This is a summary of the discussion on Day 1. This is the fifth class organized by MOE Singapore for local kindergarten teachers. MCI offers early childhood courses with emphasis on mathematics and science.

1. Organizer
Pre-School Education Unit
Ministry of Education, Singapore

2. Slides are available at Lecturer
www.i-teach-k.blogspot.com Yeap Ban Har
www.facebook.com/MCISingapore yeapbanhar@gmail.com

4. introduction
from 1992 to 2013

7. “Mathematics is an excellent
vehicle for the development
and improvement of a person’s
intellectual competencies”
Singapore Ministry of Education 2006

8. what
to teach

9. visualization

10. looking
for
patterns

11. number
sense

13. how to
teach

15. Use 3 pieces. Make a rectangle.

16. See www.facebook.com/MCISingapore under the Photo Album
Tangrams for more solutions

19. Development of
Geometric Thinking
van Hiele Model of Geometric Thinking
There are 5 levels:
• Level 0: Visualisation
• Level 1: Analysis
• Level 2: Informal Deduction
• Level 3: Deduction
• Level 4: Rigour
The levels are sequential – must start at the basic
level.

20. Level 0: Visualisation
• Recognise the appearance of the
shapes (look sort of alike)
• Properties are incidental to the shape
(implicit)
“A square is a square because it looks
like a square.”

21. Implications for Instruction
Level 0: Visualisation
• Provide concrete materials that can be
manipulated
• Include different and varied examples of
shapes
• Involve lots of sorting, identifying, and
describing of various shapes
• Provide opportunities to build, make, draw,
put together and take apart shapes

22. Level 1: Analysis
• More aware of the properties of a
shape than to its appearance
• Use properties to define categories of
shapes (able to list the properties but
not the relationships among the
properties)

23. Implications for Instruction
Level 1: Informal Deduction
• Engage in the same activities as level 0 but
the focus of the activities should be on the
properties of the shapes, not identification
• Classify shapes by properties
• Derive generalisation by studying examples
• Use appropriate vocabulary

24. Level 2: Informal Deduction
• Understand the relation of properties
within and among figures
“A square is a rectangle, a rectangle is
parallelogram which is also a
quadrilateral.”

25. Level 3: Formal Deduction
• Construct proofs to determine the
truth of a mathematic statements
Level 4: Rigour
• Highly abstract form of geometric
thought

26. Summary
 Understand the importance of visualisation
and geometric thinking (van Hiele model of
geometric thinking )
 Use activities to reinforce visualisation skills
• Tangram activity
• Grandfather Tang’s story
• Create your own picture

27. Ordinal, Cardinal & Nominal
Numbers

29. • Cardinal Number
• Ordinal Number
• Nominal Number
• Measurement Number

31. ordinal
number

33. Problem
Arrange the ten cards so
that you can do what is
shown to you.

34. Ministry of Education, Singapore

35. Method 1 – by drawing
Train-The-Trainers Programme, Rotterdam

36. Method 2 – by using the cards
Train-The-Trainers Programme, Rotterdam

37. Scarsdale Teachers’ Institute, New York

38. Professional Development for Teachers, Manila

39. rational
counting

42. Number Bonds
Core Concepts
- Whole
- Parts
Can students figure out that a given number (up to ten)
comprises of two numbers?
Convention
Do students understand a convention used
to represent number bonds?
The common convention used in Singapore
primary school textbooks is shown

43. Keys Grade School, Manila

44. Pa-Pa-Lang by one of my nephews