This document discusses strategies for teaching math pedagogy based on research. It summarizes Jerome Bruner's research showing students build understanding by moving from concrete to pictorial to abstract representations. Richard Skemp's research found relational understanding through concepts like quantity and correspondence leads to better long-term learning than instrumental understanding through procedures alone. Zoltan Dienes' research showed exposing students to concepts through multiple materials enhances conceptual understanding. The document then discusses strategies for teaching number bonds, place value, and addition and subtraction in Grades 1-3.

1. Welcome!
Munch & Mingle

2. K, 1, & 3 Were Awesome!

3. Agenda & Goals
• Review training & implementa;on plan
• Review Singapore Math Pedagogy
• Inves;gate Grade Specific Strategies

4. Math Pedagogy
Jerome Bruner’s research proved that instruc;onal strategies
build understanding for students when they move from…
• Concrete (manipula;ves) to
• Pictorial (visual models or drawings) to
• Abstract representa;ons (numbers, symbols)

5. Math Pedagogy
Richard Skemp’s research proved that for long term learning to
occur rela(onal understanding is more successful than
instrumental learning.
Rela(onal Understanding Instrumental Understanding
Conceptual Procedural
WHY before HOW How
One to One Correspondence Oral Coun;ng
Quan;;es and Values Wri;ng numbers, Spelling numbers
Each piece RELATES to all others Isolated steps or steps without meaning
Reading with understanding Phone;c or word calling

6. Math Pedagogy
Zoltan Diene’s research proved that children gain the most
conceptual understanding when they are exposed to a concept
through a variety of materials or experiences.
Perceptual Variability
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q! ;!
p! /!
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10

7. Reflec;ng On Pedagogy
Turn and Talk: Summarize each of these with your group.
 Concrete‐Pictorial‐Abstract (Bruner)
 Rela;onal Understanding (Skemp)
 Mul;ple Representa;ons (Dienes)

8. Dyscalculia
These students see numbers as fixed and solid.
7
Other students see numbers as breakable.
6,1 5,2 4,3

9. Math Strategies & Materials
Anchor to 5. Bonds to 5.

10. Composing Numbers

11. Math Strategies & Materials
Anchor to 10. Bonds to 10.

12. Grade 1 Math in Focus
Numbers to 10…………………….9 days
Number Bonds to 10……………6 days
Addi;on Facts to 10……..……..9 days
Subtrac;on Facts to 10……..…9 days
Ordinal Numbers to 10…..……7 days
40 days

13. Number Bonds

14. Composing& Decomposing Numbers

15. Composing & Decomposing Numbers
V! C!

16. Composing& Decomposing Numbers

17. Composing& Decomposing Numbers

18. Grade 1 Math in Focus
Numbers to 20…………………..….9 days
Add. & Sub. Facts to 20……..….6 days
15 days

22. Using Base Ten Blocks to Show Place Value

23. Place Value for Addi;on & Subtrac;on

24. Place Value Strips

25. Distribu;ve Method: Addi;on
Using Place Value for Rela;onal Understanding
64 + 28 =
Tens + Ones
(60 + 20) + (4+8) =
80 + 12 = 92

26. Branching Method: Addi;on
Using Number Bonds for Rela;onal Understanding
64 + 28 =
62 2
62 + 30 = 92