This course is offered to pre-school teachers by Pre-School Unit, Ministry of Education Singapore. This is Day 1 of the 12-hour course. Forty participants enrolled for the class which is the 4th Cohort.
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Development ofGeometric Thinkingvan Hiele Model of Geometric ThinkingThere are 5 levels:• Level 0: Visualisation• Level 1: Analysis• Level 2: Informal Deduction• Level 3: Deduction• Level 4: RigourThe 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 asquare.”
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 isparallelogram which is also a quadrilateral.”
Level 3: Formal Deduction• Construct proofs to determine the truth of a mathematic statements Level 4: Rigour• Highly abstract form of geometric thought
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
addition• strategies Count All• Count On• Count On + Commutative Property• Make Ten• Number Facts (1 + 1 to 9 + 9)
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