Applying the procedural analogy theory in mathematics teaching

Abstract

This study involved research into cognitive processes and mathematics education. It investigated the Procedural Analogy Theory (Ohlsson and Hall, 1990), as a basis for designing instruction in mathematics, and for explaining the value of concrete materials in teaching arithmetic skills. The use of concrete materials in the teaching of school mathematics has long been supported by mathematics educators and by teacher educators. Such materials are common in schools, but generally used by few teachers, their use tends to be largely with young children and then in idiosyncratic manners. The research literature has for many years reported contradictory findings about the effectiveness of concrete materials. The procedural analogy theory attempts to provide guidelines for the planning and comparison of pedagogies before their implementation in classrooms, particularly through the use of a formula to calculate an isomorphism index which seeks to predict the effectiveness of a given pedagogy. In addition to being concerned with planning for group instruction, this research is concerned with individuals as learners. ... Results give support to the value of the procedural analogy as a tool for both planning instruction and predicting learning outcomes, and demonstrate the importance of high level simultaneous processing for learning mathematics through concrete materials. These findings are discussed in the contexts of constructivism, good teaching and computer mediated learning in mathematics. And suggestions are made for both classroom practice and further research.