No abstract

The solution of mathematical and logical problems is the imperative element of the educational process in the technical sciences. To solidify the assimilated skills, learner need to solve a large number of educational tasks, that leads to the need of checking of a large number of solutions. In lots of cases the solution of an educational task is the chain of expression transformations. Many systems allow to compare the learner’s answer with the correct one, defined by the teacher. But in some cases, the teacher needs to set some additional information, besides the answer expression. Such additional information cannot be set for each possible pair of expressions in each possible solution chain of the task. We propose a method for verifying task solutions, based on the computational experiments between each pair of steps in solution chain. The proposed approach was tested and showed good results. Namely, in the experiments the efficiency of the teacher’s work when checking solutions increased more than 4 times.

Одним из основных элементов современного образовательного процесса в области технических наук является решение задач на преобразование символьных выражений. При решении таких задач учащимся требуется преобразовать исходное выражение так, чтобы оно удовлетворяло целевым критериям, например, являлось конъюнктивной нормальной формой или совпадало с требуемым целевым выражением. Для совершения преобразований над выражением или его подвыражениями учащийся может использовать уже изученные правила преобразования.

One of the most important elements of the modern educational process in the field of natural sciences is the solution of problems of transforming facts of symbolic expressions. When solving such problems, learners need to deduce a new solution of the problem based on the rules they have already learned. To consolidate these skills, learner need to solve a large volume of tasks, which entails the need of verification of the solutions. Many platforms have already been implemented that allow to automate the verification of solutions. Generally, these systems only check the answer, but not the progress of the problem. This approach of verification leaves the possibility of getting the correct answer and the task counted if the decision is not fully thought out or incorrect. We propose a method for automatic verification of problem solutions based on sequential verification of completed transformations by efficiently iterating through the rules that allowed these transformations to be performed. At each step of the solution, the system iterates through the allowed transformations, trying to find one, that learner used. Problems of ambiguity of the recording form are solved by a combination of testing method, unification, and structuring of the recording rules. The proposed method of automatic verification was tested on students of junior courses of the Polytechnic and Electrical engineering Universities and showed good results: the productivity of teaching staff when checking tasks increased more than 4 times.