1. CONSTRUCTING
MEANING IN COUNTING
AND 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