Abstract:

Some results of implementation of the “soft” model of geometry teaching in schools of Nizhny Novgorod region are considered. The realization is based on the ideas of experimental mathematics, according to which the content of educational materials (open problems in geometry) is selected and developed. In addition, it is contributing to the development of students’ intelligence. Thus, student models the geometric situation using open-source software actively, is mobile in the selection of the software, understands geometric facts and regularities, acquires the ability to argue (to analyze, to compare, to generalize, to make conclusions). The experience of the using computer experiments at geometry lessons is examined form psychodidactic approach’s point of view. The advantages of special educational tasks are proved: open problems in geometry, which are based on the “soft” model of teaching geometry using the ideas of experimental mathematics. The peculiarity of the proposed open problems in geometry is that they, being a projection of traditional closed classical problems in geometry, at the same time, firstly, provide the formation of the main components of the mental (cognitive, conceptual, metacognitive, intentional) experience of the student and, secondly, create conditions for the manifestation of individual cognitive styles of students. Enrichment of metacognitive experience is carried out by means of chains of tasks, which create conditions for formation of abilities to plan, predict and control the mathematical activity.

Abstract: In the article presents the classification of problems by differential geometry, which is based on the nature of the relationship between the elements of the problem and the relationship between the reproducing and creative activity of students in their decision. It is shown that an important source for the choice of texts of problems and methods of their solution are the works of scientists – creators of classical differential geometry. Work with the corresponding scientific text allows the student to master such an educational strategy as methodological reduction.

Abstract:

A service for generating and visualizing educational cards of mathematical concepts based on the ontology of school mathematics OntoMathEdu is presented. The main stages of collecting information for displaying the concept card are given. The developed service is used as a recommendation system in the distance education course of KFU "Technology for solving planimetric problems". Mathematical concepts located in the texts of lecture materials are enriched with links to the corresponding concept card on the service.

Abstract:

The aim of the paper is to demonstrate how the techniques of one of the geometries indicated in the title can be used for solving problems formulated in the framework of one of the other geometries. In particular, it is shown how problems formulated in the framework of affine or projective geometry can be solved with an appropriate choice of Euclidean scalar product.

Abstract: The translation of the school system of knowledge into a formal language to create an ontology of school educational mathematics showed that there are gaps indicating significant shortcomings in the design of the contents of the geometry course. A study among students of N.I. Lobachevsky Institute of mathematics and mechanics of KFU to determine the quality of understanding of generic concepts, graphic representations of geometric figures, the results of which showed the relationship between the problems in the presentation of the content of the school course of Plane geometry and the quality of students' knowledge.

Abstract: This article presents the results of a systematic literature review on the matter of universities’ experience with implementation of digital learning. The findings point out the advantages, disadvantages, discrepancies, problems, challenges, and possible solutions. The conclusion section contains general expectations in respect of the quality and effectiveness of digital education. Finally, the recommendations on how to minimize negative consequences are formulated.