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
INSTRUCTOR
Peggy FooMarshall Cavendish Institute
VisualizationShapes & Geometry
Spatial Visualisation
• It involves having images of objects• Spatial visualisation and geometry are
interdependent (learning of one area will lead to the other)
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” i.e. appearance of the shape
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
• Example: 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 (manipulate and identify
geometric shape)
• Grandfather Tang’s Story / Create your own picture (arrange, construct, describe in your own words)
INSTRUCTOR
Peggy FooMarshall Cavendish Institute
Conservation of Numbers
Objectives
Participants will be able to:
• Understand the importance of conservation of numbers
• Study a lesson (video) on a conservation task
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
ResponsesNumber 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
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 structures and sorting / classifying the structures
Enhance reasoning and communication skills when asked to justify one’s responses
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
INSTRUCTOR
Yeap Ban HarMarshall Cavendish Institute
Ordinal and Cardinal Numbers
B A N H A R
• Cardinal Number• Ordinal Number• Measurement Number
Siti
John
Michael
Wellington Primary School
Problem
Rearrange the sticks to show a given number of squares.
Task
• Move 3 sticks to make 3 squares.
Lesson Study Problem Wellington Primary School
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.
Problem
Arrange the ten cards so that you can do what is shown to you.
Method 1 – by drawing
Method 2 – by using the cards
Scarsdale Teachers’ Institute, New York
Think of two digits. Make the largest number. Make the smallest number. Find the difference. What do you notice?