An application of the Rasch measurement theory to an assessment of geometric thinking levels

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.