Levels and competence in solving mathematical modelling problems: a case of preservice teachers

Abstract

The problem and the aim of the study. Mathematical modelling has become an important topic in mathematics education. However, many students are not accustomed to dealing with mathematical modelling problems, which are characterized by reality relation, relevance, authenticity, openness, and the promoting sub-competencies. Students are more familiar with solving problems where all necessary data is clearly presented, despite the fact that real-life situations rarely provide complete information upfront. The ability of students to solve modelling problems is closely linked to their teachers' capabilities. In this article, we explore the modelling competencies of preservice teachers in solving mathematical modelling problems. The exploration is based on six levels of mathematical modelling competence and describes the process of solving these mathematical modelling problems through various sub-competencies. Research methods. The research is descriptive and employs a qualitative approach. The subjects in this study were 34 preservice mathematics teachers. We used instruments in the form of mathematical modelling problems and interview guidelines. Based on the written responses and interview results, we categorized the subjects according to their modeling competency levels. The categorization of modelling competency levels is based on Ludwig and Xu’s framework, while the process of solving the mathematical modelling problem is analyzed using the Blum and Leiß modeling cycle. The description of the process of solving the mathematical modelling problem was provided by a representative from each competency level who provided an insightful answer. The data was analyzed through the stages of condensation, display, and conclusion. Results. According to our research findings, the distribution of subjects across competency levels is as follows: 5.88% are at level 5, 2.94% are at level 4, 5.88% are at level 3, 11.76% are at level 2, 64.71% are at level 1, and 8.82% are at level 0. We provide a detailed description of the process of solving the mathematical modelling problem based on their respective mathematical modelling sub-competencies of one subject from each level. Conclusion. Based on the research results, the majority of preservice teachers are at level 1 (64.71%), indicating that they can understand the problem, but struggle to progress to the next stages. This is concerning because they believe they already have enough information to solve the problem, whereas solving the problem requires making assumptions. These findings reveal that the modelling competence of preservice teachers is relatively low, and it is important to focus on finding solutions to improve this. The difficulties encountered by the subjects include challenges in understanding the problem, difficulty organizing and simplifying the provided information, inability to differentiate between essential and nonessential elements, lack of algebraic skills, and limited use of various forms of representation.