| Abstract [eng] |
Teaching of mathematics is one of the most complicated and demanding disciplines in a curriculum. The aim of a teacher is not only to communicate knowledge but also to engage the students, motivate them and involve in active learning process by encouraging them to construct their knowledge and competencies. Dynamic geometry systems based on the principle of constructionist learning enable to effectively involve students into the activity by constructing their mathematical knowledge and competencies. However, teachers of mathematics find it difficult to employ the systems since the technical skills of the teachers are inadequate. The visualization of secondary school geometry by using the systems of dynamic geometry systems, i.e. interactive microworlds, can help to solve the problem. The dissertation has analysed the methods of informatics which are employed to develop learning software, the capacities of dynamic geometry systems and the concepts of constructionist teaching and learning as well as interactive visualization. A model to create interactive microworlds is presented with reference to the implemented technological capacities of dynamic geometry systems and the didactics of constructionist teaching of mathematics. The syntax and semantics of dynamic geometry objects has been formalized through the abstract data types which help to describe scenarios of interactive visualization according to a model. The model has been implemented through the visualization of 9-10 grade syllabus of mathematics. Approximately 400 microworlds have been created. The performed evaluation proved that the model can be applied in different systems of dynamic geometry while the created interactive microworlds develop student's geometric skills while studying independently or using them for demonstrations in a lesson. |
