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Outcomes

Protocols and Procedures for Fostering Mathematics Discourse - Secondary Sep 16, 2013 (1:00 pm - 1:50 pm). Outcomes. Participants will deepen their understanding of mathematics discourse, including some background and rationale.

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Outcomes

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  1. Protocols and Procedures for Fostering Mathematics Discourse - SecondarySep 16, 2013(1:00 pm - 1:50 pm)

  2. Outcomes • Participants will deepen their understanding of mathematics discourse, including some background and rationale. • Participants will experience Number Talks and consider how they might be used as part of a daily routine.

  3. Agenda • Background and rationale • Experience a variety of Number Talks • Consider implications for implementation of mathematics discourse. • Closing

  4. Enhancing Instruction for CCSSM “FAL” Mini-Unit with Forma-tive Assess-ments Number Talks Upgrading Units

  5. Hand Signals • Solution • Strategy • Question • Comment • I agree • Integers • Fractions

  6. Hand Signals • Solution • Strategy • Question • Comment • Agree • Integers • Fractions

  7. CCSS Mathematical Practices REASONING AND EXPLAINING 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others OVERARCHING HABITS OF MIND 1. Make sense of problems and persevere in solving them 6. Attend to precision MODELING AND USING TOOLS 4. Model with mathematics 5. Use appropriate tools strategically SEEING STRUCTURE AND GENERALIZING 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

  8. Four Goals for K-2 Number Talks • Developing Number Sense • Developing fluency with small numbers • Subitizing • Making Fives and Tens • Number Conservation Number Talks -Sherry Parrish

  9. Mathematical Thinking • Counting All • Counting On • Known Facts • Derived Facts • Decomposing • Recomposing Duality, Ambiguity, and Flexibility in Successful Mathematical Thinking Research by Eddie Gray and David Tall, 1994

  10. Understanding Math Discourse • Talk Formats • Whole-Class Discussion • Small-Group Discussions • Partner Talks Classroom Discussions: Using Math Talk to Help Students Learn -S. Chapin, C. O’Connor, N Anderson (2003)

  11. Understanding Math Discourse • Talk Moves • Revoicing • So you’re saying the top number in a fraction is called the numerator. • Repeating • Can you repeat what Miguel said in your own words? Classroom Discussions: Using Math Talk to Help Students Learn -S. Chapin, C. O’Connor, N Anderson (2003)

  12. Understanding Math Discourse • Talk Moves (continued) • Reasoning • Do you agree or disagree and why? • Adding On • Please add onto Jimena’s strategy. • Waiting • Please take some quite think time. Classroom Discussions: Using Math Talk to Help Students Learn -S. Chapin, C. O’Connor, N Anderson (2003)

  13. Number Talks • A planned daily routine for whole‐class instruction • Number Sense (efficiency, accuracy & flexibility) • Generalized Arithmetic-conceptual understanding • Reasoning and Problem Solving • Mental Mathematics • Preview-­Review-­Conceptual Understanding

  14. Number Talks and Time • Number Talks (about 10 minutes) • Mini-Lesson (10 to 20 minutes) • Lesson (more than 20 minutes)

  15. Number Talk Examples • Dot Patterns • Mental Math • Number Strings • True/False Statements • Dilemmas • Spatial Reasoning • What’s My Rule? • Error Analysis and Coaching

  16. Norms “No one is as smart as all of us are together.” • Respect • Individual think time • Everyone participates • Everyone helps • Leave no one behind • Be positive • Technology courtesy

  17. Socio-mathematical Norms • Errors are gifts, they promote discussion. • Share a second sentence to connect your thoughts. • The answer is important, but it is not the math. • Build on the thinking of others. • Ask questions until ideas make sense. • Think with language and use language to think.

  18. CCSS Mathematical Practices REASONING AND EXPLAINING 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others OVERARCHING HABITS OF MIND 1. Make sense of problems and persevere in solving them 6. Attend to precision MODELING AND USING TOOLS 4. Model with mathematics 5. Use appropriate tools strategically SEEING STRUCTURE AND GENERALIZING 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

  19. Lenses to Consider During Professional Development Sessions Learner Lens Teacher Lens

  20. Dot Talk How many dots do you see? How did you see them?

  21. Mental Math After a 20% discount, the price is 80% of the original price. So 80% of the original price is $140. What is the original price?

  22. Mental Math

  23. Number String (Mental Math) 35 x 8 70 x 4 140 x 2

  24. Number String (Mental Math) 3 x 50 3 x 100 3 x 149

  25. True/False = True or False? Why?

  26. True/False Number Talk

  27. Dilemma Number Talk Kirsten says that 10xy-5xy + 4xy equals xy David says that 10xy-5xy + 4xy equals 9xy Explain the mathematical reasoning that both David & Kirsten used to simplify the expression above.

  28. Order of Operations

  29. Spatial Reasoning How many cubes? How do you see them? What is the surface area?

  30. Transformations Rotate the figure 90˚ clockwise. What are the new coordinates of point A?

  31. What’s My Rule?

  32. What’s My Rule?

  33. What’s My Rule?

  34. What’s My Rule?

  35. Number Talk Examples • Dot Patterns • Mental Math • Number Strings • True/False Statements • Dilemmas • Spatial Reasoning • What’s My Rule? • Error Analysis and Coaching

  36. Number Talks and Time • Number Talks (about 10 minutes) • Mini-Lesson (10 to 20 minutes) • Lesson (more than 20 minutes)

  37. Table Talk • Have you implemented Number Talks as part of your daily routine? What were some of the benefits and challenges? • When in your daily routine could you incorporate the use of Number Talks?

  38. Questions Teachers Might Ask • Who would like to share their thinking? • Did someone solve it a different way? • Who else used this strategy to solve the problem? • How did you figure it out?

  39. Questions Teachers Might Ask • What did you do next? • What did you need to know? • Why did you do that? Tell me more. • Which strategies do you see being used?

  40. Outcomes • Participants will deepen their understanding of mathematics discourse, including some background and rationale. • Participants will experience Number Talks and consider how they might be used as part of a daily routine.

  41. Closing • Thank you! • Cecilio_Dimas@sccoe.org • The best source for Number Talks is student work (errors, strategies, and solution pathways). • Inside Mathematics • Mathematics Assessment Project

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