Modeling of didactic relationships in the OntoMath^Edu educational mathematical ontology

Abstract

We discuss the system of didactic relationships of the OntoMathEdu educational mathematical ontology. OntoMathEdu is a central component of the digital educational platform under development at Kazan Federal University, which is intended for solving such tasks as automatic knowledge tests generation and automatic recommendation of educational materials according to an individual study plan. The ontology is organized into three layers: a foundational ontology layer, a domain ontology layer, and a linguistic layer. The domain ontology layer contains math language-independent concepts from secondary school mathematics curriculums. The concepts are provided with labels in Russian, English, Spanish and Tatar. The system of didactic relationships reflects how the concepts are studied in the actual educational process according to a corresponding national curriculum. The system defines two basic didactic relations: the prerequisite relation and the relation between a concept and its educational level. An educational level is associated with the stage of student training and its profiling. The prerequisite relation determines the sequence of the studied concepts. Arrangement of concepts by educational levels, in turn, determines educational projections, i.e. projections of the ontology to national education systems. Currently, there are two projections of the ontology: on Russian and the UK education systems respectively. Educational projections can be used for curriculum planning, translation of a curriculum into other languages, and personalization of learning. The didactic relationships were introduced in the 2nd release of OntoMathEdu, which was presented at WEA 2021. While the WEA 2021 paper describes them from an engineering point of view, this paper does it from a methodological perspective.