Abstract:

For decades already, the pedagogy of mathematics education has relied primarily on the role of the teacher, who demonstrates well-functioning model examples for students to motivate and encourage their tasks. This relatively routine and stereotypical procedure: interpretation of theory - examples - independent solution of assigned tasks, we decided to research in-depth within our pedagogical practice by incorporating error as a teacher's educational strategy into mathematics teaching. We believe that explaining and justifying correct and incorrect solutions to problems is more beneficial for achieving better results in mathematics education than justifying the right solutions. Such a teaching process can lead to a more informal and better understanding of mathematical concepts. In our study, we try to reveal the potential of students' incorrect solutions in conjunction with the analysis and justification of incorrect steps when reaching the final result.

65 students of the first year of the University of Zilina Faculty of Operation and Economics of Transport and Communications participated in our experiment. The experimental group consisted of 32 students from the Air Transport Department. The teaching here was carried out experimentally. In the other groups, teaching was in a regular mode. From these groups, a control group consisting of 33 students was set up at random. The same teacher taught all groups involved in the experiment. The teaching included the analysis of incorrect solutions of assigned tasks in lectures, seminars, and homework in the experimental group. Students in the experimental group were allowed to detect errors, explain and justify errors, and discuss the correct ways to solve the assigned tasks.

In this article we want to point out the difference in mathematical success when error analysis is included in teaching, compared to the traditional teaching approach only in presenting the right solutions. We tested the hypothesis statistically: If we incorporate the justification and explanation of incorrect solutions of mathematical problems into the teaching process, it is possible to achieve better results in education compared to the traditional instructional teaching process only through correct examples. Our findings confirmed that the presence of cognitive conflict through exercises solved with errors, followed by reflection and explanation of errors, leads to a deeper understanding of mathematical concepts. Error analysis “can support a deeper and more comprehensive understanding of mathematical content as well as the essence of mathematics itself.

Keywords:

Mathematical education, potential of the errors, common errors in mathematics, pedagogical experiment, t-test.