TỔNG ÔN TẬP THI VÀO LỚP 10 MÔN TIẾNG ANH NĂM HỌC 2023 - 2024 CÓ ĐÁP ÁN (NGỮ Â...
MDSC whiteford
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
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
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
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