Interactive Educational System Based on Generative Approach, and the Problem of Answer Checking
In this paper we consider the problem of training tasks organization, delivery and support for courses that involve mathematics. Nowadays, the level of development of IT allows to offer qualitatively new approach to solving this problem, but most of the e-Learning systems do not cover this area well. Several important steps had been made in this direction, but still some problems remain unsolved. In this paper, we introduce our interactive educational system, in which we address those problem. Among others, there is a problem of automatic answer checking. This problem, in fact, refers to the problem of establishing identities in formal mathematical system. And hence it is formally unsolvable. In order to improve the situation, we suggest to reinforce function comparison algorithm with an additional pointwise checking procedure. This, of course, leads to a possible error. In this article, we provide an analysis of the probability of such an error, which appears to be quite low in most cases. In a word, this means that the suggested pointwise checking procedure can be quite successfully used in a case where there is no way to establish equality/inequality for sure.