Organizer

Pre-School Education Unit

Ministry of Education, Singapore

Slides are available at www.i-teach-k.blogspot.com www.facebook.com/MCISingapore

Lecturer Yeap Ban Har yeapbanhar@gmail.com

introduction from 1992 to 2013

Singapore Ministry of Education 2006

“Mathematics is an excellent vehicle for the development

and improvement of a person’s intellectual competencies”

what to teach

visualization

looking for

patterns

number sense

how to teach

Use 3 pieces. Make a rectangle.

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

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.

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.”

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

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)

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

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.”

Level 3: Formal Deduction

• Construct proofs to determine the

truth of a mathematic statements

• Highly abstract form of geometric

thought

Level 4: Rigour

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

Ordinal, Cardinal & Nominal Numbers

• Cardinal Number • Ordinal Number

• Measurement Number

• Nominal Number

ordinal number

Problem

Arrange the ten cards so

that you can do what is

shown to you.

Ministry of Education, Singapore

Method 1 – by drawing

Train-The-Trainers Programme, Rotterdam

Method 2 – by using the cards

Train-The-Trainers Programme, Rotterdam

Scarsdale Teachers’ Institute, New York

Professional Development for Teachers, Manila

rational counting

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

Keys Grade School, Manila

Pa-Pa-Lang by one of my nephews