A Theoretical Examination of the Mathematical Connection Skill: The Case of the Concept of Derivative

The aim of this study is to explore and interpret the mathematical connection skills of pre-service teachers within the context of the concept of derivative. In this regard, firstly the mathematical connection skill was analyzed theoretically, and an attempt was made to establish a theoretical structure that can be used in the evaluation of this skill. Then the Connection Skill Test (CST), developed by the researcher, was applied to the students in the study group composed of 51 people selected from among senior students of the Faculty of Education of a state university in Turkey. Four basic components of the test are as follows: connection between different representations, connection between concepts, connection with real life, and connection with different disciplines. The findings of the study indicate that most of the pre-service teachers have some rote-learning based pieces of knowledge from textbooks with regards to the concept of derivative, but they cannot, to a large extent, understand and use them in connection with each other. For a more meaningful and relational understanding of mathematics, it is suggested for mathematics educators to focus on conceptual understanding and include activities and practices that will enable concepts to be learned meaningfully and in connection with real life in their classes