Visualisation in High School Mathematics.

Abstract

Galton wrote in 1880, An over-readiness perceive clear mental is antagonistic the acquirement of habits of highly generalised and abstract thought and if the faculty of producing them was ever possessed by men who think hard, it is very apt be lost by disuse. The highest minds are probably those in which it is not lost, but subordinated, and is ready for use on suitable occasions.*9 [Bishop, 1980, p. 1] Galton's statement is highly relevant the learning of mathematics, which requires generalised and abstract thought [Krutetskii, 1976], and in which one might expect the ability to perceive clear mental pictures constitute an advantage: after all, diagrams are a frequent accompaniment mathematical thinking. Krutetskii's research in the U.S.S.R. made an impact on the thinking of Western researchers in mathematics education when his findings were published in English [1976] because his research suggested that, at school level, the strength of the verballogical component of thinking determines the level of mathematical abilities, while the visual-spatial component determines their type. As the writer's research confirmed, a pupil may be highly successful in the learning of school mathematics without needing resort visual thinking. The issue then arises of the learning of mathematics by pupils who prefer think in pictures. Many such pupils would like choose careers in engineering or architecture; success in school mathematics is a prerequisite. Thus the issue of identifying the strengths and limitations of visual processing in high school mathematics is an important one for mathematics educators. Together with some effects of different teaching styles on the learning of high school mathematics by visualisers, this issue is the focus of this article. But first it is necessary give a brief description of the research instrument which was used.

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