Examining the relationships among secondary school students' operational and conceptual approaches to problem solving, their mathematical modeling competencies and their attitudes towards mathematics

Today's educational needs reveal the necessity of constructing the knowledge, skills and affective qualities of students in a way that keeps up with the collaborative, competitive and rapidly changing technology required by the age. It can be said that while teaching mathematical knowledge to students, the structure of mathematical knowledge should be taken into account in order to achieve meaningful learning. In addition, it is thought that students should have various competencies in order to be good problem solvers in daily life problems. It is also clear that students need to be emotionally enthusiastic in order to realize these efforts. In this context, it can be said that while reconstructing mathematics education, first determining the existing knowledge, competencies and attitudes of students and revealing the relations between these characteristics will be an appropriate guide in the decisions to be taken The aim of this study is to determine whether the mathematical modeling competencies of secondary school students, their operational and conceptual approaches to problem solving, and their attitudes towards mathematics significantly predict each other, and if so, to what extent this prediction is. No study has been found in the literature that reveals the relationship between secondary school students' mathematical modeling competencies, their operational and conceptual approaches to problem solving, and their attitudes towards mathematics. In this respect, it differs from other studies in the literature. In this study, the relational survey model, one of the quantitative research methods, was used as the research model. The sample of the study consists of 470 students studying in three secondary schools in Seyhan and Çukurova districts of Adana province, which were determined by proportional cluster sampling method. In the study, the "Attitude Scale Towards Mathematics" developed by Önal (2013) was used to determine students' attitudes towards mathematics, and a mathematical modeling competencies questionnaire and rubric developed by Tekin Dede (2017) were used to determine mathematical modeling competencies. In order to determine the operational and conceptual knowledge levels, the "Operational and Conceptual Approach to Problem Solving Belief Scale" developed by Özyıldırım Gümüş and Umay (2018) and adapted by the researcher for the secondary school level was used. As a result of the research, it was determined that students' operational approaches to problem solving were higher than their conceptual approach levels, their mathematical modeling competencies were low, and they had moderately positive/negative attitudes towards mathematics. It was found that there is a statistically significant relationship between mathematical modeling competencies and the mean of operational and conceptual approaches to problem solving. Similarly, it was observed that there was a statistically significant relationship between attitude towards mathematics and its sub-factors, mathematical modeling competencies, and operational and conceptual approaches to problem solving. However, it was revealed that students' mathematical modeling competencies predicted their procedural and conceptual approaches to problem solving at a low level. Similarly, it was revealed that the sub-factors of attitude towards mathematics also predicted mathematical modeling competencies at a low level. It was also revealed that the sub-factors of attitude towards mathematics predicted the operational and conceptual approaches to problem solving at a moderate level. Keywords: Mathematical modeling competencies, mathematics, secondary school, procedural knowledge, conceptual knowledge, attitude towards mathematics.