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

[摘要] In this study, the geometry chapters in two textbook series (Mind Action Series andClassroom Mathematics) have been analysed and compared using the van Hiele levelsof 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 excludeddue to the idea of them leading into Optimization in Calculus, more than EuclideanGeometry. The results of the research revealed that both textbook series were weightedheavily towards Exercises. This creates an issue since they require teachersupplementation, but many teachers are unable to do so. In addition to these results, itwas discovered that neither textbook series followed the progression suggested by thevan Hiele levels. There was a distinctive absence of Order (Level 3) classifications whichis the precursor to formal geometric deduction. This could explain why learners strugglewith proof-style questions. The textbooks also have a cognitive gap when looking at theprogression of each unit of analysis. The Kernel classifications are predominantlyRecognition (Level 1), the Explanation classifications are a mix between Recognition(Level 1) and Deduction (Level 4) and the Exercise classifications are dominated byDeduction (Level 4). A correction of the progressions could have positive results forweaker and 'textbook bound” teachers.

[发布机构] University of the Witwatersrand