Abstract
I have been teaching classical geometry, descriptive geometry, and computational geometry at the Faculty of Mathematics and Physics (Charles University) in the Czech Republic for several years. I work with students who study the specialization of teaching mathematics, i.e. the prospective secondary school teachers.
I observe that the students' knowledge when they are entering my courses on geometry has been decreasing year by year. The reasons are ranging from not sufficient secondary school education (or even elementary school education) of my students to the lack of students' interest in mathematics and motivation.
The basic requirement for all my courses at university is the fundamental knowledge of planar and spatial geometry. Sometimes it is very difficult to follow up with geometry at the advanced level especially on courses intended for newcomers.
Spatial skills and abilities on a good level are very important to succeed in solving of various geometric problems. That is why I am dealing with improving of my students' spatial abilities.
In my research, I investigate innovative methods of explaining complex concepts in geometry (specifically descriptive, classical, computational geometry) and their impacts on students' successes. The innovation in explanation and didactic methods include 3D computer modelling and interactive software visualization as dynamic constructions.
My aim is to stimulate the interest of students in geometry, to increase their motivation, to improve their understanding of geometry, to improve the methods of teaching geometry currently in use, to help students achieve better results in examinations, to promote practical use of geometry, and to improve students' spatial abilities. The innovative teaching methods are aimed at strengthening the connection between classical geometry and the practical application thereof on the one hand and extending classical and descriptive geometry into computer graphics and computational geometry on the other.
The connection between classical geometry and 3D computer modelling is intuitively understood by students. I am dealing with following explorations at the present time and gathering the results regarding computer-aided education in university classroom.
I will summarize some results in the paper.. I analyse questionnaire survey which was conducted among university students attending the courses and lectures on geometric topics where computer-aided education was realized; . my survey revealed that the modern type of computer-aided education was adopted very positively among students and according to higher students' interest in geometric topics within the research projects and qualification theses they seem to be more motivated; . my experiences gained from teaching show that computer-aided classroom practice must be accompanied by traditional explanation of geometry, i.e. hand sketching and drawing on the blackboard; . using computers in teaching geometry is an efficient aid because geometrical and mathematical software (GeoGebra, Rhinoceros, Mathematica, Maple, MATLAB, ...) allow to deal with more complex tasks even in classroom practice; . proper functions and tools in mentioned software develop creativity and imagination of students; on the other hand, the ability to use geometrical or mathematical software is not equal to the knowledge of geometry and mathematics;.
I discuss advantages and disadvantages of computer-aided education of geometry (in general of mathematics).