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Summary of Reference

Author:
Vance, James, H.

Title:
Number Operations from an Algebraic Perspective

Bibliographic data:
Vance, J. H. (1998). Number operations from an algebraic perspective. Teaching Children Mathematics, pp. 282-285, January 1998.

Summary: 
Algebra is more than a set of rules for manipulating symbols: it is a way of thinking. When children realise that they can extend ideas beyond concrete examples and small numbers they exhibit algebraic thinking and experience the power of mathematics. This paper demonstrates how many key algebraic concepts can be informally developed within the number-and-operations strand in the primary grades.

Children need to be exposed to situations in which number sentences with the same meaning are expressed in different ways, for example 3+2=5; 5=3+2; and 3+2=4+1. Children also need to learn the conventions by which numbers are manipulated, for example in the way that number order may be important in computation and the circumstances in which it is. This is a communication issue.

Children also need to be become aware of the ways in which variables are used to allow arithmetic to be generalised, equations to be solved and functional relationships to be explored.

These are all forms of conceptual thinking. They need to be emphasised in the early teaching of arithmetic so that children are intellectually stimulated, so that they are prepared for algebra and so that numbers and their operations are made meaningful.