An Alternative Paradigm to Evaluate the Acquisition of the van Hiele Levels

This article presents an alternative way of analyzing the van Hiele level of students' geometrical reasoning. We evaluate the students' answers, taking into account the van Hiele level they reflect and their mathematical accuracy. This gives us a description of how accomplished the students are in applying the procedures associated with each of the van Hiele levels and allows us to determine the students' degree of acquisition of the van Hiele levels. In this way we obtain a clearer picture of the students' geometrical reasoning than with the traditional assignment of one van Hiele level to the learners. An example of the application of this method is provided: We describe a test that evaluated students' ability to reason in three-dimensional geometry, some responses of students (9 eighth-grade pupils and 41 future primary school teachers), and the classification of their responses using our method.