The spiral curriculum, integrated teaching and structured learning of mathematics at the secondary level

Abstract

The investigator's experience of teaching mathematics at a college of education since 1983 has reinforced his conviction that trainee students come to college with significant gaps, weaknesses and faults in their (mathematical) conceptual structures, probably as a result of shortcomings in the mathematics teaching to which they have been exposed. The theme of this investigation is thus a natural choice that appeared to be of immediate relevance to secondary school mathematics teaching. The analysis of the issue leads to a unified perspective: the problem is placed in a theoretical framework where Bruner [spiral curriculum], Ausubel [structured learning] and Skemp [relational understanding] are brought together. How the curriculum, textbooks and examination influence school mathematics teaching is examined in some depth and the consequences investigated. Two specific topics, viz. the generalised Pythagorean relation and absolute value are investigated in relation to published work, curriculum and textbooks, and each (topic) is presented as a unifying theme in secondary mathematics to standard 9 pupils. The classroom exercise is assessed to test the hypothesis that structured, integrated presentation around a spiral curriculum promotes "relational understanding". Analysis of results supports the hypothesis.