The document discusses key research on effective math pedagogy strategies. It summarizes Jerome Bruner's research showing that 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 procedural understanding. Zoltan Dienes' research showed exposing students to concepts through multiple materials enhances conceptual understanding. The document then provides examples of math strategies and manipulatives teachers can use to develop relational understanding, such as using place value blocks, number bonds, and the distributive and branching methods.

1. Welcome!
Munch & Mingle

2. K & 1 Were Awesome!

3. Agenda & Goals
• Review training & implementa9on plan
• Review Singapore Math Pedagogy
• Inves9gate Grade Specific Strategies

4. Math Pedagogy
Jerome Bruner’s research proved that instruc9onal strategies
build understanding for students when they move from…
• Concrete (manipula9ves) to
• Pictorial (visual models or drawings) to
• Abstract representa9ons (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 Coun9ng
Quan99es and Values Wri9ng numbers, Spelling numbers
Each piece RELATES to all others Isolated steps or steps without meaning
Reading with understanding Phone9c 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. Reflec9ng On Pedagogy
Turn and Talk: Summarize each of these with your group.
 Concrete‐Pictorial‐Abstract (Bruner)
 Rela9onal Understanding (Skemp)
 Mul9ple Representa9ons (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 10. Bonds to 10.

10. Decomposing Numbers

11. Composing Numbers

12. Composing Numbers
V!
C!

13. Decomposing Numbers

14. Decomposing Numbers

18. Using Base Ten Blocks to Show Place Value

19. Addi9on and Subtrac9on
with Base Ten Blocks
   "

20. Addi9on and Subtrac9on With Place Value Discs

21. Addi9on & Subtrac9on With Place Value Discs

22. Distribu9ve Method: Addi9on
Using Place Value for Rela9onal Understanding
64 + 28 =
Tens + Ones
(60 + 20) + (4+8) =
80 + 12 = 92

23. Branching Method: Addi9on
Using Number Bonds for Rela9onal Understanding
64 + 28 =
62 2
62 + 30 = 92

24. Mul9plica9on With Place Value Discs

25. Mul9plica9on With Place Value Discs

26. Mul9plica9on With Place Value Discs (Pictorial)

27. Distribu9ve Method: Mul9plica9on
Using Place Value for Rela9onal Understanding
22 x 3 =
(20 x 3) + (2 x 3)=
60 + 6 = 66

28. Branching Method: Mul9plica9on
Using Number Bonds
&
Place Value
For Rela9onal Understanding