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SERCC - Making Math Contextual, Visual and Concrete

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SERCC Conference Meeting in London, Ontario. Thursday November 10th, 2016.

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SERCC - Making Math Contextual, Visual and Concrete

  1. 1. Making Math Contextual, Visual, and Concrete in Grade 7-12 @MathletePearcewww.tapintoteenminds.com
  2. 2. @MathletePearcewww.tapintoteenminds.com Making Math Contextual, Visual, and Concrete in Grade 7-12
  3. 3. @MathletePearcewww.tapintoteenminds.com PROBLEM
  4. 4. @MathletePearcewww.tapintoteenminds.com
  5. 5. @MathletePearcewww.tapintoteenminds.com
  6. 6. ENGAGED YET? @MathletePearcewww.tapintoteenminds.com
  7. 7. @MathletePearcewww.tapintoteenminds.com ENGAGEMENT “There are several types/categories of engagement – academic, cognitive, intellectual, institutional, emotional, behavioural, social, psychological, to name a few.” Parsons, J., & Taylor, L. (2011). Student Engagement: What do we know and what should we do? University Partners (pp 3). University of Alberta.
  8. 8. @MathletePearcewww.tapintoteenminds.com
  9. 9. @MathletePearcewww.tapintoteenminds.com Math Class
  10. 10. @MathletePearcewww.tapintoteenminds.com Math Class
  11. 11. 1. Take Up Homework @MathletePearcewww.tapintoteenminds.com Math Class
  12. 12. @MathletePearcewww.tapintoteenminds.com 2. Definitions, Formulae, Procedures/Algorithms 1. Take Up Homework Math Class
  13. 13. @MathletePearcewww.tapintoteenminds.com 3. Examples 2. Definitions, Formulae, Procedures/Algorithms 1. Take Up Homework Math Class
  14. 14. @MathletePearcewww.tapintoteenminds.com 4. Homework 3. Examples 2. Definitions, Formulae, Procedures/Algorithms 1. Take Up Homework Math Class
  15. 15. Example 1 (a) List all combinations of three out of the four colours: red, blue, white, and green.
  16. 16. @MathletePearcewww.tapintoteenminds.com My Result: Successful in Math Unsuccessful in Math
  17. 17. @MathletePearcewww.tapintoteenminds.com A Perception Develops Good at Math Poor at Math
  18. 18. @MathletePearcewww.tapintoteenminds.com Confident in Math Class Doubtful in Math Class Students Feel…
  19. 19. @MathletePearcewww.tapintoteenminds.com Enjoying Mathematics Disliking Mathematics This May Lead To…
  20. 20. @MathletePearcewww.tapintoteenminds.com Willingness to Engage In Math Class Unwillingness to Engage In Math Class This May Lead To…
  21. 21. @MathletePearcewww.tapintoteenminds.com Moving Ahead Falling Behind This May Lead To…
  22. 22. @MathletePearcewww.tapintoteenminds.com Two Groups of Students Good at Math Poor at Math
  23. 23. @MathletePearcewww.tapintoteenminds.com Two Groups of Students Good at Math Poor at Math
  24. 24. @MathletePearcewww.tapintoteenminds.com Two Groups of Students Good at Math Poor at Math
  25. 25. @MathletePearcewww.tapintoteenminds.com Two Groups of Students Struggle with unfamiliar problems Good at Math Poor at Math
  26. 26. @MathletePearcewww.tapintoteenminds.com A VISION FOR MATHEMATICS EDUCATION VISION
  27. 27. @MathletePearcewww.tapintoteenminds.com Contextual VISION
  28. 28. @MathletePearcewww.tapintoteenminds.com Visual and Concrete Contextual VISION
  29. 29. @MathletePearcewww.tapintoteenminds.com Interconnected Visual and Concrete Contextual VISION
  30. 30. @MathletePearcewww.tapintoteenminds.com Interconnected Visual and Concrete Contextual CONFIDENCE
  31. 31. @MathletePearcewww.tapintoteenminds.com Interconnected Visual and Concrete Contextual PERCEPTION
  32. 32. @MathletePearcewww.tapintoteenminds.com Interconnected Visual and Concrete Contextual STUDENT SUCCESS
  33. 33. Change @MathletePearcewww.tapintoteenminds.com
  34. 34. Change @MathletePearcewww.tapintoteenminds.com
  35. 35. Change @MathletePearcewww.tapintoteenminds.com Immune to
  36. 36. http://www.vancouversun.com/life/From+geek+chic/6296707/story.html Photograph by: Maggie Wong @MathletePearcewww.tapintoteenminds.com
  37. 37. @MathletePearcewww.tapintoteenminds.com https://mathstrategies.wordpress.com/tag/numb3rs/
  38. 38. http://www.wykamath.com/
  39. 39. entertainment engagement = @MathletePearcewww.tapintoteenminds.com
  40. 40. @MathletePearcewww.tapintoteenminds.com algorithm
  41. 41. what’s this?
