A mathematician, like a painter or a poet, is a maker of patterns.

If his patterns are more permanent than theirs, it is because they are made with

ideas.

Godfrey Harold Hardy“A Mathematician’s Apology”

What is mathematics ?

Mathematics can be defined simply as the science of patterns

Devlin (2000).

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Objectives

Identify and discuss key characteristics of early algebra

Explore a variety of approaches to expose children to algebraic concepts.

To support children to think ‘algebraically’ in order to develop good number sense.

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The New Zealand CurriculumLevel One

Equations and Expressions• Communicate and explain counting, grouping,and equal sharing

strategies using words, numbers and pictures. Patterns and Relationships• Generalize that the next counting number gives the result of

adding one object to a set and that counting in a set tell how many.

• Create and continue sequential patterns.

Level Two

Equations and Expressions• Communicate and interpret simple additive structures using

words, diagrams,and symbols.Patterns and Relationships• Generalize that whole numbers can be partitioned in many ways.• Find rules for the next member of a sequential pattern.

These two aspects of the algebra curriculum are intimately related and best developed together

We need to encourage young children to notice and describe the many types of patterns found in their world.

How does the algebra part of national standards for years 1 - 4 relate to the curriculum document?

PatternsRepeating patterns

Clap, stamp, clap, stamp…Red, blue, red blue…

“read your pattern”“what comes next”“why is it a pattern”“can you make a pattern using three colours?”

Increase the level of pattern complexity by using other attributes

e.g.size, shape, position, “wings, no wings, wings, no wings”“top, side, front, top, side, front

Make a pattern that increases or decreases by one

Use concrete representation

Read your pattern to your partner

Make a pattern that increases by more than one and doesn’t start at zero

“How big are the steps”

Steps

Understanding equality

Children need many experiences with recognising, defining, creating and maintaining equality.

Scales“equal/not equal, same/different, more/less,

fair/not fair, balanced/unbalanced”

“You know it’s balanced when it’s really straight.Yeah it’s not going to one side - and that’s what balance is all about.”

Equality continued…

• Link cubes that are equal in quality and therefore equal in height

• String beads and discuss why one is longer than the other

• Use empty tens frames to show equality e.g 4 green and 6 red counters v/s 5 green and 5 red

“they are both 10. It doesn’t matter that mine has more red than his”“can you make another one that is equal to this?”

The meaning of equals

Many children have an incomplete knowledge of what the equals sign signifies.

2 + 3 =

They come to think of the equals sign as meaning find the answer.

What can we do to change this perception?

We need to offer many experiences with varied types of patterns.

We can enhance young children’s learning by giving appropriate challenges that incrementally increase the level of complexity and by asking questions that promote mathematical dialogue

(Jennifer Taylor-Cox, 2003)