Supporting Rigorous Mathematics Teaching and Learning

1. 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

2. 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. Accountable Talk is a registered trademark of the University of Pittsburgh.

3. 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.

4. 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.

5. Review theAccountable Talk Features and Indicators:Learn Moves Associated With the Accountable Talk Features

6. Linking to Research/Literature: The QUASAR Project The Mathematical Tasks Framework TASKS as set up by the teachers TASKS as implemented by students TASKS as they appear in curricular/ instructional materials Student Learning Stein, Smith, Henningsen, & Silver, 2000

7. 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

8. 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 learningcommunity. • Accountability to accurate, relevant knowledge. • Accountability to discipline-specific standards of rigorous thinking.

9. 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.

10. 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?

11. Accountable Talk Moves

12. Accountable Talk Moves (continued)

13. Pictures Manipulative Models Written Symbols Real-world Situations Oral & Written Language Five Representations of Mathematical IdeasWhat role do the representations play in a discussion? Modified from Van De Walle, 2004, p. 30

14. Engage and Reflect on a LessonThe Sticker Task

15. The Sticker Task • 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? 153 + 274 + 296

16. The Cognitive Demand of the Task Why is this considered to be a cognitively demanding task?

17. The Mathematical Task Analysis Guide Stein and Smith, 1998; Stein, Smith, Henningsen, & Silver, 2000 and 2008.

18. 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?

19. The CCSS for Mathematical Content: Grade 2 Common Core State Standards, 2010

20. The CCSS for Mathematical Content: Grade 2 Common Core State Standards, 2010

21. The CCSS for Mathematical Content: Grade 2

22. The CCSS for Mathematical Content: Grade 2

23. The CCSS for Mathematical Content: Grade 2 Common Core State Standards, 2010

24. Table 1: Common Addition and Subtraction Situations Common Core State Standards, 2010, p. 88, NGA Center/CCSSO

25. The CCSS for Mathematical Practice Common Core State Standards, 2010 • 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.

26. 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.

27. The Sticker Task • 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? 153 + 274 + 296

28. 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.

29. 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.

30. 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?

31. 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?

32. 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?

33. Pictures Manipulative Models Written Symbols Real-world Situations Oral & Written Language Five Representations of Mathematical IdeasWhat role did tools or representations play in scaffolding student learning? Modified from Van De Walle, 2004, p. 30

34. 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. 

35. The Sticker Task • 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? 153 + 274 + 296

36. 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: 149 + 269 + 281 Plan to refer to the model of wooden craft sticks or base ten blocks when discussing the solution path.

37. Reflection: The Use of Accountable Talk discussionand Tools to Scaffold Student Learning What have you learned?

38. 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.