Supporting Rigorous Mathematics Teaching and Learning

Supporting Rigorous Mathematics Teaching and Learning
Strategies for Scaffolding Student Understanding: Academically Productive Talk and the Use of Representations Tennessee Department of Education Elementary School Mathematics Grade 2 Overview of the Module: In this module, teachers will consider how Accountable Talk discussions are a means of developing students’ understanding of the CCSS for Mathematical Content and the CCSS for Mathematical Practice. Teachers will learn about the power of engaging students in Accountable Talk discussions in which evidence of accountability to the learning community, to knowledge, and to rigorous thinking exists. Accountability in all three of these areas is the means by which students make sense of mathematical ideas while teachers assess student understanding of mathematical content and practices. Talk (specifically, Accountable Talk) is the means by which teachers can support students as they work on challenging tasks without taking over the process of thinking for them (NCTM, 2000). Materials: Slides with notes pages Facilitator’s overview of module Participant handouts The CCSS DVD of the The Stickers Task with Brandy Hays

Rationale Teachers provoke students’ reasoning about mathematics through the tasks they provide and the questions they ask. (NCTM, 1991) Asking questions that reveal students’ knowledge about mathematics allows teachers to design instruction that responds to and builds on this knowledge. (NCTM, 2000) Questions are one of the only tools teachers have for finding out what students are thinking. (Michaels, 2005) Today, by analyzing a classroom discussion, teachers will study and reflect on ways in which Accountable Talk® (AT) moves and the use of representations support student learning and help teachers to maintain the cognitive demand of a task. Directions: Read the rationale or paraphrase the ideas in the rationale. Accountable Talk is a registered trademark of the University of Pittsburgh.

Session Goals Participants will learn about:
Accountable Talk moves to support the development of community, knowledge, and rigorous thinking; Accountable Talk moves that ensure a productive and coherent discussion and consider why moves in this category are critical; and representations as a means of scaffolding student learning. Directions: Give participants a minute to read the rationale slide. or Paraphrase the rationale, if desired. (SAY) Engaging students in rigorous academic tasks accompanied by Accountable Talk moves will promote effective teaching. By seeing how students develop an understanding of mathematical ideas and strategies, teachers can prepare ways to advance student learning of the mathematical ideas.

Overview of Activities
Participants will: analyze and discuss Accountable Talk moves; engage in and reflect on our engagement in a lesson in relationship to the CCSS; analyze classroom discourse to determine the Accountable Talk moves used by the teacher and the benefit to student learning; design and enact a lesson, making use of the Accountable Talk moves; and learn and apply a set of scaffolding strategies that make use of the representations. Directions: Read the activities.

Review the Accountable Talk Features and Indicators: Learn Moves Associated With the Accountable Talk Features (SAY) Before we watch a video lesson in which a teacher is attempting to engage students in an Accountable Talk discussion, let’s look at the Accountable Talk moves.

Linking to Research/Literature: The QUASAR Project
The Mathematical Tasks Framework TASKS as set up by the teachers TASKS as they appear in curricular/ instructional materials TASKS as implemented by students Student Learning (SAY) Look at the Mathematical Task Analysis Guide. We will start with a high-level task because it isn’t worth focusing on Accountable Talk moves unless you are using a high-level task. We will talk about the goals for the lesson and then we will focus on the Accountable Talk moves that can be used with the task in order to prevent us from lowering the cognitive demand of the task. Stein, Smith, Henningsen, & Silver, 2000

The Structures and Routines of a Lesson
MONITOR: Teacher selects examples for the Share, Discuss, and Analyze Phase based on: Different solution paths to the same task Different representations Errors Misconceptions Set Up of the Task Set Up the Task The Explore Phase/Private Work Time Generate Solutions The Explore Phase/Small Group Problem Solving Generate and Compare Solutions Assess and Advance Student Learning 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 PATH COMPARE: Students discuss similarities and differences between solution paths. FOCUS: Discuss the meaning of mathematical ideas in each representation. REFLECT by engaging students in a quick write or a discussion of the process. Share, Discuss, and Analyze Phase of the Lesson 1. Share and Model 2. Compare Solutions 3. Focus the Discussion on Key Mathematical Ideas 4. Engage in a Quick Write Directions: Our discussion in this module will focus on the Share, Discuss, and Analyze Phase of the lesson. To remind you, this phase of the lesson follows the Explore Phase of the lesson. The teacher has a sense of the different solution paths used by students as s/he enters this part of the lesson. Today we will discuss ways in which the teacher can facilitate this portion of the lesson.

