Fifth Central- and Eastern European Conference
on Computer Algebra- and Dynamic Geometry Systems
in Mathematics Education

According to the result of our questionnaire survey, one major opinion of collegiate mathematics teachers in Japan is that there is no necessity to use high-quality graphics in education. However, from our experience, graphics use seems to play a crucial role in some classroom situations. Though we have been attempting some statistical efficiency assessments for teaching materials containing graphics, it is not so easy to separate the effect of using graphics from other factors like context of classroom or communications between students. The aim of this research is to verify the effect of using high-quality graphics in collegiate mathematics education through some cognitive scientific experiments. The experiments were designed in the following two ways:

(1) Detecting the change of students’ brain activity after their seeing effective figures through EEG (ElectroEncephaloGram) measurement

(2) Observing the difference in time needed for students to answer a question between before and after their seeing effective figures

In fact, we picked up the case of the comparison of growth degree between exponential function y=2^x and power function y=x^4. We prepared some graphs of these functions by gradually changing the scale in y direction, so that students can recognize that the growth of y=2^x is greater than that of y=x^4 when x becomes sufficiently large. We showed these graphics step by step to three students and detected their brain activities through EEG (ElectroEncepharoGram) measurement. As a result, the judgment of these students changed when they saw a triggering figure, and some change in the trend of EEG signal and solution time was observed at that time.

These results indicate that using effective figures should have great influence on students’ reasoning processes.

The Web Geometry Laboratory} (WGL) platform is a collaborative blended-learning Web-environment for geometry, it integrates a dynamic geometry systems (DGS) and it provides a collaborative environment for students and teachers. Its use is possible in the context of a classroom or remotely. Apart from its development its evaluation is being done through a series of case studies, sustained through a qualitative approach (interpretive research), being conducted in Portugal and Serbia (Prototype in hilbert.mat.uc.pt/WebGeometryLab).

An initial case study in Portugal, with groups of secondary students (17 years old) was done, using various gathering information techniques: quizzes; tests; direct observation; record interactions on the platform; challenges. We analysed the use of the WGL collaborative environment by the students.

Another case study, in Serbia, was conducted in the context of remote access to the platform (homework). The study included 50 secondary students (15 years old). All students attended the traditional classes in school. Half of the students used WGL platform for homework and the other half did their homework the traditional way. We investigated the impact of collaborative work to the motivation level and level of achievement.

Using an action research approach, the platform is being developed. These studies revealed some aspects that could be enhanced, e.g. a chat feature. More and wider case studies are being prepared allowing the validation and further development of the WGL platform.

These studies also indicates that there is a significant improvement in the motivation of students and a slight improvement in their achievement when using the WGL platform.

The WGL platform will include in future stages of development the implementation of an adaptive environment allowing the construction of students' profiles and learning paths. A final stage will be the integration of a geometric automated theorem prover and its use in the learning process.