Abstract:

Modern technologies provide means for new forms of dialog and interaction of students with educational environment. Traditional ways of education and personal contact of teacher with students can be partly replaced with educational environment, that is based on interactive electronic teaching materials and communication means which enable active learning. Stimulations of active learning can be based on providing gradual tutoring depending on individual needs of students and feedback which generates conditions for control and managing the educational process. The different forms of interactivity connected with the feedback and gradual tutoring belong to the decisive factors of quality and serviceability of e-learning courses. Some possibilities of using general schemes for implementation of the interactivity elements and feedback in the problem solving according to the requirements for effective learning are described in the paper. The possibilities of using general schemes are illustrated by an actual mathematical content.
Database environment for mathematical problems management based on web technologies presents another form of the e-learning support for mathematical education. The electronic collection of tasks may be useful for teachers in planning various stages of lessons. The structure of the electronic collection of tasks and the criteria for assigning the tasks to the collection are described in the second part of the paper.

Keywords:

educational environment, interactivity, feedback, gradual tutoring, electronic collection of tasks.