Supporting Rigorous Mathematics Teaching and Learning

1. Supporting Rigorous Mathematics Teaching and Learning Tennessee Department of Education High School Mathematics Algebra 1 Shaping Talk in the Classroom: Academically Productive Talk Features and Indicators

2. Rationale Teachers’ questions are crucial in helping students make connections and learn important mathematics and science concepts. Teachers need to know how students typically think about particular concepts, how to determine what a particular student or group of students thinks about those ideas, and how to help students deepen their understanding (Weiss & Pasley, 2004). By analyzing a transcript of an Accountable Talk® discussion, participants will consider the benefits to student learning when the Accountable Talk features and indicators are present in the Share, Discuss, and Analyze Phase of the lesson. Accountable Talk® is a registered trademark of the University of Pittsburgh.

3. Session Goals Participants will: • learn about Accountable Talk features and indicators; and • learn about the benefits of using indicators of all three Accountable Talk features in a classroom discussion.

4. Overview of Activities • Participants will: • analyze transcripts, identify Accountable Talkfeatures and indicators, and consider the benefits of fostering this community; and • plan for an Accountable Talk discussion.

5. Accountable Talk Features and Indicators • Read the list of Accountable Talk indicators related to each of the features. • Accountability to the Learning Community • Accountability to Knowledge • Accountability to Rigorous Thinking • How do the features differ from one another?

6. Accountable Talk Features and Indicators Accountability to the Learning Community • Actively participate in classroom talk. • Listen attentively. • Elaborate and build on each others’ ideas. • Work to clarify or expand a proposition.

7. Accountable Talk Features and Indicators Accountability to Knowledge • Specific and accurate knowledge • Appropriate evidence for claims and arguments • Commitment to getting it right

8. Accountable Talk Features and Indicators 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. Accountable Talk Discussion Turn and Talk with your partner about what you would expect teachers and students to be saying during an Accountable Talk discussion for each of the features. • accountability to the learningcommunity • accountability to accurate, relevant knowledge • accountability to discipline-specific standards of rigorous thinking

10. Accountable Talk Features and Indicators Indicators of all three Accountable Talk features need to be evident in a lesson. Lessons should be: • accountable to the learning community; • accountable to knowledge; and • accountable to rigorous thinking. Why might it be important to have indicators of all three features of Accountable Talk discussions in a conversation?

11. Preparing for the Share, Discuss, and Analyze (SDA) Phase of the Lesson

12. 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 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: 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

13. No Place Like Home Sandy miles Janet minutes Two sisters, Janet and Sandy, each represented their travels from home by sketching their paths on the graph shown below. The x-axis represents the time of their journeys in minutes and the y-axis represents the distance from home in miles.

14. No Place Like Home • Decide whether you agree or disagree with each of the following statements. Support your answer mathematically, using specific points or time intervals where appropriate. • Janet traveled mostly uphill while Sandy traveled mostly downhill. • Sandy traveled at a faster rate than Janet. • Sandy and Janet were at the same place at the same time once during their journeys. • Each girl always traveled at a constant rate. • Both girls were at home at some point during their journeys. • Sandy stopped walking at 14 minutes.  • Each girl’s journey represents a function.

15. No Place Like Home Task

16. The CCSS for Mathematical ContentCCSS Conceptual Category – Algebra 1 Common Core State Standards, 2010

17. 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.

18. Analyzing Student Work • Use the student work to further your understanding of the task. • Consider: • What do the students know? • How did the students solve the task? • How do their solution paths differ from each other?

19. Group A

20. Group B

21. Group C

22. Group D

23. Group E 23

24. Selecting Students’ Work The teacher selected work from Groups E, B, and C for the Share, Discuss, and Analyze Phase of the lesson. Consider the following: • Why might the teacher have chosen these pieces of student work for this lesson phase? • What mathematical concepts can be targeted by the teacher using the student work that s/he chose?

25. Analyzing Teaching and Learning No Place Like Home Task Vignettes: Two classrooms are solving and discussing solution paths to the No Place Like Home Task . Read a short transcript from Classroom A and Classroom B. What are students learning in each classroom?

26. Analyzing Teaching and Learning What is similar and different between the opportunities to learn in Classroom A and Classroom B?

27. The Share, Discuss, and Analyze Phase of the Lesson What made it possible for this learning to occur?

28. Accountable Talk Features and Indicators Which of the Accountable Talk features and indicators were illustrated in the transcript from Teacher A’s classroom?

29. The Share, Discuss, and Analyze Phase of the Lesson In what ways did students engage in an Accountable Talk discussion? What purpose did the Accountable Talk features serve in the lesson? 29

30. Your Turn Consider the essential understanding below: • The language of change and rate of change (increasing, decreasing, constant, relative maximum or minimum) can be used to describe how two quantities vary together over a range of possible values What would you need to hear from students to know that they had this understanding?

31. Your Turn continued At your tables, plan questions and possible student responses for a classroom discussion that will get at the essential understanding. How will you hold them accountable to the learning community, knowledge, and rigorous thinking?

32. Your Turn continued What did you notice about planning questions and anticipating student responses? What are some things you said and did to hold students accountable to the learning community, knowledge, and rigorous thinking?

33. Step Back: Reflecting on the Benefits What are the benefits of using Accountable Talk features and indicators as a tool for reflecting on the classroom discussion? For planning?