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This course focuses on the WHAT and HOW of numeracyprogrammes in early childhood education. You will complete fourmodules ...
Visualization                               Shapes & Geometry         INSTRUCTOR       Peggy FooMarshall Cavendish Institute
Spatial Visualisation• It involves having images of objects• Spatial visualisation and geometry are  interdependent (learn...
Development of              Geometric Thinkingvan Hiele Model of Geometric ThinkingThere are 5 levels:• Level 0: Visualisa...
Level 0: Visualisation• Recognise the appearance of the shapes (look  sort of alike)• Properties are incidental to the sha...
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• Example: a square is a recta...
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...
Conservation of                                  Numbers         INSTRUCTOR       Peggy FooMarshall Cavendish Institute
ObjectivesParticipants will be able to:• Understand the importance of conservation of  numbers• Study a lesson (video) on ...
Conservation of Numbers• The number of a set remains the same even if  the items of the set are rearranged (Piaget, 1952)•...
ResponsesNumber Conservation by Counting:• I counted themNumber Conservation by Justification:• Nothing is added or taken ...
Conservation Task• Using 4 cubes, make as many different  structures as you can
Learning points• What can we achieve using conservation  tasks?   Enhance visualisation skills by constructing different  ...
Summary•   Importance of conservation of numbers    (basis of number knowledge, start with    concept of equality and one-...
Ordinal and Cardinal                                    Numbers         INSTRUCTOR     Yeap Ban HarMarshall Cavendish Inst...
B   A   N   H   A   R
• Cardinal Number• Ordinal Number• Measurement Number                 SitiMichael          John
ProblemRearrange the sticks toshow a given numberof squares.                          Wellington Primary School
Task                Lesson Study Problem                                 Wellington Primary School• Move 3 sticks to make ...
Task• Move 3 sticks to make 3 squares.
Task• Move 3 sticks to make 3 squares.
Task• Move 3 sticks to make 2 squares.
Task• Move 3 sticks to make 2 squares.
Task• Move 3 sticks to make 2 squares.
ProblemArrange the ten cards sothat you can do what isshown to you.
Method 1 – by drawing
Method 2 – by using the cards
Scarsdale Teachers’ Institute, New York
Think of two digits. Makethe largest number. Makethe smallest number. Findthe difference. What doyou notice?
Development of Early Numeracy
Development of Early Numeracy
Development of Early Numeracy
Development of Early Numeracy
Development of Early Numeracy
Development of Early Numeracy
Development of Early Numeracy
Development of Early Numeracy
Development of Early Numeracy
Development of Early Numeracy
Development of Early Numeracy
Development of Early Numeracy
Development of Early Numeracy
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Development of Early Numeracy

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This course is for early childhood educators.

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Development of Early Numeracy

  1. 1. This course focuses on the WHAT and HOW of numeracyprogrammes in early childhood education. You will complete fourmodules in this course.By the end of this course, you will learn• selected key content areas such as ordinal numbers, cardinal numbers (counting), addition and subtraction, measurements and geometry• the importance of visualization, generalization and number sense• the need to include ‘soft’ skills such as communication and metacognition, creativity and curiosity, and so on• strategies• learning theories
  2. 2. Visualization Shapes & Geometry INSTRUCTOR Peggy FooMarshall Cavendish Institute
  3. 3. Spatial Visualisation• It involves having images of objects• Spatial visualisation and geometry are interdependent (learning of one area will lead to the other)
  4. 4. Development of Geometric 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
  5. 5. 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” i.e. appearance of the shape
  6. 6. 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
  7. 7. 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)
  8. 8. 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
  9. 9. Level 2: Informal Deduction• Understand the relation of properties within and among figures• Example: a square is a rectangle, a rectangle is parallelogram which is also a quadrilateral
  10. 10. Level 3: Formal Deduction• Construct proofs to determine the truth of a mathematic statements
  11. 11. Level 4: Rigour• Highly abstract form of geometric thought
  12. 12. Summary Understand the importance of visualisation and geometric thinking (van Hiele model of geometric thinking ) Use activities to reinforce visualisation skills • Tangram activity (manipulate and identify geometric shape) • Grandfather Tang’s Story / Create your own picture (arrange, construct, describe in your own words)
  13. 13. Conservation of Numbers INSTRUCTOR Peggy FooMarshall Cavendish Institute
  14. 14. ObjectivesParticipants will be able to:• Understand the importance of conservation of numbers• Study a lesson (video) on a conservation task
  15. 15. Conservation of Numbers• The number of a set remains the same even if the items of the set are rearranged (Piaget, 1952)• Basis of number knowledge• Based on understanding the concept of equality and one to one correspondence• Reveal/ assess children’s knowledge of numbers
  16. 16. ResponsesNumber Conservation by Counting:• I counted themNumber Conservation by Justification:• Nothing is added or taken away• I can put them back in the same position so they look like as they did before
  17. 17. Conservation Task• Using 4 cubes, make as many different structures as you can
  18. 18. Learning points• What can we achieve using conservation tasks? Enhance visualisation skills by constructing different structures and sorting / classifying the structures Enhance reasoning and communication skills when asked to justify one’s responses
  19. 19. Summary• Importance of conservation of numbers (basis of number knowledge, start with concept of equality and one-to-one correspondence)• Aspects of lesson which support visualisation and reasoning skills
  20. 20. Ordinal and Cardinal Numbers INSTRUCTOR Yeap Ban HarMarshall Cavendish Institute
  21. 21. B A N H A R
  22. 22. • Cardinal Number• Ordinal Number• Measurement Number SitiMichael John
  23. 23. ProblemRearrange the sticks toshow a given numberof squares. Wellington Primary School
  24. 24. Task Lesson Study Problem Wellington Primary School• Move 3 sticks to make 3 squares.
  25. 25. Task• Move 3 sticks to make 3 squares.
  26. 26. Task• Move 3 sticks to make 3 squares.
  27. 27. Task• Move 3 sticks to make 2 squares.
  28. 28. Task• Move 3 sticks to make 2 squares.
  29. 29. Task• Move 3 sticks to make 2 squares.
  30. 30. ProblemArrange the ten cards sothat you can do what isshown to you.
  31. 31. Method 1 – by drawing
  32. 32. Method 2 – by using the cards
  33. 33. Scarsdale Teachers’ Institute, New York
  34. 34. Think of two digits. Makethe largest number. Makethe smallest number. Findthe difference. What doyou notice?

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