Development of Early Numeracy

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?