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MDSC whiteford

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  • 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. 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. 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.  Arrow cards – Interactive Arrow Cards Digiblocks Numicon Free on-line Interactive manipulatives Additional math resources
  • 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. The Triangle of Meaning 5 “Five”
  • 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. 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. 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. Some Andrew• A prom goer• A snowboarder
  • 11. More Andrew• An incredible Wii Player• A Fisherman• A High School Graduate
  • 12. More Andrew• A Basketball Player• A Chef• An “Arab”
  • 13. More Andrew• A Drummer• A Guitarist• A Worker
  • 14. More Andrew• A Scientist• An unhappy Red Sox fan
  • 15. Some Applications •Wii •iPad2 •Board Games •Toys •Health •Fitness •Calendar •Clocks
  • 16.  The Nintendo Wii System Math, math and more math.
  • 17. More Wii Play Together• Socially Dynamic• Language-based• Physical exercise• Intuitive- why is he so good?
  • 18. iPAD2 4 U 2• Free Apps• Apps with good math• Easy to use• Intuitive• Portable
  • 19. Sorry and Box It• Math-based board games such as Sorry• Activity games such as Shut the Box
  • 20. Hot Wheel Muscle Cars• Sorting• Racing• Dates
  • 21. Watch Those Calories• Counting calories• Daily allowance
  • 22. What’s The Date• Calendar• Every morning
  • 23. Clocks• What is the time?• Analog and digital• One-handed clock
  • 24. The Telephone and Remote• Important telephone numbers• TV channels
  • 25. Credit Card and Calculator• Andrew uses his own credit card• He uses a calculator to solve problems (we’re working on it)
  • 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.  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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