  42. 42. @MathletePearcewww.tapintoteenminds.com
  43. 43. @MathletePearcewww.tapintoteenminds.com
  44. 44. @MathletePearcewww.tapintoteenminds.com
  45. 45. @MathletePearcewww.tapintoteenminds.com
  46. 46. @MathletePearcewww.tapintoteenminds.com
  47. 47. algorithm @MathletePearcewww.tapintoteenminds.com
  48. 48. algorithms engagement = @MathletePearcewww.tapintoteenminds.com
  49. 49. algorithms engagement = understanding or @MathletePearcewww.tapintoteenminds.com
  50. 50. Notice? Wonder?
  51. 51. How many packs of paper would it take to reach the ceiling? OUR FIRST QUESTION:
  52. 52. @MathletePearcewww.tapintoteenminds.com PREDICTIONS
  53. 53. @MathletePearcewww.tapintoteenminds.com REQUEST INFORMATION
  54. 54. @MathletePearcewww.tapintoteenminds.com How many packs of paper will it take to reach a height of 273 cm? height 273cm 24.75cm
  55. 55. QUESTION @MathletePearcewww.tapintoteenminds.com
  56. 56. QUESTION @MathletePearcewww.tapintoteenminds.com Mr. Pearce stacks reams of paper vertically against a wall. If the height of 5 reams is 24.75 cm and the height of the room is 273 cm, how many reams of paper would he need to reach the ceiling?
  57. 57. QUESTION @MathletePearcewww.tapintoteenminds.com Mr. Pearce stacks reams of paper vertically against a wall. If the height of 5 reams is 24.75 cm and the height of the room is 273 cm, how many reams of paper would he need to reach the ceiling?FUN, RIGHT?
  58. 58. AnswerKey:55.15 QUESTION @MathletePearcewww.tapintoteenminds.com Mr. Pearce stacks reams of paper vertically against a wall. If the height of 5 reams is 24.75 cm and the height of the room is 273 cm, how many reams of paper would he need to reach the ceiling?
  59. 59. Making Connections @MathletePearcewww.tapintoteenminds.com
  60. 60. @MathletePearcewww.tapintoteenminds.com How many packs of paper will it take to reach a height of 273 cm? height 273cm 24.75cm
  61. 61. @MathletePearcewww.tapintoteenminds.com 273cm 24.75cm = 24.75cm24.75cm
  62. 62. @MathletePearcewww.tapintoteenminds.com 273cm = 24.75cm 24.75cm 24.75cm
  63. 63. @MathletePearcewww.tapintoteenminds.com 273cm = 24.75cm 24.75cm 24.75cm
  64. 64. @MathletePearcewww.tapintoteenminds.com 273cm = 25cm 25cm 25cm Friendly Numbers
  65. 65. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm 25cm Friendly Numbers
  66. 66. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm 25 cm Friendly Numbers Height
  67. 67. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 25 cm 25 cm Height 50 cm
  68. 68. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 25 cm 25 cm Height 25 cm 75 cm
  69. 69. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 25 cm 25 cm Height 25 cm 25 cm 100 cm
  70. 70. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 25 cm 25 cm Height 25 cm 25 cm 200 cm 25 cm 25 cm 25 cm 25 cm
  71. 71. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 100 cm Height 300 cm 100 cm 100 cm
  72. 72. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 100 cm Height 275 cm 100 cm 75 cm
  73. 73. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 100 cm Height 275 cm 100 cm 75 cm
  74. 74. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers “Array”
  75. 75. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers Area Model
  76. 76. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 5packs 11 groupsArea Model
  77. 77. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 5packs 11 groups 55 packs Area Model
  78. 78. 5packs 11 groups @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 5packs 11 groups 55 packs 5packs 11 groups 55 packs Area Model
  79. 79. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 5packs 11 groups 55 packs 5packs 11 groups 55 packs 25cm 11 groups Area ModelDouble
