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

Authors: Gerrit Stols, Caroline Long and Tim Dunne

A six-month geometry course was given to pre-service teachers at the University of Pretoria. To see what, if any, difference it had made to the students’ proficiency. The CDASSG Van Hiele Geometry Test was administered both before and after the course.

This test evaluates students’ performance in terms of the Van Hiele theory of levels of thought and understanding in learners’ experience of geometry. The test has made a significant impact on geometry education worldwide. The theory proposes five levels of geometric development, depending on a learner’s experience – from visual recognition at the earliest stage, to analysis of properties, informal deduction, formal deduction, and finally ‘rigor’, or advanced logical reasoning. Several researchers have found that level 3, informal deduction, is very difficult for many students, and may not be achieved even by those who have passed high school maths. The same problem was found in the Pretoria test.

The authors applied the Rasch psychometric model to assess both the Van Hiele theory and the CDASSG test in order to find if they could usefully be applied to their educational frame of reference. They found that both had some limitations, notably because they were testing knowledge rather than reasoning. However, they did highlight limitations in the geometry course that had been given to the students. In fact, they raised concerns about future teachers’ knowledge and geometric reasoning skills.

Based on the results, the authors concluded that a geometry course for teachers should not assume the mastering of even the basic levels. The authors recommended that such a course should address and develop geometric reasoning skills on all the Van Hiele levels.

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