine which Accountable Talk moves you used during that class and the frequency of each move.

• Which one(s) do you use most often? Why? Which one(s) do you use the least? Why? Are your moves organic or do they seem forced? Which AT moves would help improve that lesson? Why?

Documents

Supporting Rigorous Mathematics Teaching and Learning