Abstract:

This study investigated the geometric cognitive growth of pre-service mathematics teachers in terms of the Van Hiele levels in a technology-enriched environment, as opposed to that of students in a learning environment without any technological enhancements.

Following in the footsteps of Piaget, Pierre and Dina Van Hiele identified five hierarchical, sequential and discrete levels of geometric development that are dependent on a learner’s experience. According to their model, learners have to master a level to be able move to a higher level. The levels, as described by Mason (2009, pp. 4-5) are as follows:
Level 1: Visualisation,
Level 2 Analysis,
Level 3: Abstraction,
Level 4: Deduction, and
Level 5: Rigor.

In order to investigate this, a quasi-experimental non-equivalent comparison group design was used. Similar course content was used for both the control and experimental groups. The students worked through a series of geometry activities and problems. The difference between the groups was that dynamic geometry software was integrated into the teaching of the experimental group. The Cognitive Development and Achievement in Secondary School Geometry (CDASSG) Van Hiele Geometry Test was used to determine all the students’ level of geometric thinking before and after the course.

The results of the study suggest that the pre-service mathematics teachers did not have a sound understanding of more advanced Euclidian geometry. The majority of students did not reach Van Hiele levels 4 or 5 in both groups and only about half reached Van Hiele level 3. It came as a surprise that not all pre-service students scored full marks on Van Hiele levels 1, 2 and 3 in both the control and experimental groups – not even after the course had been presented. There was a definite descending trend from level 1 through to level 4, as predicted by the literature. This was, however, not the case with the level 5 questions.

The results suggest that the technology enriched environment helped to improve the conceptual geometric growth of students on Van Hiele levels 1, 2 and 4 which is about geometric visualisation, recognition of properties of geometric figures, and the construction of proofs. The results also show that the use of dynamic geometry software, as opposed to a traditional learning environment of the control group, may have a negative impact on the geometric development on Van Hiele levels 3 and 5. These levels are about informal argumentation and the formal aspects of deduction. Dynamic geometry software cannot improve Van Hiele level 4 reasoning directly because deductive reasoning is about the understanding of axioms and the construction of proofs. The results of this study therefore contradict some of the findings of other studies, as mentioned in the problem statement, which suggest that the use of technology always supports the development of higher-order thinking.

References:
[1] Mason, M. (2009). The Van Hiele levels of geometric understanding. Professional Handbook for Teachers: Geometry: explorations and applications. McDougal Littell Inc.

Keywords:

Geometry, software, Van Hiele levels.