The usefulness of the van Hiele model for geometric reasoning in Engineering Graphics and Design

Abstract

Abstract For many students, conceptual understanding in Engineering Graphics and Design (EGD) is problematic, where well-develop reasoning skills are essential but lacking. Through visuospatial and analytical reasoning, the EGD practitioner produces graphical solutions to engineering problems within the shared axiomatic system of geometry. Currently there is no learning model in terms of visuospatial and analytical reasoning within EGD’s system of conventions that supports conceptual understanding. A model is needed to facilitate the development of conceptual understanding as the foundation upon which procedural knowledge is built. The value of the van Hiele model of geometric reasoning is well known but its useful application in EGD has not been demonstrated. This study's purpose was to investigate the usefulness of a particularised version of the van Hiele model in an EGD context.

The van Hiele model of geometric reasoning was used as a conceptual framework by aligning EGD content with the hierarchical cognition levels of the model. In constructing a conceptual framework that added three-dimensional reasoning, I integrated the New Typology proposed by Newcombe and Shipley. This inclusion allowed for the cognitive descriptors based on Euclidean geometry to bridge the two-dimensional limitations of the van Hiele model. This study followed a sequential-explanatory mixed-methods approach by employing a single case-study design, and a pragmatist epistemology guided me. Thirty-eight secondary EGD school teachers participated in the study. Data was collected through a mixed-methods approach by utilising a pretest-posttest instrument and a survey on solid geometry thought. Quantitative task and test scores were used to qualitatively explain the degree of van Hiele level acquisition through key cognitive descriptors particularised for EGD.

Although reasoning in EGD encompasses the constructs of visuospatial reasoning, analytical reasoning within a system of subject-specific conventions, I only reported on visuospatial reasoning as a medium to demonstrate the usefulness of the van Hiele model of geometric reasoning. The results obtained from the data analysis suggests that the van Hiele model relates conceptually well to EGD content. In demonstrating the usefulness of the particularised model, I was able to apply the models' hierarchical cognitive descriptors to explain the instances and types of cognitive deficiencies that proved to be persistent.

Within the scope of the EGD content this study was limited to, the particularised model confirmed that participants displayed shallow conceptual understanding and that their range of procedural knowledge was limited to familiar classroom content. Although this study focused on visuospatial reasoning, the particularised cognitive descriptors identified analytical reasoning and convention knowledge to be equally shallow. The study's main conclusion is that the van Hiele model of geometric reasoning is well suited to be particularised to EGD. Furthermore, it embodies the inclusion of visuospatial reasoning, analytical reasoning, and convention knowledge as major constructs to be included in a signature pedagogy for EGD. The particularisation process I used in this study can be extrapolated to all content areas of EGD in combination with the learning phases espoused by the original van Hiele model of geometric reasoning. The cognitive descriptors utilised in this study are not all-inclusive and further research is needed to develop the complete scope of cognition in EGD based on visuospatial reasoning, analytical reasoning and convention systems.

The van Hiele model of geometric reasoning shows a strong relationship with reasoning in EGD. Future educators and students of EGD could benefit from a signature pedagogy where a teaching and learning model forms the core of hierarchical progression through EGD’s reasoning levels.