Exploring pre-university students' mathematical connections when solving Calculus application problems

Mathematical connections play an important role in achieving mathematical understanding. Therefore, in this article, we report research whose objective was to identify mathematical connections that pre-university students make when they solve problems that involve the derivative and the integral. In this research, we consider a mathematical connection like a true relationship between two or more concepts, definitions, theorems, or meanings amongst themselves, with other disciplines or with real life. Task-based interviews that included four application problems were used to collect data from 25 students (18 males and 7 females) and Thematic Analysis was used to analyse them. Our results indicate that mathematical connections are dependent on each other, and because of this, they form systems of mathematical connections around the reversibility connection between the derivative and the integral. We found connections of five types: different representations, procedural, features, reversibility and meaning as a mathematical connection.