An Investigation into the Assessment of Students' Van Hiele Levels of Understanding in Geometry

Abstract

This study investigated the difficulties associated with the design of appropriate test items, and the advantages of different methods of assessing the understanding of students within the framework of the van Hiele theory. It is based on the diagnostic instrument developed by Mayberry (1981) for assessing van Hiele levels in geometry, and addresses the four design problems which Mayberry identified as associated with her study. A detailed testing and interview program of 60 first-year primary-teacher trainees was undertaken. Initially, the responses of students to a written version of the Mayberry items were assessed using her method of evaluation. The QUEST program (which utilises the Rasch measurement theory) was applied to the results, leading to the identification of design problems in the original test, and the development of an amended version of the Mayberry test. Finally, Mayberry's method of assessment was compared with the method developed by Gutierrez, Jaime and Fortuny (1991). The testing of four research themes provided the context for the investigation. The highest van Hiele level of understanding for the majority of students (77%) was shown to be Level 2, even though 60% had studied a senior secondary geometry course in which the instruction was assumed to be at least Level 3 content. Apparent inconsistencies in the thinking of some of the students also emerged. Interviews, while supporting the levels displayed by the students in the test, did not clarify reasons for the inconsistencies. Application of the QUEST program confirmed the results of the test. Two issues related to the inconsistencies emerged. First, the difficulty thresholds of some items indicated their unsuitability to measure reasoning at the specified thought levels. Second, the setting of the subjective success criteria for the Mayberry method of assessment did not appear to be consistent.