A Conceptual and Procedural Research on the Hierarchical Structure of Mathematics Emerging in the Minds of University Students: An Example of Limit-Continuity-Integral-Derivative

Abstract

In this present study, it was aimed to investigate whether the hierarchical structure of mathematics emerged in university students’ minds or not, considering the concepts of limit, continuity derivative and integral from the perspective of students in the department of secondary school mathematics teacher training and the department of mathematics in the faculty of science and letters. The study, designed with the case study methodology, was carried out with 100 participants. Data were collected with the research group via a survey form including totally five questions; one of which is conceptual the other four are operational and analysed with the descriptive analysis. From the results of the research, it was found out that the participants could not learn the concepts of limit-continuity-derivative-integral conceptually and could not constitute the hierarchical structures among these concepts in their minds. Nevertheless, it was determined that the participants learned the procedural knowledge of each concept independent from the other. From these results, it can be recommended that placing activities emphasizing on the relationships among the concepts in teaching the concepts should be applied more.