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Prompting productive maths discussions ~ Amie Albrecht
This document discusses strategies for prompting productive mathematical discussions. It provides examples of different types of prompts, including prompts that: - Encourage responses with no single right answer. - Stimulate deep thinking by moving beyond procedural fluency to conceptual understanding. - Require precise vocabulary. - Start "maths fights" by having students justify their positions. - Provide multiple approaches with no single right method. The document recommends using open-ended prompts to build curiosity and encourage varied responses and thinking. Examples are given from visual patterns, adding decimals, and slope to illustrate different kinds of rich prompts.
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Prompting productive maths discussions ~ Amie Albrecht
- 1. Prompting productive mathematical discussions DrAmie Albrecht University of South Australia www.tinyurl.com/MatConf16-aa-discussions @nomad_penguin 2016 MAT Annual Conference (14 May 16) amiealbrecht.com #MATConf16
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- 4. More: Notice andWonder Ever Wonder What They’d Notice? (Annie Fetter’s NCTM 2011 Ignite Talk) www.youtube.com/watch?v=a-Fth6sOaRA&feature=youtu.be @maxmathforum Chapter 4 of ‘Powerful Problem Solving’ (but also just google ‘Notice and Wonder’) #noticewonder #tmwyk (Talking Math WithYour Kids) #wcydwt (What CanYou Do With This?) Activities for Sense Making with the Mathematical Practices Max Rayof The Math Forum @ Drexel Powerful Problem Solving Foreword by Susan O’Connell Hidden Decision-Making in the Math Classroom (Or:‘All What, No Why’?) (Annie Fetter’s Asilomar 2015 Ignite Talk) https://www.youtube.com/watch?v=LK2eXdYdHjs&feature=youtu.be
- 5. Prompts to helpBUILD CURIOSITY
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- 14. More: MTBoS To readthe hashtag without joining Twitter: twitter.com/hashtag/mtbos To find out more about MTBoS (it’s not just Twitter!): exploremtbos.wordpress.com
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- 18. Write down thefirst question that comes to mind
- 19. Write down thefirst question that comes to mind
- 20. • How manytoothpicks does he have? Write down the first question that comes to mind
- 21. • How manytoothpicks does he have? • How many smaller triangles are in the larger triangle? Write down the first question that comes to mind
- 22. • How manytoothpicks does he have? • How many smaller triangles are in the larger triangle? • Does he complete the whole formation or does he stop in the middle? Write down the first question that comes to mind
- 23. • How manytoothpicks does he have? • How many smaller triangles are in the larger triangle? • Does he complete the whole formation or does he stop in the middle? • How big does the triangle get? (In terms of number of layers.) Write down the first question that comes to mind
- 24. • How manytoothpicks does he have? • How many smaller triangles are in the larger triangle? • Does he complete the whole formation or does he stop in the middle? • How big does the triangle get? (In terms of number of layers.) • How many toothpicks are used in each layer? Write down the first question that comes to mind
- 25. • How manytoothpicks does he have? • How many smaller triangles are in the larger triangle? • Does he complete the whole formation or does he stop in the middle? • How big does the triangle get? (In terms of number of layers.) • How many toothpicks are used in each layer? • How long is it going to take? Write down the first question that comes to mind
- 26. • How manytoothpicks does he have? • How many smaller triangles are in the larger triangle? • Does he complete the whole formation or does he stop in the middle? • How big does the triangle get? (In terms of number of layers.) • How many toothpicks are used in each layer? • How long is it going to take? • What is the perimeter of the entire triangle? Write down the first question that comes to mind
- 27. • How manytoothpicks does he have? • How many smaller triangles are in the larger triangle? • Does he complete the whole formation or does he stop in the middle? • How big does the triangle get? (In terms of number of layers.) • How many toothpicks are used in each layer? • How long is it going to take? • What is the perimeter of the entire triangle? • What is the area of the entire triangle? Write down the first question that comes to mind
- 28. • How manytoothpicks does he have? • How many smaller triangles are in the larger triangle? • Does he complete the whole formation or does he stop in the middle? • How big does the triangle get? (In terms of number of layers.) • How many toothpicks are used in each layer? • How long is it going to take? • What is the perimeter of the entire triangle? • What is the area of the entire triangle? • What is the end product going to look like? Write down the first question that comes to mind
- 29. • How manytoothpicks does he have? • How many smaller triangles are in the larger triangle? • Does he complete the whole formation or does he stop in the middle? • How big does the triangle get? (In terms of number of layers.) • How many toothpicks are used in each layer? • How long is it going to take? • What is the perimeter of the entire triangle? • What is the area of the entire triangle? • What is the end product going to look like? • Is he going to clean the mess up afterwards? Write down the first question that comes to mind