  80. 80. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 5packs 11 groups 55 packs 5packs 11 groups 55 packs 25cm 11 groups 275 cm Area ModelDouble
  81. 81. @MathletePearcewww.tapintoteenminds.com 275cm 25cm Friendly Numbers Double Number Line
  82. 82. Friendly Numbers Double Number Line 275cm 25cm 0 0
  83. 83. Friendly Numbers Double Number Line 275cm 25cm 0 0 Number of Packs Total Height
  84. 84. Friendly Numbers Double Number Line 275cm 25cm 0 0 5 25 Number of Packs Total Height
  85. 85. Friendly Numbers Double Number Line 275cm 25cm 0 0 5 25 50 10 Number of Packs Total Height
  86. 86. Friendly Numbers Double Number Line 275cm 25cm 0 0 5 25 50 10 75 15 250 50 Number of Packs Total Height 20 100 125 25 150 30 35 175 200 40 225 45 55 275
  87. 87. Friendly Numbers Double Number Line 275cm 25cm 0 0 5 25 50 10 Number of Packs Total Height
  88. 88. Friendly Numbers Double Number Line 275cm 25cm 0 0 5 25 50 10 Number of Packs Total Height 20 100
  89. 89. Friendly Numbers Double Number Line 275cm 25cm 0 0 5 25 50 10 Number of Packs Total Height 20 100 200 40
  90. 90. Friendly Numbers Double Number Line 275cm 25cm 0 0 5 25 50 10 Number of Packs Total Height 20 100 200 40 250 50 225 45 55 275
  91. 91. Friendly Numbers Double Number Line 275cm 25cm 0 0 5 25 50 10 Number of Packs Total Height 20 100 200 40 250 50 225 45 55 275275 5 25
  92. 92. Friendly Numbers Double Number Line 275cm 25cm 0 0 Number of Packs Total Height 275 x 275 5 25 5 25
  93. 93. Friendly Numbers Double Number Line 275cm 25cm 0 0 Number of Packs Total Height 275 x5 25 5 ?x 27525
  94. 94. Friendly Numbers Double Number Line 275cm 25cm 0 0 Number of Packs Total Height 275 x 275 5 25 5 25 ?x = 11111111
  95. 95. Friendly Numbers Double Number Line 275cm 25cm 0 0 Number of Packs Total Height 275 x 275 5 25 5 25 x = 1111 11 11
  96. 96. Friendly Numbers Double Number Line 275cm 25cm 0 0 Number of Packs Total Height 275 x 275 5 25 5 25 x = 11 11 11 x 11
  97. 97. Friendly Numbers Double Number Line 275cm 25cm 0 0 Number of Packs Total Height 275 x 275 5 25 5 25 x = 11 11 11 x 11x = 5555
  98. 98. Friendly Numbers Double Number Line 275cm 25cm 0 0 Number of Packs Total Height 275 275 5 25 5 25 x = 11 11 11 x 11x = 55 55
  99. 99. How many packs of paper would it take to reach the ceiling? @MathletePearcewww.tapintoteenminds.com How many packs of paper will it take to reach a height of 273 cm? packs of paper height 273cm 4.95 cm
  100. 100. How many packs of paper would it take to reach the ceiling? @MathletePearcewww.tapintoteenminds.com How many packs of paper will it take to reach a height of 273 cm? packs of paper height 273cm 4.95 cm
  101. 101. @MathletePearcewww.tapintoteenminds.com packs of paper height Independent Dependent 273cm 4.95 cm
  102. 102. @MathletePearcewww.tapintoteenminds.com 0 0 packs of paper height Independent Dependent
  103. 103. @MathletePearcewww.tapintoteenminds.com 0 0 1 4.95 packs of paper height Independent Dependent
  104. 104. @MathletePearcewww.tapintoteenminds.com 0 0 1 4.95 2 9.9 packs of paper height Independent Dependent
  105. 105. @MathletePearcewww.tapintoteenminds.com 0 0 1 4.95 2 9.9 packs of paper height Independent Dependent 4 19.8
  106. 106. @MathletePearcewww.tapintoteenminds.com 0 0 1 4.95 2 9.9 packs of paper height Independent Dependent 4 19.8 40 198
  107. 107. @MathletePearcewww.tapintoteenminds.com 0 0 1 4.95 2 9.9 packs of paper height Independent Dependent 4 19.8 40 198
  108. 108. @MathletePearcewww.tapintoteenminds.com packs of paper height:
  109. 109. @MathletePearcewww.tapintoteenminds.com packs of paper height
  110. 110. @MathletePearcewww.tapintoteenminds.com packs of paper height 24.75 cm 5 reams =
  111. 111. @MathletePearcewww.tapintoteenminds.com 24.75 cm 5 reams = 273 cm How Many?
