1. K‐3 Jan.‐Feb. Math Trainings
• 2 hours of Singapore pedagogy & strategies
• 1 hour classroom visit and discussion
WQW !
• 2 hours applying Singapore strategies to IMI
(Make & Take)

2. Math Pedagogy
Jerome Bruner’s research proved that instrucGonal strategies
build understanding for students when they move from…
• Concrete (manipulaGves) to
• Pictorial (visual models or drawings) to
• Abstract representaGons (numbers, symbols)

3. 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 CounGng
QuanGGes and Values WriGng numbers, Spelling numbers
Each piece RELATES to all others Isolated steps or steps without meaning
Reading with understanding PhoneGc or word calling

4. RelaGonal Understanding (Kindergarten)

5. RelaGonal Understanding (1st Grade)

6. RelaGonal Understanding (2nd Grade)

7. 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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8. Perceptual Variability (K)

9. Perceptual Variability (1st)

10. Perceptual Variability (2nd)

11. ReflecGng On Pedagogy
Turn and Talk: Summarize each of these with your group.
 Concrete‐Pictorial‐Abstract (Bruner)
 RelaGonal Understanding (Skemp)
 MulGple RepresentaGons (Dienes)

12. K‐2 Singapore Models
• Ten Frames
• Number Bonds (& Part‐Part‐Whole)
• Linker Cubes (KaGe Kubes)
• Base Ten Blocks

13. Kindergarten
Anchor to 5. Bonds to 5.

14. Beginning Look & Say (Math Talk)
Count together
One to One Corr.
Intermediate
Student counts
Touching objects
TransiGoning from
manipulaGves
Advanced
Group similar objects
Grouping for counGng
Making number bonds
Challenge
CounGng beyond pic
If one more frog…
If one less frog…
Making stories

15. Using a Picture to Compose Numbers

16. Composing Numbers

17. K & 1st
Anchor to 10. Bonds to 10.

18. Grade 1 Math in Focus
Numbers to 10…………………….9 days
Number Bonds to 10……………6 days
AddiGon Facts to 10……..……..9 days
SubtracGon Facts to 10……..…9 days
Ordinal Numbers to 10…..……7 days
40 days

19. Number Bonds

20. Number Bonds

21. Number Bonds

22. Composing & Decomposing Numbers

23. 2nd Grade: Part‐Part‐Whole

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

27. 1st Grade: 2‐digit Regrouping

28. 2nd Grade: Place Value Strips

29. RelaGonal Understanding
and MulGple RepresentaGons

30. 2nd Grade: MulGplicaGon