Abstract:
The purpose of this study is to apply the Rasch model to investigate both the Van Hiele
theory for geometric development and an associated test. In terms of the test, the objective is
to investigate the functioning of a classic 25-item instrument designed to identify levels of
geometric proficiency. The data set consists of responses by 244 students (106 for a pre-test
and 138 for a post-test) of which 76 students sat both the pre-test and the post-test. The
summary item statistics do not show statistically discernible differences between observed
and expected scores under the Rasch model (Chi-square statistic). The Rasch analysis
confirms to some strong extent the Van Hiele theory of geometric development. The study
identifies some problematic test items as they only require knowledge of a specific aspect of
geometry instead of testing geometric reasoning. In terms of the Van Hiele theory, the Rasch
analyses identified as problematic some items about class inclusion, an issue which has also
been raised in other studies.
