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Organizer
Pre-School Education Unit
Ministry of Education, Singapore
Slides are available at         Lecturer
www.i-teach-k.blogspot.com      Yeap Ban Har
www.facebook.com/MCISingapore   yeapbanhar@gmail.com
ECM101 3 September 2012
introduction
      from 1992 to 2013
ECM101 3 September 2012
ECM101 3 September 2012
“Mathematics is an excellent
 vehicle for the development
and improvement of a person’s
  intellectual competencies”
                 Singapore Ministry of Education 2006
what
  to teach
visualization
looking
   for
  patterns
number
   sense
ECM101 3 September 2012
how to
  teach
ECM101 3 September 2012
Use 3 pieces. Make a rectangle.
See www.facebook.com/MCISingapore under the Photo Album
Tangrams for more solutions
ECM101 3 September 2012
ECM101 3 September 2012
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

          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
Ordinal, Cardinal & Nominal
          Numbers
ECM101 3 September 2012
•   Cardinal Number
•   Ordinal Number
•   Nominal Number
•   Measurement Number
ECM101 3 September 2012
ordinal
  number
ECM101 3 September 2012
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
ECM101 3 September 2012
ECM101 3 September 2012
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

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ECM101 3 September 2012

  • 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
  • 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
  • 33. Problem Arrange the ten cards so that you can do what is shown to you.
  • 35. Method 1 – by drawing Train-The-Trainers Programme, Rotterdam
  • 36. Method 2 – by using the cards Train-The-Trainers Programme, Rotterdam
  • 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
  • 44. Pa-Pa-Lang by one of my nephews