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 dataset of responses by 244 students (106 for a pre-test and 138 for a post-test) of whom 76 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 a 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 that has also been raised in other studies.

Keywords:

• Item difficulty
• geometric thinking levels
• Rasch analyses
• Van Hiele theory
• model fit

Notes

1 For a detailed explanation of the Rasch model and its requirements see Andrich (1988) and Dunne et al. (2012).

2 The stack analysis was deemed preferable over the rack analysis for our exploratory purposes as the second approach declares a large segment of missing data in this study. For more detail on this analytic approach see Marais and Andrich (2011).

3 A second phase could include awarding graded marks for highest sense of correct (2 marks) and partially correct (1 mark).