supporting rigorous mathematics teaching and learning

LEARNING RESEARCH AND DEVELOPMENT CENTER © 2013 UNIVERSITY OF PITTSBURGH

Supporting Rigorous Mathematics Teaching and Learning

Using Academically Productive Talk Moves: Orchestrating a Focused Discussion

Tennessee Department of EducationElementary School MathematicsGrade 3

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.

LEARNING RESEARCH AND DEVELOPMENT CENTER © 2013 UNIVERSITY OF PITTSBURGHLEARNING RESEARCH AND DEVELOPMENT CENTER © 2013 UNIVERSITY OF PITTSBURGH 3

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

• align CCSS and essential understandings (EUs) to a fraction task 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

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

LEARNING RESEARCH AND DEVELOPMENT CENTER © 2013 UNIVERSITY OF PITTSBURGH 7

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 Bubble

Gum 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 Representation.REFLECT: 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 Bubble Gum 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 Bubble Gum Task

4 friends each bought a roll of bubble gum tape.

• Carlos chewed of his gum.

• Helen chewed of her gum.

• Jamal chewed of his gum.

• Lizbeth chewed of her gum.

1. Use the number line below to illustrate:

Which friend chewed the most gum?

Which friend chewed the smallest piece?

Which 2 friends chewed the same sized piece?

2. Explain how you can use to help you determine the value of and when each fraction refers to the same whole.

Adapted from DMI Making Meaning for Operations, 2007


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?


Aligning the CCSS to the Bubble Gum Task

• Study the Grade 3 and 4 CCSS for Mathematical Content within the Number and Operations-Fractions domain.

Which standards are students expected to demonstrate when solving the fraction task?

• Identify the CCSS for Mathematical Practice required by the written task.

The CCSS for Mathematical Content: Grade 3

Common Core State Standards, 2010, p. 24, NGA Center/CCSSO

Number and Operations—Fractions 3.NFDevelop understanding of fractions as numbers.

3.NF.A.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

3.NF.A.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram.

3.NF.2a Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

3.NF.A.2b Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.



Number and Operations—Fractions 3.NFDevelop understanding of fractions as numbers.

3.NF.A.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

3.NF.A.3a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

3.NF.A.3b Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.

3.NF.A.3c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.

3.NF..A3d Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.



Number and Operations—Fractions 4.NFExtend understanding of fraction equivalence and ordering.

4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.



Number and Operations—Fractions 4.NFBuild fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

4.NF.B.3a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.



Number and Operations—Fractions 4.NFBuild fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

4.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

4.NF.B.4a Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x(1/4).

4.NF.B.4b Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 x (2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a)/b.)

4.NF.B.4c Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

The CCSS for Mathematical Practice

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Common Core State Standards, 2010, p. 6-8, NGA Center/CCSSO


Determining the Cognitive Demand of the Task:

The Bubble Gum 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 Bubble Gum 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.


The Bubble Gum Task:A Doing Mathematics Task

• Requires complex and non-algorithmic thinking (i.e., there is not a predictable, well-rehearsed approach or pathway explicitly suggested by the task, task instructions, or a worked-out example).

• Requires students to explore and to understand the nature of mathematical concepts, processes, or relationships.

• Demands self-monitoring or self-regulation of one’s own cognitive processes.

• Requires students to access relevant knowledge and experiences and make appropriate use of them in working through the task.

• Requires students to analyze the task and actively examine task constraints that may limit possible solution strategies and solutions.

• Requires considerable cognitive effort and may involve some level of anxiety for the student due to the unpredictable nature of the solution process required.


Accountable Talk Moves


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 Representation.REFLECT: Engage students in a Quick Write or a discussion of the process.

Set Up the TaskSet Up of the Task


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)


Reflection Question

As you watch the short video segment, consider what students are learning and where you might focus the discussion in order to discuss mathematical ideas listed in the CCSS.

Identify:• the specific Accountable Talk moves used by the

teacher; and • the purpose that the moves served.

