Procedural and relational understanding of pre-service mathematics teachers regarding spatial perception of angles in pyramids

In this study, we aim to explore the extent of mathematics pre-service teachers’ ability to apply their procedural understanding combined with spatial perception for drawing conceptual conclusions related to angles in a pyramid. The participants are 16 pre-service high school mathematics teachers. They have studied solid geometry during one academic year, solving problems with various 3-D geometric figures including pyramids and engaging in activities designed to develop spatial perception. At the end of the year, they have taken a final test which examines procedural understanding of 3-D geometric figures as well as relational understanding and spatial perception regarding angles in pyramids. The results illustrate that attainments of the majority of the pre-service teachers in problems requiring only procedural understanding are higher than the attainments in problems which require relational understanding. The results also lead to the assumption that relational understanding of learned material requires application of special teaching methods. Hence, we recommend integrating in the syllabus appropriate courses that focus on the development of this type of understanding.