A FLYING START TO ALGEBRA

Algebra learning has its roots in the early grades, when children notice regularities in the ways that numbers work. This is recognized in the Curriculum and Evaluation Standards for School Mathematics (1989) which states that in Grades K-4 children should be encouraged to

• recognize, describe, extend, and create a wide variety of patterns;

• represent and describe mathematical relationships.

From Grade 5, according to the Standards, students should

• extend their understanding of whole number operations to fractions, decimals, integers, and rational numbers;

• understand how the basic arithmetic operations are related to one another.

We have conducted research over several years with middle school and high school students learning algebra (references are given at the end of this article). The results consistently highlight that students find algebra hard to learn unless they have a good knowledge of number properties and basic operations. They need to have thought about the general effects of operations on numbers, and not just focussed their attention on getting answers to computations. As well, they need to feel comfortable using large numbers, fractions and decimals, so that they can recognize when a general relationship or rule applies to the whole range of numbers. Children's discoveries about how numbers work form the building blocks of generalised number knowledge, which is developed and expressed in later years as algebra.

This article concentrates on how number work in the elementary school can be extended to prepare students for algebra. We suggest some practical strategies for teachers to work on several problem sites for learning algebra:

• understanding equality

• recognising the operations

• using a wide range of numbers

• understanding important properties of numbers

• describing patterns and functions.

Teachers can incorporate these strategies into their existing programs. For example, it is often worthwhile to spend time on variants of one problem, encouraging children to find out what happens when different numbers are used or when a pattern is extended. Teachers will find many more ways in which the K-6 curriculum can be enriched to prepare students for algebra in the February 1997 focus issue of Teaching Children Mathematics on algebraic thinking.