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OrganizerPre-School Education UnitMinistry of Education, Singapore
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Slides are available atwww.i-teach-k.blogspot.comwww.facebook.com/MCISingapore
LecturerYeap Ban [email protected]
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introductionfrom 1992 to 2013
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Singapore Ministry of Education 2006
“Mathematics is an excellent vehicle for the development
and improvement of a person’s intellectual competencies”
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visualization
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lookingforpatterns
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numbersense
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whatto teach
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how toteach
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Use 3 pieces. Make a rectangle.
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See www.facebook.com/MCISingapore under the Photo Album Tangrams for more solutions
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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.
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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.”
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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
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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)
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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
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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.”
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Level 3: Formal Deduction
• Construct proofs to determine the truth of a mathematic statements
• Highly abstract form of geometric thought
Level 4: Rigour
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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
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Ordinal, Cardinal & Nominal Numbers
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• Cardinal Number• Ordinal Number
• Measurement NumberSiti
John
Michael
• Nominal Number
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ordinal number
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Problem
Arrange the ten cards so that you can do what is shown to you.
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Method 1 – by drawing
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Method 2 – by using the cards
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Scarsdale Teachers’ Institute, New York
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rationalcounting
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additionstrategies• Count All
• Count On• Count On + Commutative Property• Make Ten• Number Facts (1 + 1 to 9 + 9)
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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
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Manila, The Philippines
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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.
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Ministry of Education Singapore
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Pa-Pa-Lang by one of my nephews