Accountable Talk Discussion
Review the Accountable Talk features and indicators. Turn and Talk with your partner about what you recall about each of the Accountable Talk features. Accountability to the learning community. Accountability to accurate, relevant knowledge. Accountability to discipline-specific standards of rigorous thinking. (SAY) Turn and Talk with your partner. What do you recall about the features of an Accountable Talk discussion? Probing Facilitator Question with Possible Responses: What would an Accountable Talk discussion sound like? Students listen to each other. Students add on to each other. Students ask questions. All students speak during the lesson and their talk builds on one another’s contributions.

Accountable Talk Features and Indicators
Accountability to the Learning Community Active participation in classroom talk. Listen attentively. Elaborate and build on each other’s 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. Directions: Direct participants’ attention to the Accountable Talk Features and Indicators in their participant handout. Give them an opportunity to independently read the features and indicators. Probing Facilitator Questions and Possible Responses: (10 min.) Who can recall why the authors claim that evidence of all three Accountable Talk features must be present? Whoever talks the most learns the most. Students need to be the ones talking because the teacher can assess what they know or don’t know. It is the students’ knowledge and reasoning that we need to hear, not just any kind of talk. Why is the press for rigorous thinking the MOST IMPORTANT feature of Accountable Talk discussions, and yet you can’t have a press for rigorous thinking and reasoning without an accountability to the community and the knowledge core? What do we mean by this? It is difficult for students to share their thinking and reasoning so often students co-construct or there has to be a period of time in which students make sense of the ideas before they are able to share their reasoning.

Accountable Talk Moves
Consider: In what ways are the Accountable Talk moves different in each of the categories? – Support Accountability to Community – Support Accountability to Knowledge – Support Accountability to Rigorous Thinking There is a fourth category called “To Ensure Purposeful, Coherent, and Productive Group Discussion.” Why do you think we need the set of moves in this category? Directions: Give individuals 5 minutes to study the Accountable Talk moves. Then engage the group in a discussion of the questions on the slide. Probing Facilitator Questions and Possible Responses: In what ways are the Accountable Talk categories similar? Different? All of the moves are talk moves. The community moves prompt students to listen to each other. The category related to encouraging productive talk seems different than the other three categories. What is different about the set of community moves? One move is about linking student contributions. The first two moves differ from each other because one is about making sure students just hear each other, and the other is about asking students to add on to others’ contributions.

Accountable Talk Moves
Function Example To Ensure Purposeful, Coherent, and Productive Group Discussion Marking Direct attention to the value and importance of a student’s contribution. It is important to say describe to compare the size of the pieces and then to look at how many pieces of that size. 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. You said 3, yes there are three columns and each column is 1/3 of the whole 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 Community Keeping 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? (SAY) What do you notice about the Accountable Talk moves? Probing Facilitator Questions and Possible Responses: Do you agree or disagree with the way the Accountable Talk moves are grouped? It is really helpful to have all of the talk moves related to a feature together. It is easier to compare the community moves because they are grouped. We can see that there are two reasoning prompts. One is a press for reasoning and one expands the reasoning. One precedes the other. What do you notice about the two moves under rigor? One is expanding reasoning and one is pressing for it. Why do you think we need a category called “To Ensure Purposeful, Coherent, and Productive Group Discussion”? What is the difference between recapping and marking? Marking is a critical move because it is the teacher’s method of making sure students know the knowledge or reasoning that is correct or accurate. Recapping, when done by the teacher or the student, is a means of summarizing or bringing ideas together in a more concise way. Challenging is one of those moves that we have to use carefully. What do we mean by this? Challenging is a move that a teacher or student will make later in the lesson when the knowledge is sound enough that students can agree or disagree with the challenge. Why are the moves in this category so important?

To Support Accountability to Knowledge To Support Accountability to
Accountable Talk Moves (continued) 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 to Rigorous 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?

Five Representations of Mathematical Ideas What role do the representations play in a discussion?
Pictures Written Symbols Manipulative Models Real-world Situations Oral & Written Language (SAY) What role does the use of representations play when the lesson is enacted? Is it important to reference a context? To refer to manipulatives? We will return to this question after we watch the video. My questions that I will be asking are: Why are the Accountable Talk moves not enough to support students? Why do we need to move between the representation when using Accountable Talk moves. Modified from Van De Walle, 2004, p. 30

Engage and Reflect on a Lesson The Sticker Task
(SAY) In preparation for analyzing the classroom discourse, we will discuss the Stickers Task and consider the different ways that students might solve the task. We will not engage in the task as learners because it is not an adult task. We will solve the task and anticipate possible solution paths that students might use when solving the task.

