How do students use basic aspects of functional thinking when learning mathematics in a chemistry context?

Abstract

The mathematical concept of function is challenging for students in first-year undergraduate mathematics courses, especially when the concept is applied in the context of STEM courses. This difficulty is often due to a lack of conceptual understanding of functions. From a normative perspective, conceptual understanding of functions involves 1) dealing with the different representations of a function, namely table, graph, analytical term and verbal description, while 2) considering three different aspects of functions, namely correspondence, covariation and object. Previous research suggests that the covariation aspect is essential for achieving a sophisticated conceptual understanding of functions. In order to promote the conceptual understanding of functions, a digital self-learning environment was developed and implemented in the first-year basic mathematics course at the School of Life Sciences, University of Applied Sciences and Arts Northwestern Switzerland (FHNW). To facilitate the transfer of mathematical knowledge to applied STEM courses, the mathematical learning environment focuses on chemical reactions, where the concentration of the reactants is analysed. Initial findings from the qualitative content analysis show 1) how students use the different aspects of mathematical functions in the context of chemical reactions and 2) how the covariation and object aspects support students in linking the chemical context to mathematical representations.