Alternative conceptions emerging in pre-university students while making mathematical connections in derivative and integral tasks

Understanding students’ alternative conceptions is important, as such conceptions can prevent them from making mathematical connections, thereby hindering their conceptual development. For this reason, this research aimed to identify the alternative conceptions that emerge when a group of pre-university students engage with derivative and integral tasks presented in algebraic, graphical and application problems contexts. Alternative conceptions were defined as conceptions inconsistent with those accepted by the mathematical community. Twenty-five students from a Mexican public institution participated. Data were collected through task-based interviews and analysed using thematic analysis. Nine alternative conceptions were identified. The most frequent included: the integral of the derivative of a polynomial function is obtained by finding the derivative and the integral separately and, the instantaneous velocity of an object is calculated using the formula v=d/t. These findings highlight the importance of explicitly addressing such conceptions in mathematics instruction to promote deeper conceptual learning.