Mark times during the lesson when you would call the lesson academically rigorous.


The Bubble Gum Lesson Context• Visiting Teacher: Victoria Bill• School #26, Grade 3 • Paterson Public Schools, New Jersey

The teacher wants students to use a linear model of fractions and to understand how a benchmark fraction, such as one-half, can help students think about and compare fractions. The teacher also wants to expose students to the benefit of finding common denominators when comparing fractions.

The students work privately for 5 minutes and then they work in small groups to discuss the solution paths. While students work, the teacher circulates, asking assessing and advancing questions. As the teacher is asking assessing and advancing questions, students are struggling to use the number line model and as a result, it is difficult to advance student learning. The Engage phase is shortened and instead the teacher co-constructs a solution path with the students.


Norms for Collaborative Study

The goal of all conversations about episodes of teaching (or artifacts of practice in general) is to advance our own learning, not to “fix” the practice of others.

In order to achieve this goal, the facilitator chooses a lens to frame what you look at and to what you pay attention. Use the Accountable Talk features and indicators when viewing the lesson.

During this work, we:• agree to analyze the episode or artifact from the identified

perspective;• cite specific examples during the discussion that provide

evidence of a particular claim;• listen to and build on others’ ideas; and• use language that is respectful of those in the video and in the

group.

The Bubble Gum Task 4 friends each bought a roll of bubble gum tape.

• Carlos chewed of his gum.

• Helen chewed of her gum.

• Jamal chewed of his gum.

• Lizbeth chewed of her gum.

1. Use the number line below to illustrate:

Which friend chewed the most gum?

Which friend chewed the smallest piece?

Which two friends chewed the same sized piece?

2. Explain how you can use to help you determine the value of and when each fraction refers to the same whole.

Adapted from DMI Making Meaning for Operations, 2007


Reflecting on the Accountable Talk Discussion

Step back from the discussion. What are some patterns that you notice?

What mathematical ideas does the teacher want students to discover and discuss?


Essential Understandings

Study the essential understandings the teacher considered in preparation for the Share, Discuss, and Analyze phase of the lesson.


Essential UnderstandingsEssential Understanding CCSS

Comparing Fractions with Like DenominatorsFractions with the same size pieces, or common denominators, can be compared with each other because the size of the pieces is the same.

3.NF.A.3d

Using Benchmarks to Make ComparisonsComparison to known benchmark quantities can help determine the relative size of a fractional piece because the benchmark quantity can be seen as greater, less than, or the same as the piece.

3.NF.A.2a

Recognizing Equivalent FractionsWhen creating equivalent fractions, all of the pieces in a whole are subdivided or partitioned, thus the amount of pieces named in the numerator are automatically partitioned in the same way. What is created is an equivalent fraction.

3.NF.A.3a

Making Equivalent FractionsWhen you multiply a fraction by a fraction equivalent to one, a/a (a > 1), the denominator is partitioned into a new designated number of pieces that are smaller in size but larger in the number of pieces than the original; as a result of partitioning all of the pieces, those pieces referenced by the numerator end up being partitioned in the same way.

3.NF.A.3b


Characteristics of an Academically Rigorous Lesson

This task is a cognitively demanding task; however, it may not necessarily end up being an academically rigorous task.

What do we mean by this statement?


Academic Rigor in a Thinking Curriculum

The principle of learning, Academic Rigor in a Thinking Curriculum, consists of three features:

• A Knowledge Core• High-Thinking Demand• Active Use of Knowledge

In order to determine if a lesson has been academically rigorous, we have to determine the degree to which student learning is advanced by the lesson.

What do we have to hear and see in order to determine if the lesson was academically rigorous?


Essential UnderstandingsEssential Understanding CCSS

Comparing Fractions with Like DenominatorsFractions with the same size pieces, or common denominators, can be compared with each other because the size of the pieces is the same.

