The Van Hiele Levels of Geometric Thought in Undergraduate Preservice Teachers

Abstract

This study operationally defined and studied the five learning levels hypothesized by P. M. van Hiele and D. van Hiele-Geldof. Tasks were designed for the first four levels using seven common geometric concepts and revised after review by 11 mathematics educators. Audiotaped interviews were given to 19 preservice elementary teachers, 13 of whom had studied high school geometry. Guttman's scalogram analysis showed that the tasks representing the levels formed a hierarchy. A test of consensus revealed that students were on different levels for different concepts. Responses, in general, showed that the typical student in the study was not ready for a formal deductive geometry course.