Supporting Rigorous Mathematics Teaching and Learning

1. Supporting Rigorous Mathematics Teaching and Learning Using Academically Productive Talk Moves: Orchestrating a Focused Discussion Tennessee Department of Education Middle School Mathematics Grade 6-8

2. 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.

3. Session Goals • Participants will: • learn about Accountable Talk® features and indicators and consider the benefit of all being presentin 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

4. Overview of Activities • Participants will: • review the Accountable Talk features and indicators; • identify and discuss Accountable Talk moves in avideo; and • zoom in for a more specific look at key moves for engaging in productive talk (marking, recapping, challenging, and revoicing).

5. 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 Setting Goals Selecting Tasks Anticipating 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® discussions Accountable Talk®is a registered trademark of the University of Pittsburgh

6. Accountable Talk Features and Indicators

7. 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 learningcommunity; • accurate, relevant knowledge; and • standards of rigorous thinking.

8. Accountable Talk Features and Indicators Accountability 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.

9. Solving and Discussing the Cognitive Demand of the Light Bulb Task

10. The Structure 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 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. Share, Discuss, and Analyze Phase of the Lesson 1. Share and Model 2. Compare Solutions Focus the Discussion on Key Mathematical Ideas 4. Engage in a Quick Write

11. 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.

12. 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.

13. Reflecting on Our Engagement in the Lesson The observer should share some observations about the group’s engagement in an Accountable Talk discussion.

14. 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?

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

16. 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.)

17. 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.

18. Accountable Talk Moves

19. 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”?

20. Accountable Talk: Features and Indicators Accountability 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.

21. Accountable Talk Moves

22. Accountable Talk Moves (continued)

23. 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?

24. 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?

25. 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?