Academic journal article Australian Mathematics Teacher

A Square Around

Academic journal article Australian Mathematics Teacher

A Square Around

Article excerpt

Paul Scott's article [pi] round and round in the recent edition of AMT provided a most valuable set of investigations dealing with the pi ratio and the circumference and area of circles. The activities emphasise relational, rather than instrumental learning. However, despite the best efforts of mathematics educators, too many school students and adults still tend to be rule-bound in their mathematical endeavours. This is very noticeable with problems involving area and perimeter, and applies to both polygons and circles.

Estimation is a relational process, which can help overcome rule-bound habits. It is a process which is regularly used by everyone--no matter what their vocation. Yet it would be true to say that estimation skills get scant attention in most mathematics classrooms. A maxim should be: Estimate before calculating or measuring.

[FIGURE 1 OMITTED]

The process of estimation generally requires a reference. In the case of calculating circumferences and areas of circles, a square is a useful reference. Despite knowledge of pi, incorrect formulas are often used. This diagram (Figure 1) can facilitate estimation and lead to the meaningful use of the correct formula for the problem at hand. …

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