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OrganizerPre-School Education UnitMinistry of Education, Singapore
Slides are available at         Lecturerwww.i-teach-k.blogspot.com      Yeap Ban Harwww.facebook.com/MCISingapore   yeapba...
introduction      from 1992 to 2013
“Mathematics is an excellent vehicle for the developmentand 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 AlbumTangrams for more solutions
Development ofGeometric Thinkingvan Hiele Model of Geometric ThinkingThere are 5 levels:• Level 0: Visualisation• Level 1:...
Level 0: Visualisation• Recognise the appearance of the   shapes (look sort of alike)• Properties are incidental to the sh...
Implications for InstructionLevel 0: Visualisation• Provide concrete materials that can be  manipulated• Include different...
Level 1: Analysis• More aware of the properties of a  shape than to its appearance• Use properties to define categories of...
Implications for InstructionLevel 1: Informal Deduction• Engage in the same activities as level 0 but  the focus of the ac...
Level 2: Informal Deduction• Understand the relation of properties  within and among figures“A square is a rectangle, a re...
Level 3: Formal Deduction• Construct proofs to determine the  truth of a mathematic statements          Level 4: Rigour• H...
Summary Understand the importance of visualisation  and geometric thinking (van Hiele model of  geometric thinking ) Use...
Ordinal, Cardinal & Nominal          Numbers
•   Cardinal Number•   Ordinal Number•   Nominal Number•   Measurement Number
ordinal  number
ProblemArrange the ten cards sothat you can do what isshown to you.
Ministry of Education, Singapore
Method 1 – by drawingTrain-The-Trainers Programme, Rotterdam
Method 2 – by using the cardsTrain-The-Trainers Programme, Rotterdam
Scarsdale Teachers’ Institute, New York
Professional Development for Teachers, Manila
rational   counting
Number BondsCore Concepts- Whole- PartsCan students figure out that a given number (up to ten)comprises of two numbers?   ...
Keys Grade School, Manila
Pa-Pa-Lang by one of my nephews
ECM101 3 September 2012
ECM101 3 September 2012
ECM101 3 September 2012
ECM101 3 September 2012
ECM101 3 September 2012
ECM101 3 September 2012
ECM101 3 September 2012
ECM101 3 September 2012
ECM101 3 September 2012
ECM101 3 September 2012
ECM101 3 September 2012
ECM101 3 September 2012
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ECM101 3 September 2012

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This is a summary of the discussion on Day 1. This is the fifth class organized by MOE Singapore for local kindergarten teachers. MCI offers early childhood courses with emphasis on mathematics and science.

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ECM101 3 September 2012

  1. 1. OrganizerPre-School Education UnitMinistry of Education, Singapore
  2. 2. Slides are available at Lecturerwww.i-teach-k.blogspot.com Yeap Ban Harwww.facebook.com/MCISingapore yeapbanhar@gmail.com
  3. 3. introduction from 1992 to 2013
  4. 4. “Mathematics is an excellent vehicle for the developmentand improvement of a person’s intellectual competencies” Singapore Ministry of Education 2006
  5. 5. what to teach
  6. 6. visualization
  7. 7. looking for patterns
  8. 8. number sense
  9. 9. how to teach
  10. 10. Use 3 pieces. Make a rectangle.
  11. 11. See www.facebook.com/MCISingapore under the Photo AlbumTangrams for more solutions
  12. 12. 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 basiclevel.
  13. 13. 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 lookslike a square.”
  14. 14. 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
  15. 15. 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)
  16. 16. 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
  17. 17. Level 2: Informal Deduction• Understand the relation of properties within and among figures“A square is a rectangle, a rectangle isparallelogram which is also aquadrilateral.”
  18. 18. Level 3: Formal Deduction• Construct proofs to determine the truth of a mathematic statements Level 4: Rigour• Highly abstract form of geometric thought
  19. 19. 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
  20. 20. Ordinal, Cardinal & Nominal Numbers
  21. 21. • Cardinal Number• Ordinal Number• Nominal Number• Measurement Number
  22. 22. ordinal number
  23. 23. ProblemArrange the ten cards sothat you can do what isshown to you.
  24. 24. Ministry of Education, Singapore
  25. 25. Method 1 – by drawingTrain-The-Trainers Programme, Rotterdam
  26. 26. Method 2 – by using the cardsTrain-The-Trainers Programme, Rotterdam
  27. 27. Scarsdale Teachers’ Institute, New York
  28. 28. Professional Development for Teachers, Manila
  29. 29. rational counting
  30. 30. Number BondsCore Concepts- Whole- PartsCan 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
  31. 31. Keys Grade School, Manila
  32. 32. Pa-Pa-Lang by one of my nephews

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