Abstract:

This work is devoted to the development of a personalized digital model of teaching school mathematics (hereinafter P-model) at the distance education site of Kazan Federal University (KFU), Russia. When developing this model, we drew on the experience of applying digital technologies in educational practice in different countries.

The main principle of developing the P-model is the principle of emergent stratification. According to this principle, multi-level, different, but interrelated subsystems are developed such as a subsystem of computing resources, an ontological subsystem, a didactic subsystem and a management subsystem. These systems ensure the creation of the digital area of the student's activity.

The design of the P-model and its application by users is based on a system of principles. It contains three groups: the principles of the organization of the P-model, the principles of the student's activity, and the principles of the teacher's activity. The first group of principles highlights granularity of educational material, openness of the P-model, quality assurance of educational material, free collection of educational material, independence in the individualization of the educational space, collaboration, gamification and active visualization, and interoperability of the P-model. The principles of the student's activity within the P-model include individual integration, level differentiation of training, personification and openness. Among the principles of the teacher's activity, we should note the availability of modifications, authorship, cooperation, transposability, and ensuring the individualization of training.

One of the results of designing the P-model is an intelligent recommendation system. The development of this system is based on the OntoMathEdu ontology of school mathematics, developed by the authors. The novelty of the proposed approach consists in the integration of both mathematical and methodological conceptualization.

The principles of the P-model are the basis for the implementation of an electronic course on planimetry for schoolchildren at the distance education site of KFU. This course actively uses the OntoMathEdu ontology as an intellectual knowledge base, providing differentiation, personification and openness in learning. Differentiation and personification are provided by a system of didactic relations that allow taking into account the level of training of the student, who can independently regulate their needs in training and receive appropriate methodological recommendations. To organize this process, we offer automatic recommendations and suggestions – what additional material one needs to study, what tasks one needs to solve to form the required skills. The principle of openness is provided by linking the ontology with external training resources, using a system of linked open data.

Designing a learning environment based on the principles of the P-model allows one to implement a model of self-regulated learning that meets the high standards of modern education.

Keywords:

Digital learning environment, personalization, ontology, OntoMathEdu.