The Sticker Task Type of Sticker Jackson Adela Sports Stickers 153 149 Animal Stickers 274 269 Sparkle Stickers 296 281 Use what you know about place value to help you solve for Jackson’s total number of stickers. Show and explain how you used place value to help you solve for the total. Use what you know about place value to help you solve for Adela’s total number of stickers. Show and explain how you used place value to help you solve for the total. Jackson claims that he can look at the amounts and move them around in order to make amounts that are easier to add. How might he have changed the amounts without changing the total? How do the changes make the problem easier to solve? Directions: How might students solve this task? = ___ = = 500 = = 180 = = 19 = = 699 = 210 = 13 = 723 _____________ OR = = = 725 = 700 Take off two because we rounded up. = 723 So what is the point? It is easier to round and make hundreds and tens. It is easy to work with 75, 25s, and 50s.

The Cognitive Demand of the Task
Why is this considered to be a cognitively demanding task? (SAY) This is a high-level task because we have to decompose quantities and explain how to use hundreds, tens, and ones. It is high-level because we have to think of a second strategy that involves juggling the amounts. Working flexibly with quantities and noticing relationships is required when solving the problem two ways.

The Mathematical Task Analysis Guide
Lower-Level Demands Memorization Tasks involve either producing previously learned facts, rules, formulae, or definitions OR committing facts, rules, formulae, or definitions to memory. cannot be solved using procedures because a procedure does not exist or because the time frame in which the task is being completed is too short to use a procedure. are not ambiguous – such tasks involve exact reproduction of previously seen material and what is to be reproduced is clearly and directly stated. have no connection to the concepts or meaning that underlie the facts, rules, formulae, or definitions being learned or reproduced. Procedures Without Connections Tasks are algorithmic. Use of the procedure is either specifically called for or its use is evident based on prior instruction, experience, or placement of the task. require limited cognitive demand for successful completion. There is little ambiguity about what needs to be done and how to do it. have no connection to the concepts or meaning that underlie the procedure being used. are focused on producing correct answers rather than developing mathematical understanding. require no explanations, or explanations that focus solely on describing the procedure that was used. Higher-Level Demands Procedures With Connections Tasks focus students’ attention on the use of procedures for the purpose of developing deeper levels of understanding of mathematical concepts and ideas. suggest pathways to follow (explicitly or implicitly) that are broad general procedures that have close connections to underlying conceptual ideas as opposed to narrow algorithms that are opaque with respect to underlying concepts. usually are represented in multiple ways (e.g., visual diagrams, manipulatives, symbols, problem situations). Making connections among multiple representations helps to develop meaning. require some degree of cognitive effort. Although general procedures may be followed, they cannot be followed mindlessly. Students need to engage with the conceptual ideas that underlie the procedures in order to successfully complete the task and develop understanding. Doing Mathematics Tasks require 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). require students to explore and to understand the nature of mathematical concepts, processes, or relationships. demand self-monitoring or self-regulation of one’s own cognitive processes. require students to access relevant knowledge and experiences and make appropriate use of them in working through the task. require students to analyze the task and actively examine task constraints that may limit possible solution strategies and solutions. require considerable cognitive effort and may involve some level of anxiety for the student due to the unpredictable nature of the solution process required. (SAY) This is called the Mathematical Task Analysis Guide. It comes from a research study called the QUASAR Project. Teachers who learned about high-level task characteristics and worked to give their students a steady diet of high-level tasks performed well on open-ended assessments. The right-hand side of the chart shows the characteristics of high-level tasks. The bottom task is a “Doing Mathematics” task. Read the characteristics of the “Doing Mathematics” task. Do they describe the Sticker Task? Probing Facilitator Questions and Possible Responses: What mathematical relationships might students discover? They might discover that there is more than one way to break the amounts down and to combine them. All that matters is that you combine all of them. Is a pathway given in the written task? No. Do teachers sometimes end up giving students a pathway? Yes, and if this happens, then the teacher has lowered the cognitive demand of the written task. This happens 67% of the time during a lesson. We are told to use place value, but we are not shown how to use place value, in a way in which no pathway is given. Do students have to self-regulate? Yes. What if a teacher tells students what to do and how to do the problem? If the teacher does this, then the teacher has lowered the cognitive demand of the task.. Stein and Smith, 1998; Stein, Smith, Henningsen, & Silver, 2000 and 2008.