  112. 112. @MathletePearcewww.tapintoteenminds.com 5 reams = x 24.75 cm 273 cm x ??
  113. 113. @MathletePearcewww.tapintoteenminds.com 5 reams = x 24.75 cm 273 cm x ??
  114. 114. @MathletePearcewww.tapintoteenminds.com 5 reams = x24.75 cm 273 cm x ??
  115. 115. @MathletePearcewww.tapintoteenminds.com 5 reams = x24.75 cm 273 cm x ?? 11.03
  116. 116. @MathletePearcewww.tapintoteenminds.com 24.75 cm 5 reams = 273 cm 11.03x x
  117. 117. @MathletePearcewww.tapintoteenminds.com 24.75 cm 5 reams = 273 cm 55.15 reams 11.03 x 11.03 x
  118. 118. @MathletePearcewww.tapintoteenminds.com VISION Visual and Concrete Contextual TASKS
  119. 119. Visual and Concrete Contextual TASKS INQUIRY Construct Conceptual Understanding VISION @MathletePearcewww.tapintoteenminds.com
  120. 120. Connect to Prior Knowledge Visual and Concrete Contextual TASKS CONNECTIONS INQUIRY Construct Conceptual Understanding VISION @MathletePearcewww.tapintoteenminds.com
  121. 121. Visual and Concrete Contextual TASKS CONSOLIDATE INQUIRY Move Towards Procedural Fluency Connect to Prior Knowledge CONNECTIONS Construct Conceptual Understanding VISION @MathletePearcewww.tapintoteenminds.com
  122. 122. 3 Act Math Tasks iTunes U kylep.ca/curiousmath1p @MathletePearcewww.tapintoteenminds.com
  123. 123. kylep.ca/curiousmath1p iTunes U @MathletePearcewww.tapintoteenminds.com
  124. 124. kylep.ca/curiousmath1p iTunes U @MathletePearcewww.tapintoteenminds.com
  125. 125. kylep.ca/curiousmath1p iTunes U @MathletePearcewww.tapintoteenminds.com Tap
  126. 126. 3 Act Math Tasks tapintoteenminds.com/3act-math @MathletePearcewww.tapintoteenminds.com fishing4tech.com/mtbos.html
  127. 127. @MathletePearcewww.tapintoteenminds.com The CN Tower has a height of 553 m and your stack of 5 packages of paper have a height of approximately 0.25 m. Approximately how many packages of paper would you need to stack up to the height of the CN Tower? 24.75cm
  128. 128. Concreteness Fading
  129. 129. Concreteness Fading 1 Enactive
  130. 130. Concreteness Fading 1 Enactive Concrete
  131. 131. Concreteness Fading 1 2 Enactive Concrete Iconic
  132. 132. Concreteness Fading 1 2 Enactive Concrete Iconic Visual
  133. 133. Concreteness Fading 1 2 3 Enactive Concrete Iconic Visual Symbolic
  134. 134. Concreteness Fading 1 2 3 Enactive Concrete Iconic Visual Symbolic Abstract
  135. 135. Concreteness Fading 1 2 3Enactive Concrete Iconic Visual Symbolic Abstract
  136. 136. Concreteness Fading 1 2 3Enactive Concrete Iconic Visual Symbolic Abstract
  137. 137. Concreteness Fading 1 2 3Enactive Concrete Iconic Visual Symbolic Abstract
  138. 138. Concreteness Fading 1 2 3Enactive Concrete Iconic Visual Symbolic Abstract 2 2x 2 6 1 044 21 3 + 275
  139. 139. Making Math Contextual, Visual, and Concrete @MathletePearcewww.tapintoteenminds.com

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