- 30. • How manytoothpicks does he have? • How many smaller triangles are in the larger triangle? • Does he complete the whole formation or does he stop in the middle? • How big does the triangle get? (In terms of number of layers.) • How many toothpicks are used in each layer? • How long is it going to take? • What is the perimeter of the entire triangle? • What is the area of the entire triangle? • What is the end product going to look like? • Is he going to clean the mess up afterwards? • Why is he doing this? Write down the first question that comes to mind
- 31. • How manytoothpicks does he have? • How many smaller triangles are in the larger triangle? • Does he complete the whole formation or does he stop in the middle? • How big does the triangle get? (In terms of number of layers.) • How many toothpicks are used in each layer? • How long is it going to take? • What is the perimeter of the entire triangle? • What is the area of the entire triangle? • What is the end product going to look like? • Is he going to clean the mess up afterwards? • Why is he doing this? Write down the first question that comes to mind
- 32. • How manytoothpicks does he have? • How many smaller triangles are in the larger triangle? • Does he complete the whole formation or does he stop in the middle? • How big does the triangle get? (In terms of number of layers.) • How many toothpicks are used in each layer? • How long is it going to take? • What is the perimeter of the entire triangle? • What is the area of the entire triangle? • What is the end product going to look like? • Is he going to clean the mess up afterwards? • Why is he doing this? • How many rows does he create with his toothpicks? Write down the first question that comes to mind
- 33. • How manytoothpicks does he have? • How many smaller triangles are in the larger triangle? • Does he complete the whole formation or does he stop in the middle? • How big does the triangle get? (In terms of number of layers.) • How many toothpicks are used in each layer? • How long is it going to take? • What is the perimeter of the entire triangle? • What is the area of the entire triangle? • What is the end product going to look like? • Is he going to clean the mess up afterwards? • Why is he doing this? • How many rows does he create with his toothpicks? Write down the first question that comes to mind
- 34. • How manytoothpicks does he have? • How many smaller triangles are in the larger triangle? • Does he complete the whole formation or does he stop in the middle? • How big does the triangle get? (In terms of number of layers.) • How many toothpicks are used in each layer? • How long is it going to take? • What is the perimeter of the entire triangle? • What is the area of the entire triangle? • What is the end product going to look like? • Is he going to clean the mess up afterwards? • Why is he doing this? • How many rows does he create with his toothpicks? Write down the first question that comes to mind Act 1: The Hook
- 35. Act 1I: TheJourney
- 36. Act III: TheResolution threeacts.mrmeyer.com @ddmeyer
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- 39. Act IV: TheSequel mrkraft.wikispaces.com/Triangle+of+Toothpicks @nathankraft1
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- 45. 11 22 12 42 45 54 13 1415 21 23 24 72 25 63 81 64 31 61 71 73 83 32 11 33 35 41 43 53 84 55 11 74 37 52 13 51 17 75 82 41 85 17 44 11 65 13 62 31 34 17 91 13 92 23 93 31 94 47 95 19 4 5321 16 56 36 96 76 19 86 43 46 23 66 11 26 13 6 17 27 67 97 37 47 57 19 77 11 87 29 7 18 28 98 48 58 29 78 13 68 17 38 19 88 11 8 19 29 59 79 89 49 69 23 39 13 99 11 9 50 20 60 30 100 70 40 90 80 10 11 What do you notice? What do you wonder? mathforlove.com/games
- 46. Prompts to helpBUILD CURIOSITY No ‘right’ question
- 47. Prompts that ENCOURAGERESPONSES No single ‘right’ answer
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- 53. Shade a quarterof a cross. Be as creative as you can! Quarter of a cross
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- 55. @DavidKButlerUoA 5/4 = 1+1/4 5/4= 1/2 + 3/4 5/4 = 2*(5/8) 5/4 = 1/2*(5/2)
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- 61. Prompts with MULTIPLEAPPROACHES No single ‘right’ method
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- 69. How many circlesare in stage 10? …stage 100? Inspired by visualpatterns.org
- 70. How many circlesare in stage 10? …stage 100? Inspired by visualpatterns.org Sketch a graph. Inspired by visualpatterns.org
- 71. Create a table. Inspiredby visualpatterns.org How many circles are in stage 10? …stage 100? Inspired by visualpatterns.org Sketch a graph. Inspired by visualpatterns.org
- 72. Create a table. Inspiredby visualpatterns.org How many circles are in stage 10? …stage 100? Inspired by visualpatterns.org Sketch a graph. Inspired by visualpatterns.org Write an equation. Inspired by visualpatterns.org
- 73. Prompts that stimulateDEEP THINKING Procedural fluency ↓ Conceptual understanding
- 74. Find the mean,median and mode: 5 3 6 3 3 Instead of: nrich.maths.org/6267
- 75. Find the mean,median and mode: 5 3 6 3 3 Instead of: Suppose that the mean, median and mode for five positive integers were: mean: 4 median: 3 mode: 3 Would you be able to tell me the numbers? Try: nrich.maths.org/6267
- 76. Find the slopeof the line passing through the points: (3,5) and (8,4) Instead of: @MJFenton
- 77. Find the slopeof the line passing through the points: (3,5) and (8,4) Instead of: and Use four different whole numbers (from 2 to 9) to determine a line whose slope is least/greatest/closest to zero. Try: ( , ) ( , ) @MJFenton
- 79. Use the numbers1 through 9, exactly once each, to fill in the boxes and make three decimals whose sum is as close to 1 as possible. Adding decimals 0. 0. 0.+ www.openmiddle.com @robertkaplinsky
- 81. Prompts that requirePRECISE VOCABULARY
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- 88. Prompts that startMATHS FIGHTS Justify your position
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