Designing Applets to Build on Intuition

Abstract

You have a match box containing an unknown number of matches, and are told that if you had 2 more matches then you would have 9 matches altogether: how many matches are in the box? Even before studying linear equations, most school students correctly answer 7 to this question. However, many students find it difficult to explain clearly how they arrived at the answer – for example, a common response is ‘because 2 plus 7 is 9’, which is a demonstration that the answer is correct rather than a explanation of the method of solution. In this paper we consider the issues underlying the creation of applets to specifically build on this basic mathematical intuition. One beneficial outcome is that intuition itself is enhanced. We illustrate the general ideas underlying the use of ICT to help develop mathematical skills at the junior level by looking at an applet created specifically to support learners’ intuition in solving simple linear equations like the matchbox problem above. The aim is not only to help improve learners’ skills in solving more general linear equations, but also to let them become aware that these skills (the appropriate use of the operations of addition, subtraction, multiplication and division) have built upon, and grown out of, their ‘natural’ intuitive approaches.