Development of a methodological strategy using GeoGebra, adapted to the specifics of the EIT/NMT for learning to solve problems with parameters

Abstract

An analysis of the content of the exams taken by school graduates for admission to higher education institutions in Ukraine (EIT/NMT) and official reports on the results of the EIT/ NMT over the years allows us to make the following conclusions: the most difficult tasks for participants in both the EIT and NMT were those requiring detailed answers, which belong to the highest cognitive level and are usually considered to tasks of increased complexity, in particular problems with parameters, combinatorics problems, and stereometry problems. The concise analysis of scientific and online sources presented in this paper demonstrates the relevance of developing and implementing methodological approaches to teaching school mathematics sections that include problems of increased complexity and problems with parameters. The aim of this paper is to develop an approach to learning how to solve problems with parameters using GeoGebra visualizations, taking into account the experience of recent years EIT /NMT mathematics exams, and can be used as a basis for analyzing problems during collective “student-teacher” work, individual study of the material, or individual research. The research represents a methodological strategy for learning how to solve problems with parameters, based on the principle of step-by-step processing of problems with parameters through the use of interactive digital demonstration models created in GeoGebra, adapted to the specifics of recent years EIT/NMT mathematical problems. The proposed step-by-step scheme for working with problems involving parameters is accompanied by methodological comments on the activities of teachers and students using GeoGebra demonstration models at each stage. All stages of the proposed scheme are demonstrated using the problem from the main session of the 2021 External Independent Testing (EIT). An analysis of the practical application of GeoGebra in the educational activities of specialized educational institutions shows that the formation of interactive visual representations for mathematical problems of increased complexity using this system in the process of preparing for the NMT is a powerful instrument for the development of research and innovative activities of students.