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Outcomes

Protocols and Procedures for Fostering Mathematics Discourse - Elementary Sep 16, 2013 (2:00 pm - 2:50 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 - ElementarySep 16, 2013(2:00 pm - 2:50 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 • Rekenreks • Five and Ten Frames • Mental Math • Number Strings • True/False Statements • Dilemmas • Spatial Reasoning • What’s My Rule?

  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. Dot Talk I saw ______dots. I grouped the dots…. I also saw ___ dots, but I grouped the dots differently. I …

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

  23. Dot Talk

  24. Rekenrek DVD K.2

  25. Five Frames

  26. Ten Frames

  27. Ten Frames How many dots do you see? How did you see them?

  28. Ten Frames How many dots do you see? How did you see them?

  29. Mental Math 26 + 27

  30. Mental Math 32 x 15

  31. Number String (Mental Math) 7+6 8+7 14+13 25+26

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

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

  34. True/False 7 = 4 + 3 True or False? Why?

  35. True/False 17-16= 9-8 True or False? Why?

  36. True/False 8 x 7= 8 x (5+2) True or False? Why?

  37. True/False 15 x 24 = 30 x 12 True or False? Why?

  38. True/False

  39. Dilemma Kirsten says that 9 is the missing number in 5 = - 4 David says that 1is the missing number in 5 = - 4 Explain the mathematical reasoning that both Kirsten & David used to simplify the expression above.

  40. Dilemma Kirsten says that 9 is the missing number in 5 = + 4 10-5+4 David says that 1is the missing number in 5 = + 4 Explain the mathematical reasoning that both Kirsten & David used to simplify the expression above.

  41. Dilemma Kirsten says that 10-5+4 is equal to 1 David says that 10-5+4 is equal to 9 Explain the mathematical reasoning that both David & Kirsten used to simplify the expression above.

  42. Order of Operations

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

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

  45. What’s My Rule?

  46. What’s My Rule?

  47. What’s My Rule?

  48. Number Talk Examples • Dot Patterns • Rekenreks • Five and Ten Frames • Mental Math • Number Strings • True/False Statements • Dilemmas • Spatial Reasoning • What’s My Rule?

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

  50. 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?

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