Development of Numeracy in Early Childhood Education
1.
2. This course focuses on the WHAT and HOW of numeracy
programmes in early childhood education. You will complete four
modules 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
4. Spatial Visualisation
• It involves having images of objects
• Spatial visualisation and geometry are
interdependent (learning of one area will lead
to the other)
5. 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
6. 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” i.e. appearance of the shape
7. 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
8. 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)
9. 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
10. 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
11. Level 3: Formal Deduction
• Construct proofs to determine the truth of a
mathematic statements
13. 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)
14. Conservation of
Numbers
INSTRUCTOR
Peggy Foo
Marshall Cavendish Institute
15. Objectives
Participants will be able to:
• Understand the importance of conservation of
numbers
• Study a lesson (video) on a conservation task
16. 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
17. Responses
Number Conservation by Counting:
• I counted them
Number 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
19. 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
20. 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
21. Ordinal and Cardinal
Numbers
INSTRUCTOR
Yeap Ban Har
Marshall Cavendish Institute