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Discourse and Mathematics: Get Connected! Rosann Hollinger and Bernard Rahming Milwaukee Public Schools April 27, 2012 NCTM Annual Meeting Philadelphia

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Learning Intention We Are Learning To… deepen our understanding of structures/conditions that lead to productive math talk in the classroom.

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Success Criteria We will know we are successful when we can… describe productive talk moves that promote discourse, and explain how to integrate some of the ideas raised today into our classroom/school practice.

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Connecting Discourse to Assessment “ Classroom discourse provides a supportive context for students to share partial understandings and misconceptions, and instructionally embedded assessment allows teachers to gather information about students’ partial understandings or misconceptions and to further investigate students’ intended meaning through additional probing, guiding and reframing of questions.” Webb (2004) Webb, David. (2004) Enriching assessment opportunities through classroom discourse. In Romberg, T (ed) Standards-based Mathematics Assessment in Middle School. NY: Teachers College Press, p. 170

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Classroom Discussions Using Math Talk to Help Students Learn Suzanne H. Chapin, Catherine O’Connor, Nancy Canavan Anderson “… we believe that the ways we used talk in the classroom helped these students make their thinking public; it helped students to explicate and elaborate their reasoning; it allowed them to model, build on, and add to the development of complex ideas; and in at least some cases, it provided a socially grounded motivation to learn.”

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Wisconsin Common Core Standards for Mathematics ROSANN

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Standard 3: Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

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Productive Talk Moves 1. Revoicing: Teacher repeats some or all of what the student has said. Students verify what was said. 2. Repeating: Asking students to restate someone else’s reasoning. 3. Reasoning: Asking students to apply their own reasoning to someone else’s reasoning. 4. Adding on: Prompting students for further participation. 5. Waiting: Using wait time.

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In action … Think: individual time to think through prompt Pair: small group (use graphic organizer) Share: whole group reporting out

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Productive Talk Formats Whole-Class Discussion Small-Group Discussion Partner Talk

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Conditions need to be right! Classroom culture Ground rules for respectful and courteous talk What do you have to do to bring out productive talk?

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Troubleshooting The same few students do all the talking. I’m falling behind in my curriculum.

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Focusing Discourse with Questions Which questions might be helpful if your lesson design looked like this: Launch, Explore, Summarize

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Implementation Ideas As you think about what you know about discourse, how might you plan to have this practice become part of your classroom/school culture?

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Success Criteria We will know we are successful when we can… describe productive talk moves that promote discourse, and explain how to integrate some of the ideas raised today into our classroom/school practice.

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