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MDSC whiteford

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MDSC whiteford

  1. 1. CONSTRUCTINGMEANING IN COUNTINGAND NUMERACY Tim Whiteford Ph.D. Andrew’s Dad and Associate Professor St. Michael’s College Colchester Vermont twhiteford@smcvt.edu
  2. 2. Some Theory• Knowledge – 2 types • Procedural – 3, $, +, x, =, 4(3+2) • Conceptual – joining, separating, area• Understanding – 2 types • Fragile – rote, rules without reason • Robust – making meaningful connection
  3. 3. Some Math• Manipulatives - Arrow cards - Digiblocks• Numeracy – Number names• The Triangle of Meaning – 3 “languages”• Place Value• The Referent Unit – what is the One• Meanings of the Operations – join, separate compare, part-part-whole
  4. 4.  Arrow cards – Interactive Arrow Cards Digiblocks Numicon Free on-line Interactive manipulatives Additional math resources
  5. 5. Numeracy • Number name sequence – zero, one, two etc • Subitizing – regular and irregular • One to One correspondence – one word, one object • Cardinality – last counting word names the group
  6. 6. The Triangle of Meaning 5 “Five”
  7. 7. Place Value• Base Ten is groups of groups of tens• 0 – 9 is repeated in each place• 10 ones make (or are regrouped) as one ten etc• The 100, 10, 1 pattern is repeated in ones, thousands, millions and so on. Millions Thousands Ones 100 10 1 100 10 1 100 10 1
  8. 8. The Referent Unit• Changes a numeral into a magnitude 5• Gives meaning to numbers• Can be culturally derived• Can change within a number sentence or problem
  9. 9. Meanings of the Operations• Visualize problem solving by thinking about what is happening. • Addition and subtraction Part-Part-Whole • Join • Separate • Compare • Multiplication and Division (some examples) • Equal groups • Area • Then use a calculator
  10. 10. Some Andrew• A prom goer• A snowboarder
  11. 11. More Andrew• An incredible Wii Player• A Fisherman• A High School Graduate
  12. 12. More Andrew• A Basketball Player• A Chef• An “Arab”
  13. 13. More Andrew• A Drummer• A Guitarist• A Worker
  14. 14. More Andrew• A Scientist• An unhappy Red Sox fan
  15. 15. Some Applications •Wii •iPad2 •Board Games •Toys •Health •Fitness •Calendar •Clocks
  16. 16.  The Nintendo Wii System Math, math and more math.
  17. 17. More Wii Play Together• Socially Dynamic• Language-based• Physical exercise• Intuitive- why is he so good?
  18. 18. iPAD2 4 U 2• Free Apps• Apps with good math• Easy to use• Intuitive• Portable
  19. 19. Sorry and Box It• Math-based board games such as Sorry• Activity games such as Shut the Box
  20. 20. Hot Wheel Muscle Cars• Sorting• Racing• Dates
  21. 21. Watch Those Calories• Counting calories• Daily allowance
  22. 22. What’s The Date• Calendar• Every morning
  23. 23. Clocks• What is the time?• Analog and digital• One-handed clock
  24. 24. The Telephone and Remote• Important telephone numbers• TV channels
  25. 25. Credit Card and Calculator• Andrew uses his own credit card• He uses a calculator to solve problems (we’re working on it)
  26. 26.  Websites  TJW math page  http://academics.smcvt.edu/twhiteford/Math/Math. htm  TJW iPAD2 page  http://academics.smcvt.edu/twhiteford/Math/Math %20Apps.htm  TJW iPAD2 and Special Education FaceBook page http://www.facebook.com/#!/groups/1158972518321 73/
  27. 27.  Quick Guides to Inclusion – Giangreco and Doyle - Brookes Publishing Making sense – Teaching and Learning Math with Understanding - Hebert et al – Heinneman Children’s Mathematics – Carpenter at al – Heinneman Teaching Math to People with Down Syndrome - Horstmeier Woodbine House publishing

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