Abstract:

Digitalization of education requires the creation of intellectual subject databases. The specifics of the modern educational environment should take into account the variability of the knowledge system in accordance with the level of training of the student.

The purpose of this research is to build an educational ontology in mathematics in accordance with the existing programs of secondary education in Russia. The section "Plane Geometry" of school mathematics was chosen as a pilot project.

The first task of our study was to construct the concepts of plane geometry course in the form of formal taxonomy.

Our experience in developing ontology of professional mathematics OntoMathPro was used in the design of taxonomy. The concepts of using ontologies in professional and school mathematics are different. The article compares and highlights the fundamental differences between the ontologies of professional mathematics and the projected educational ontology. The ontologies of professional mathematics are intended for intellectual processing of scientific content, in particular, semantic search. The new ontology takes into account the educational specifics and reflects the conceptualization of school mathematics.

When designing the taxonomy, we have analyzed the system of concepts in the school geometry course. This analysis has shown the conceptual incompleteness, lack of system and late submission of information in the content of the plane geometry course at school. Not only the problems of translation of plane geometry into formal language, but also the imperfection of the methodical system of teaching this branch of mathematics are revealed.

The constructed taxonomy includes such classes as "Plane figure", "Euclidean plane geometry axiom", "Euclidean plane geometry theorem", "Euclidean plane geometry problem", "Unit of measurement", "Plane transformation", "Metric property of a plane figure", "Comparison relation between plane figures", "Arrangement of plane figures".

We have estimated the taxonomy. The study involved students of the N. I. Lobachevsky Institute of Mathematics and Mechanics of Kazan Federal University. A test to study the quality of students' understanding of generic concepts and graphical representations of geometric figures have been worked out. The results of the study showed the relationship of problems in the submission of the content of the school course of plane geometry with the quality of students' knowledge.

Keywords:

Taxonomy, conceptualization of mathematical knowledge, plane geometry, ontology, OntoMathEdu.