PRE-SERVICE MATHEMATICS TEACHER EDUCATION: TESTING AND IMPROVEMENTS OF SPATIAL SKILLS

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 abilities from lecturing geometric and mathematics courses at the Faculty of Mathematics and Physics, Charles University, the Czech Republic. We work with 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 certain spatial abilities for solving and cause difficulty for students. The two major categories of spatial abilities what we consider are spatial visualization and spatial orientation. Based on these observations we prepared a pretest first and then a modified test for students to formally measure the specific correlations. The purpose of the tests 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 tests consist 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 abilities are used. The students were asked to describe solving strategies in the subsequent questionnaire. Moreover, the students were observed during the tests and we also discussed their strategies with them after the tests. The primary research questions are: Do students prefer any spatial abilities 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 December 2019, 24 students of the specialization of teaching mathematics (the 2nd year at university) were asked to solve geometric problems in the individual test and answer the questionnaire afterwards. The test together with the questionnaire was designed according to a pretest which was taken by another group of students a month ago. A quasi-experimental study revealed that the students use the both spatial abilities, i.e. spatial visualization and orientation. Students preferred to solve the tasks on the cube (3D geometric problems) using spatial orientation abilities or by the combination of the both spatial visualization and spatial orientation. In all tasks, we observed clear indications of a sex difference in favor of males. The results of the study will be described in the paper in detail. On the ground of our research 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.