Constructive Problems in Discrete Mathematics: a Comparative Analysis of the Exam with and without a Computer

Abstract

The paper analyzes an experiment on the use of manipulators for solving constructive tasks related to the different concepts in teaching discrete mathematics students of a technical university. These concepts include a logical circuit, a finite automaton, a regular expression, a Turing machine, etc. In these problems, it was required to build some construction with given properties. The constructed structures could be tested on the data entered by the user, that is, the possibilities of feedback could be used when searching for a solution. However, the computer tools used --- manipulators --- did not allow checking the correctness of the input solution. The data of the experiment, in which about 100 students participated, are presented. In the experiment, one part of the students was asked to take the exam on a computer with the possibility of using manipulators, while others solved the same tasks «on paper». About half of the tasks were not equipped with manipulators, that is, they were theoretical tasks typical of a written exam. In the proposed set, some constructive and theoretical tasks had a common object, so the study studied the possible impact of constructive activities on the subsequent solution of a theoretical task on the same topic. Also in this experiment, the same problem statement was used for different forms of representation of the mathematical essence, for example, in the terminology of constructing a finite automaton, regular expression, grammar, algorithm. On the basis of statistical processing of the results, conclusions were drawn about a significantly better solving of constructive problems with computer support and about the negative impact of a computer in solving problems that required mental operations that do not have an adequate representation in computer support, for example, on a computer with instrumental support, it is much more effective to solve problems by printed aids. Based on the analysis of the results, some other hypotheses were stated, which are not statistically confirmed, but can serve as a starting point for further research.