The influence of creativity and divergent thinking in Geometry education

Abstract

The teaching of geometry has been neglected at the expense of other disciplines of mathematics such as algebra in most secondary schools for Africans in South Africa.

The research aimed at establishing the extent to which creativity and divergent thinking enhance the internalisation of geometry concepts using the problem-based approach and on encouraging learners to be creative, divergent thinkers and problem solvers.

In the research, Grade 7 learners were guided to discover the meaning of geometric concepts by themselves (self-discovery) and to see concepts in a new and meaningful way for them. This is the situation when learners think like the mathematicians do and re-invent mathematics by going through the process of arriving at the product and not merely learn the product (axioms and theorems), for example, discover properties of two- and three-dimensional shapes by themselves. Furthermore, learners were required to use metaphors and analogies, write poems, essays and posters; compose songs; construct musical instruments and use creative correlations in geometry by using geometric shapes and concepts. They tessellated and coloured polygons and pentominoes in various patterns to produce works of art.

Divergent thinking in geometrical problem solving was evidenced by learners using cognitive processes such as, amongst others, conjecturing, experimenting, comparing, applying and critical thinking.

The research was of a qualitative and a quantitative nature. The problem-based approach was used in teaching episodes.

The following conclusions and recommendations were arrived at: * Geometric shapes in the learner's environment had not been used as a basis for earning formal geometry. * Second language learners of mathematics have a problem expressing themselves in English and should thus be given the opportunity to verbalize their perceptions in vernacular. * Learners should be made to re-invent geometry and develop their own heuristics/strategies to problem solving. * Learners should be trained to be creative by, for example, composing songs using geometric concepts and use geometric shapes to produce works of art, and * Activities of creativity and divergent thinking should be used in the teaching and learning of geometry. These activities enhance the internalisation of geometry concepts. Groupwork should be used during such activities.