OrganizerPre-School Education UnitMinistry of Education, Singapore

Slides are available atwww.i-teach-k.blogspot.comwww.facebook.com/MCISingapore

LecturerYeap Ban Haryeapbanhar@gmail.com

introductionfrom 1992 to 2013

Singapore Ministry of Education 2006

“Mathematics is an excellent vehicle for the development

and improvement of a person’s intellectual competencies”

visualization

lookingforpatterns

numbersense

whatto teach

how toteach

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 InstructionLevel 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 InstructionLevel 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 NumberSiti

John

Michael

• Nominal Number

ordinal number

Problem

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

Method 1 – by drawing

Method 2 – by using the cards

Scarsdale Teachers’ Institute, New York

rationalcounting

additionstrategies• Count All

• Count On• Count On + Commutative Property• Make Ten• Number Facts (1 + 1 to 9 + 9)

I see 8 and 5 so I should

say the sum. 13

These two players with cards on their forehead cannot see their own card but can see the other person’s card. The goal is to say what number is on her own forehead.

Santiago, Chile

Manila, The Philippines

What if a child is already proficient in counting – which is the main purpose of the activity? They may be asked to observe a pattern to suggest a winning strategy.

Ministry of Education Singapore

Pa-Pa-Lang by one of my nephews