Transfer of three dimensional spatial visualisation to two dimensions : an investigation into the effect of using manipulatives on the transfer of three dimension dimensional spatial visualisation : a thesis presented in partial fulfilment of the requirements for the degree in Master of Education Studies (Mathematics), Massey University
This investigation attempted to determine the effect of using manipulatives on the transfer of spatial visualisation of three dimensions to its two dimensional representation. The research was carried out in three sections investigating the three topics of the School Certificate prescription that require the visualisation of three dimensions. These topics were 1. Volume of prisms 2. Isometric drawings 3. Three dimensional trigonometry The method used was to qualitatively assess students' three dimensional spatial visualisation before and after using appropriate manipulatives. The theoretical basis of the study was linked to the van Hiele levels as it was believed that these are a valuable tool for teachers to evaluate students mathematical thinking and to develop appropriate teaching programmes. The lack of appropriate descriptors and assessments for determining levels of spatial visualisation made it difficult to carry out quantitative testing. As a consequence of the study suitable descriptors were proposed which should enable teachers to determine their students thinking processes. The study was carried out in a secondary school with approximately 75 fifth formers and the worksheets formed part of the normal teaching programme for the three topics being investigated. This caused the least disruption for the students but led to some difficulties with administration and collection of their responses. The results are inconclusive except for the visualisation of angles between lines and lines and between lines and planes in the third topic, this showed an improvement after constructing three dimensional models. This may have been due to the fact that identifying angles in three dimensions is a new concept to students and therefore affected to a greater extent by the use of manipulatives. There was not the same improvement shown for angles between planes, teachers comments supported the conclusion that the manipulatives used were not as appropriate for reinforcing this concept.