Abstract:

This paper addresses the spatial abilities and skills of pre-service teachers from the perspective of their solving strategies and success rate in spatial orientation and visualization tasks. We are aware of the serious students’ lack of spatial skills from lecturing geometric and mathematics courses at the Faculty of Mathematics and Physics, Charles University, the Czech Republic. We work with the group of students who study the specialization of teaching mathematics. We prepare them for their future career in the secondary schools; we focus on the improvement of students’ spatial skills which are needed to succeed in the solving of various geometric problems.

We have already gained experiences from geometric courses especially regarding the identification of geometric tasks which require spatial skills for solving and cause difficulty for students. The two major categories of spatial skills what we consider are spatial visualization and spatial orientation. Based on these observations we prepared the pretest for students to formally measure the specific correlations. The purpose of the pretest was to explore the students’ solving strategies in the solution of tasks which can be categorized as spatial visualization as well as spatial orientation tasks.

The pretest consists of two groups of geometric tasks – the maps navigation tasks and the path on the cube. We assume the both types of tasks can be solved in different ways based on which spatial skills are used. The students were asked to describe solving strategies in the subsequent questionnaire. Moreover; the students were observed during the pretest and we also discussed their strategies with them after the pretest.

The primary research questions are: Do students prefer any spatial skill to solve particular types of spatial tasks? Is there a difference in students’ success rate when they use different solving approaches? Do they use any visual aid to solve geometric tasks? If they do, are they more successful than those who do not?

In November 2019, 21 students of the specialization of teaching mathematics (the third year at university) were asked to solve geometric problems in the individual pretest and answer the questionnaire afterwards. A quasi-experimental study revealed that the students use the both spatial skills, i.e. spatial visualization and orientation. Students preferred to solve maps navigation tasks (2D geometric problems) using spatial visualization skills (mentally moved an object). On the other hand, the tasks on the cube (3D geometric problems) were solved more likely using spatial orientation skills or by the combination of the both approaches. In all tasks, we observed clear indications of a sex difference in favor of males.

A modified test (based on the pretest) together with the questionnaire will be taken by another groups of students. The results will be described in the paper in detail. On the ground of our study we will determine the optimal training methods to improve students’ spatial visualization and orientation skills. We assume this research can significantly help to improve the pre-service mathematics teacher education.

Keywords:

Spatial skills, spatial orientation, spatial visualization, pre-service mathematics teachers.