Abstract:

The developed educational projections, levels and prerequisites of the mathematical educational multilingual ontology OntoMath^Edu are presented. Educational projection is viewed as the formalization of a certain system of subject training in mathematics. It is a subset of OntoMathEdu ontology concepts, which are structured at this stage of ontology development using two didactic relationships – educational level and prerequisites.

Educational levels are allocated on the basis of the teaching standards of the corresponding education system, the relation of prerequisites is determined by the sequence of the studied concepts in a particular education system.

The OntoMath^Edu ontology defines two projections representing the educational systems of Russia and Great Britain. The algorithm for constructing an ontology through linking various projections allows it to be further replenished with new educational projections, which can later be used in the system of multilingual teaching of mathematics.

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.