This document provides an overview of math pedagogy strategies including: 1) Jerome Bruner's research on moving from concrete to pictorial to abstract representations to build student understanding. 2) Richard Skemp's research finding that relational understanding through concepts like one-to-one correspondence leads to better long-term learning than instrumental understanding of isolated steps. 3) Zoltan Dienes' research showing that exposing students to concepts through multiple materials and experiences leads to stronger conceptual understanding.

1. Welcome!
Munch & Mingle

2. Kindergarten Was Awesome!

3. Agenda & Goals
• Review training & implementa8on plan
• Review Singapore Math Pedagogy
• Inves8gate Grade Specific Strategies

4. Math Pedagogy
Jerome Bruner’s research proved that instruc8onal strategies
build understanding for students when they move from…
• Concrete (manipula8ves) to
• Pictorial (visual models or drawings) to
• Abstract representa8ons (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 Coun8ng
Quan88es and Values Wri8ng numbers, Spelling numbers
Each piece RELATES to all others Isolated steps or steps without meaning
Reading with understanding Phone8c 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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p! /!
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q!

8. Reflec8ng On Pedagogy
Turn and Talk: Summarize each of these with your group.
 Concrete‐Pictorial‐Abstract (Bruner)
 Rela8onal Understanding (Skemp)
 Mul8ple Representa8ons (Dienes)

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

10. Composing Numbers

11. Composing Numbers
V!
C!

12. Composing Numbers

13. Composing Numbers

14. Decomposing Numbers

15. Decomposing Numbers

16. Decomposing Numbers

17. Decomposing Numbers

18. Number Bonds

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

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

21. Decomposing Numbers

22. Decomposing Numbers