© 2013 UNIVERSITY OF PITTSBURGH Supporting Rigorous Mathematics Teaching and Learning Shaping Talk in the Classroom: Academically Productive Talk Features and Indicators Tennessee Department of Education High School Mathematics Algebra 1

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. 2

© 2013 UNIVERSITY OF PITTSBURGH Session Goals 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. Participants will: 3

© 2013 UNIVERSITY OF PITTSBURGH Overview of Activities Participants will: analyze transcripts, identify Accountable Talk features and indicators, and consider the benefits of fostering this community; and plan for an Accountable Talk discussion. 4

© 2013 UNIVERSITY OF PITTSBURGH 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? 5

© 2013 UNIVERSITY OF PITTSBURGH 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. Accountable Talk Features and Indicators 6

© 2013 UNIVERSITY OF PITTSBURGH Accountability to Knowledge Specific and accurate knowledge Appropriate evidence for claims and arguments Commitment to getting it right Accountable Talk Features and Indicators 7

© 2013 UNIVERSITY OF PITTSBURGH 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 Features and Indicators 8

© 2013 UNIVERSITY OF PITTSBURGH 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 learning community −accountability to accurate, relevant knowledge −accountability to discipline-specific standards of rigorous thinking 9

© 2013 UNIVERSITY OF PITTSBURGH 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? Accountable Talk Features and Indicators 10

© 2013 UNIVERSITY OF PITTSBURGH Preparing for the Share, Discuss, and Analyze (SDA) Phase of the Lesson 11

© 2013 UNIVERSITY OF PITTSBURGH The Structures and Routines of a Lesson The Explore Phase/Private Work Time Generate Solutions The Explore Phase/Small Group Problem Solving 1.Generate and Compare Solutions 2.Assess and Advance Student Learning 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 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. Set Up of the Task 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 12

© 2013 UNIVERSITY OF PITTSBURGH No Place Like Home 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. miles Janet Sandy minutes 13

© 2013 UNIVERSITY OF PITTSBURGH No Place Like Home 1.Decide whether you agree or disagree with each of the following statements. Support your answer mathematically, using specific points or time intervals where appropriate. a.Janet traveled mostly uphill while Sandy traveled mostly downhill. b.Sandy traveled at a faster rate than Janet. c.Sandy and Janet were at the same place at the same time once during their journeys. d.Each girl always traveled at a constant rate. e.Both girls were at home at some point during their journeys. f.Sandy stopped walking at 14 minutes. g.Each girl’s journey represents a function. 14

© 2013 UNIVERSITY OF PITTSBURGH No Place Like Home Task 15

The CCSS for Mathematical Content CCSS Conceptual Category – Algebra 1 Common Core State Standards, 2010 Interpreting Functions (F-IF) Interpret functions that arise in applications in terms of the context F-IF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. ★. F-IF.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. ★ Reasoning with Equations and Inequalities (A-REI) Represent and solve equations and inequalities graphically A.-REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. ★ ★ Mathematical Modeling is a Standard for Mathematical Practice (MP4) and a Conceptual Category, and specific modeling standards appear throughout the high school standards indicated with a star ( ★ ). Where an entire domain is marked with a star, each standard in that domain is a modeling standard. 16

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,

© 2013 UNIVERSITY OF PITTSBURGH 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? 18

© 2013 UNIVERSITY OF PITTSBURGH Group A 19

© 2013 UNIVERSITY OF PITTSBURGH Group B 20

© 2013 UNIVERSITY OF PITTSBURGH Group C 21

© 2013 UNIVERSITY OF PITTSBURGH Group D 22

© 2013 UNIVERSITY OF PITTSBURGH Group E 23

© 2013 UNIVERSITY OF PITTSBURGH 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? 24

© 2013 UNIVERSITY OF PITTSBURGH 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? 25

© 2013 UNIVERSITY OF PITTSBURGH Analyzing Teaching and Learning What is similar and different between the opportunities to learn in Classroom A and Classroom B? 26

© 2013 UNIVERSITY OF PITTSBURGH The Share, Discuss, and Analyze Phase of the Lesson What made it possible for this learning to occur? 27

© 2013 UNIVERSITY OF PITTSBURGH Accountable Talk Features and Indicators Which of the Accountable Talk features and indicators were illustrated in the transcript from Teacher A’s classroom? 28

© 2013 UNIVERSITY OF PITTSBURGH 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

© 2013 UNIVERSITY OF PITTSBURGH 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? 30

© 2013 UNIVERSITY OF PITTSBURGH 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? 31

© 2013 UNIVERSITY OF PITTSBURGH 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? 32

© 2013 UNIVERSITY OF PITTSBURGH 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? 33