Abstract:

My experiences gained from teaching planar and spatial geometry at grammar school (providing upper secondary education – ISCED 3) and Euclidean, descriptive, and computational geometry at the Faculty of Mathematics and Physics in the Czech Republic show serious gaps in students’ understanding of geometry and in students’ spatial abilities. This brings me to the idea to analyze the current content of mathematics with respect to geometric tasks. Firstly, I focus on upper secondary school education (specifically on grammar schools) because geometry which is taught there represents the basics for university studies too.

The analysis is done with the intention of identifying what spatial abilities are required to solve certain types of geometric tasks. Furthermore, my aim is to investigate concrete students’ problems in geometry and introduce several approaches, new types of geometric exercises, and activities which could help students to achieve better results in understanding of geometry.

The research on geometric content in Czech upper secondary school education is conducted in two steps:
- The search and the collection of learning outcomes in the national curriculum documents for Czech upper secondary school education.
- The search and the collection of geometric content in Czech textbooks for upper secondary school education.

Afterwards, the geometric content is analyzed according to types of spatial abilities which are required for finding the solution. This means that I am examining and discussing standard solving methods which are introduced to student. The basic two categories of spatial abilities what I consider are spatial visualization and spatial orientation. Students’ results are continuously measured in my instructions and I am comparing their success in these different types of geometric exercises.

I am dealing with these explorations at the present time and gathering the results to answer following research questions. I will summarize some results in the paper.
- What is the geometric content in Czech upper secondary school education?
- What types of spatial abilities are mostly used in Czech mathematics textbook in solutions of geometric exercises?
- Is there any difference in students’ success rate if they solve spatial visualization or spatial orientation tasks?

On the ground of my research I am determining innovative training methods and new geometric tasks which can improve students’ spatial abilities. Spatial abilities on a good level are very important to succeed in solving of various geometric problems and even to orient ourselves in the environment and to solve everyday tasks.

Regarding the future work, I plan to extend my research to international level and compare educational content of geometry in several countries.

Keywords:

Teaching geometry, geometric content, Czech upper secondary education, spatial abilities.