Analysing geometry in the classroom mathematics and mind action series mathematics textbooks using the van Hiele levels

Abstract

In this study, the geometry chapters in two textbook series (Mind Action Series and Classroom Mathematics) have been analysed and compared using the van Hiele levels of geometric thought. They were analysed using the matrix presented by Hoffer (1981), and the units of analysis that were used were from Foxman (1999), i.e. Explanation, Kernel and Exercise. The chapters leading into three-dimensional shapes were excluded due to the idea of them leading into Optimization in Calculus, more than Euclidean Geometry. The results of the research revealed that both textbook series were weighted heavily towards Exercises. This creates an issue since they require teacher supplementation, but many teachers are unable to do so. In addition to these results, it was discovered that neither textbook series followed the progression suggested by the van Hiele levels. There was a distinctive absence of Order (Level 3) classifications which is the precursor to formal geometric deduction. This could explain why learners struggle with proof-style questions. The textbooks also have a cognitive gap when looking at the progression of each unit of analysis. The Kernel classifications are predominantly Recognition (Level 1), the Explanation classifications are a mix between Recognition (Level 1) and Deduction (Level 4) and the Exercise classifications are dominated by Deduction (Level 4). A correction of the progressions could have positive results for weaker and “textbook bound” teachers.