HKIER

Abstract

This study investigated the geometric thinking levels (GTLs) of pre- and in-service mathematics teachers at various stages of their education in Israel. It focused on the first three GTLs according to van Hiele’s theory. Furthermore, it examined whether there are differences in their mastery of GTLs in three main geometric topics.

The results indicate that the GTLs of pre-service teachers at their third and fourth years of education were similar to those in-service teachers studying for a master’s degree in mathematics education. The GTLs of pre-service teachers in their first year and those of academics making a career change to mathematics teachers were the lowest. All the five participating groups demonstrated higher mastery of GTLs in triangles and quadrilaterals than in circles and three-dimensional geometric figures. In addition, regarding triangles and quadrilaterals, a large number of participants demonstrated that they had mastered the third level of geometric thinking. Fewer participants assimilated the third level in circles. All participants were not versed in the two higher levels regarding three-dimensional geometric figures. Most of them internalized only the first level or not even that level at all. The rest of them were diagnosed as “inconsistent” in mastering the GTLs.

Keywords: van-Hiele theory; geometric thinking levels; pre- and in-service mathematics teachers; academics making a career change to mathematics teachers

摘要

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