Abstract:

Many students have difficulties in stereometric learning which may be explained by the following factors: a low level of visual thinking; a lack of skills required to create and work on projection drawings; poor ability to establish relationships between stereometric and planimetric objects. Dynamic 3D models which created in the GeoGebra help students overcome these difficulties. Teachers in Russia have ten years of experience in successfully using these opportunities to teach stereometry in secondary schools.

In 2017, it became possible to use GeoGebra for creating augmented reality. Mathematics teachers have a task: how to effectively use the new features of GeoGebra in teaching stereometry. The GeoGebra community tries to help teachers solve this problem. GeoGebra.com contains many worksheets and e-books that instruct teachers and students in creating AR-models. There are many videos on YouTube that present the using of ready-made models. But all of these does not answer the question: how and for what purposes to include AR-models and tasks for their creation and its research in the system of geometry training tools. Authors offer to use AR-modeling in GeoGebra for help students see reality through the prism of geometry.

The formation of geometric concepts in teaching using dynamic geometry systems has four stages of life: visualization of an intuitive model of a real object, dynamization of the model, constructing the theoretical model by experimenting with a dynamic model and application of the theoretical model. The article presents scenarios of using augmented reality for each of them. The scenario for the first stage is called "Geometric modeling from nature", for the second stage - "Animation of geometric fantasies", for the third stage - "Research games with the geometry of reality", and the scenario for the fourth stage is called "Implementation of geometric ideas".

The integrated implementation of these scenarios allows students to study stereometry by creating and exploring AR models of architectural and engineering structures or household items. Students also have the opportunity to use augmented reality to visually test proposed changes to reality.

These scenarios can only be implemented if students have no difficulty using the GeoGebra tools. The authors offered them to pilot schools of the international project "Methods and information technologies in education (MITE)". Students enjoyed to study the geometry outside of the classrooms with mobile devices. They saw the practical application of geometry. They were able to overcome the difficulties associated with the construction and use of projection drawings.

Keywords:

Augmented reality, mathematics education, stereometry, dynamical geometry software, GeoGebra.