3.NF.A.3d

Using Benchmarks to Make ComparisonsComparison to known benchmark quantities can help determine the relative size of a fractional piece because the benchmark quantity can be seen as greater, less than, or the same as the piece.

3.NF.A.2a

Recognizing Equivalent FractionsWhen creating equivalent fractions, all of the pieces in a whole are subdivided or partitioned, thus the amount of pieces named in the numerator are automatically partitioned in the same way. What is created is an equivalent fraction.

3.NF.A.3a

Making Equivalent FractionsWhen you multiply a fraction by a fraction equivalent to one, a/a (a > 1), the denominator is partitioned into a new designated number of pieces that are smaller in size but larger in the number of pieces than the original; as a result of partitioning all of the pieces, those pieces referenced by the numerator end up being partitioned in the same way.

3.NF.A.3b

Five Representations

Adapted from Lesh, Post, & Behr, 1987


Focusing on Key Accountable Talk Moves

The Bubble Gum Task


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)


Focusing on Accountable Talk Moves

Read the description of each move and study the example that has been provided for each move.

What is distinct about each of the moves?• Revoice student contributions; • Mark significant contributions; • Challenge with a counter-example; or • Recap the components of the lesson.


Revoicing

• Extend a student’s contribution.• Connect a student’s contribution to the text or to

other students’ contributions. Align content with an explanation. Add clarity to a contribution. Link student contributions to accurate

mathematical vocabulary. Connect two or more contributions to advance

the lesson.


An Example of Revoicing

S: and then and then .

Halfway between and is .

T: So I see , , and . So the

should not be written on

the number line here. What

is the pattern?


Marking

Explicitly talk about an idea.• Highlight features that are unique to a situation.• Draw attention to an idea or to alternative ideas.


An Example of Marking

S: is the same as . When you cut the number line into 4 parts and then you cut it into 8 parts, you end up in the same place on the number line.

T: You’re right, is equivalent to . They are both located on the same point on the number line.


Recapping

Summarize or retell.• Make explicit the large idea.• Provide students with a holistic view of the

concept.


Student Work: Recapping Example


An Example of Recapping

T: How do you know who ate the most bubble gum?S: is the most ‘cause it is one away from 1.S: is one away from 1 but it is a bigger one away from the 1.S: is less than so is more because it is closer to the 1. All

you need is more and you have 1. S: is a lot more away from 1.T: So what you are saying is is greater than because is

one-sixth away from 1 and is one-fourth away from 1. Since a sixth is smaller than a fourth, this means that is closer to 1.


Challenging

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

• Share a counter-example and ask students to compare problems.

• Question the meaning of the math concept.


An Example of Challenge

T: Now that you know that is closest to 1, what if I told you we had of a piece of bubble gum? Which would be longer, or , and how do you know?


Appropriation

The process of appropriation is reciprocal and

sequential. • If appropriation takes place, the child transforms

the new knowledge or skill into an action in a new and gradually understood activity.

• What would this mean with respect to classroom discourse? What should we expect to happen in the classroom?


Orchestrating Discussions

Read the segments of transcript from the lesson.Decide if examples 1 – 4 illustrate marking, recapping, challenging, or revoicing.

Be prepared to share your rationale for identifying a particular discussion move.

Write the next discussion move for examples 5 and 6 and be prepared to share your move and your rationale for writing the move.


Reflecting on Talk Moves

What have you learned about:• 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• Choose a high-level task. • Identify the key mathematical ideas that are the goals of

the lesson. • Anticipate student responses. • Plan an Accountable Talk discussion that utilizes the

moves of marking, challenging, recapping, and revoicing.

• Record or have a colleague scribe the Share, Discuss, and Analyze phase of the lesson.

• Write a reflection on how planning and using these moves impacted student learning.

• Bring back: a copy of the task, your planning notes, and written reflection.

supporting rigorous mathematics teaching and learning

Documents

mathematical reasoning

students ideas

mathematical practice

mathematical tasks

accountable talk discussions

accountable talk moves

sense of mathematical

means of developing