The Common Core State Standards (CCSS)
Solve the task. Examine the CCSS for Mathematics. Which CCSS for Mathematical Content will students discuss when solving the task? Which CCSS for Mathematical Practice will students use when solving and discussing the task? Directions: Take about 10 minutes for this slide. (SAY) Which of the CCSS for Mathematical Content would students need to demonstrate when solving the task?

The CCSS for Mathematical Content: Grade 2
Operations and Algebraic Thinking OA Represent and solve problems involving addition and subtraction. 2.OA.A.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1 Add and subtract within 20. 2.OA.B.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. Directions: Read the standards. Probing Facilitator Questions and Possible Responses: 2.OA.A.1: Which student work demonstrates that the student has met the standards? What kind of story problem is this? Why is it a “putting together” story problem? This is a “putting together” story problem because static amounts are given and there is not activity. Take a look at the table of story problems in your handouts. Do you think it is important to consider the type of story problem? Where is the unknown in the situation? The sum is the unknown. When we deal with three addends, we put the unknown in the first position. 2.OA.A.2: Although this is not one of your focus standards, how might working this way develop students’ fluency with adding? Common Core State Standards, 2010

Number and Operations in Base Ten NBT Understand place value. 2.NBT.A.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: 100 can be thought of as a bundle of ten tens—called a “hundred.” The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). Directions: Read the standards. (SAY) Which student work demonstrates that the student has met the standards? Probing Facilitator Questions and Possible Responses: 2.NBT.B.6: Did we work on this standard? Yes, we added up to three-digit numbers. We used place value and compensation to make sense of the amounts we added. 2.NBT.B.7: Did we meet this standard? Yes, because we used concrete models. We also worked with three-digit numbers. We decomposed and recomposed quantities. 2.NBT.B.8: Why aren’t we working on this standard? What questions would we have to ask in order to be working on this standard? We would need to say – what is , , , , ? How did I know that would go over 400? 2.NBT.B.9: Explain why addition and subtraction strategies work, using place value and the properties of operations. Common Core State Standards, 2010

Number and Operations in Base Ten NBT Understand place value. 2.NBT.A.2 Count within 1000; skip-count by 5s, 10s, and 100s. 2.NBT.A.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. 2.NBT.A.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

Number and Operations in Base Ten NBT Use place value understanding and properties of operations to add and subtract. 2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 2.NBT.B.6 Add up to four two-digit numbers using strategies based on place value and properties of operations.

Number and Operations in Base Ten NBT Use place value understanding and properties of operations to add and subtract. 2.NBT.B.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. 2.NBT.B.8 2.NBT.B.9 Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. Explain why addition and subtraction strategies work, using place value and the properties of operations. Directions: Read the standards. Which standards will students have opportunities to understand? See the previous slide. Common Core State Standards, 2010

Table 1: Common Addition and Subtraction Situations
(SAY) We will zoom in now to Standard 2.OA.A.1. This standard calls for students to understand a variety of situational word problems. Is this a “putting together” or an “add to” type of addition problem? Probing Facilitator Question and Possible Responses: Besides solving an addition problem, what else is going on here? Place value understanding and decomposing and recomposing quantities. Common Core State Standards, 2010, p. 88, NGA Center/CCSSO

The CCSS for Mathematical Practice
Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Directions: (10 min.) Lead a group discussion related to the mathematical practices. If time permits, participants benefit from an opportunity to turn and talk prior to a group discussion. (SAY) Which mathematical practices do students demonstrate in their work? Which mathematical practices do the written tasks require that they demonstrate? Which practices are we assessing and advancing? Probing Facilitator Questions and Possible Responses: Which CCSS for Mathematical Practice did students use and how do you know? We know that students must attempt to make sense of the problem and to make connections from one problem to the next. Students work abstractly and quantitatively. What would you have to hear from students to know they are working abstractly and quantitatively? Some students referred to the context on their own as they were explaining how they solved for the total number of stickers. Does anything about this task require that students construct a viable argument? Students have to explain how they used place value and they have to explain how they made easier amounts to add. What counts as place value and what is an easier number to add is the argument. In what ways did this task require students to use repeated reasoning? Students had to use place value to determine Tim’s and Jill’s amounts. Students could also be asked to create friendly amounts for Tim’s amounts as well as Jill’s amounts and this would be repeated use of a strategy. What structure of mathematics does this task engage students in thinking about? Decomposing and recomposing via place value and other amounts to make amounts of tens that are easier to add. Common Core State Standards, 2010 25

Analyzing a Lesson: Lesson Context
Teacher: Brandy Hays Grade: 2 School: Sam Houston Elementary School School District: Lebanon School District The students and the teacher in this school have been working to make sense of the Common Core State Standards for the past two years. The teacher is working on using the Accountable Talk moves and making sure she targets the mathematics standards in very deliberate ways during the lesson. Directions: Read the context of the problem.

Instructional Goals Brandy’s instructional goals for the lesson are:
students will decompose hundreds, tens, and ones and find the sum of the stickers. students can decompose and recompose quantities in order to make “friendly numbers” that are easier to add together. Directions: These are the teacher’s instructional goals for the lesson. Read the slide.

Reflection Question (Small group discussion)
As you watch the video segment, consider what students are learning about mathematics. Name the moves used by the teacher and the purpose that the moves served. Directions: Watch the video and then

Reflecting on the Accountable Talk Discussion (Whole group 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? How does talk scaffold student learning? Keith and Erin Once we have the transcript I will fill in these slides

Characteristics of an Academically Rigorous Lesson (Whole group discussion)
In what ways was the lesson academically rigorous? What does it mean for a lesson to be academically rigorous? (SAY) 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? Turn and Talk with a colleague. FILL THIS IN ONCE WE HAVE THE VIDEOS

Academic Rigor in a Thinking Curriculum
Academic Rigor in a Thinking Curriculum consists of indicators that students are accountable to: A Knowledge Core High-Thinking Demand Active Use of Knowledge Most importantly it is an indication that student learning/understanding is advancing from its current state. Did we see evidence of rigor via the Accountable Talk discussion? THIS TEXT WAS COPIED FROM GRADE 1… Facilitator Notes: Ask the questions below and facilitate a whole group discussion about academic rigor and rigorous thinking. Directions: Read the features of Academic Rigor. (SAY) Academic Rigor is related to Accountable Talk discussions. We can’t have an Academically Rigorous lesson NOR determine if the students are engaging in a rigorous lesson without having an Accountable Talk discussion. Why is this? Why are the two principles – rigor and talk directly related to each other?

Five Representations of Mathematical Ideas What role did tools or representations play in scaffolding student learning? Pictures Written Symbols Manipulative Models Real-world Situations Oral & Written Language THIS TEXT WAS COPIED FROM GRADE 1… Facilitator Notes: Ask the questions below and facilitate a whole group discussion. Reference specific places in the video where representations were used. Directions: (SAY) In what ways did the teacher make use of these representations during the lesson? How was student learning supported by reference to them or lack of reference to them? Modified from Van De Walle, 2004, p. 30

Giving it a Go: Planning for An Accountable Talk Discussion of a Mathematical Idea
Identify a person who will be teaching the lesson to others in your small group. Plan the lesson together. Anticipate student responses. Write Accountable Talk questions/moves that the teacher will ask students in order to advance their understanding of a mathematical idea. THIS TEXT WAS COPIED FROM GRADE 1… (SAY) We are going to work in three groups. Together you will plan a lesson, and then one person in your group will teach the lesson. The person will only teach your group not the larger group. Identify a teacher now. This is an important part of the process because this person usually keeps the group moving. While you are planning, actually write out the questions. Keep the moves in front of you so you can determine if you are encouraging the community to listen, to engage, or if you are pressing for reasoning. Your goal is to get to the mathematical idea listed in your handout.

Focus of the Discussion
Use compensation to make easier numbers when solving for Adela’s amount of stickers. Plan to engage students in a discussion of: Plan to refer to the model of wooden craft sticks or base ten blocks when discussing the solution path. ADD TEXT? CAN IT BE COPIED FROM GRADE 1?

Reflection: The Use of Accountable Talk discussion and Tools to Scaffold Student Learning
What have you learned? (SAY) Let’s have a group discussion. Was there any evidence of the Accountable Talk features and indicators? If so, which ones, and what benefit did the features and indicators serve? (20 min). Possible Responses: The Third Grade Teacher

Bridge to Practice Plan a lesson with colleagues. Create a high-level task that we didn’t use in this session. Anticipate student responses. Discuss ways in which you will engage students in talk that is accountable to community, to knowledge, and to standards of rigorous thinking. Specifically, list questions that you will ask during the lesson. Check that you have thought about all of the moves. Engage students in an Accountable Talk discussion. Ask a colleague to scribe a segment of your lesson, or audio or videotape your own lesson and transcribe it later. Analyze the Accountable Talk discussion in the transcribed segment of the talk. Identify questions and anticipated student responses. Bring a segment of the transcript so you can identify specific moves made during the lesson. Directions: Read the Bridge to Practice.

Supporting Rigorous Mathematics Teaching and Learning

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