Undergraduate physics students’ understanding of abstract and applied mathematics : A case study on vectors

Mathematical competence is considered crucial for physics learning; besides knowing abstract mathematics, students need to apply mathematical skills to different physical concepts. It is hypothesised that the development of this applied physical competence requires some threshold of mathematical competence. However, the relation between these two competences remains unclear. Furthermore, research on undergraduate physics education is scarce within the Finnish national context. To bridge these research gaps, this study addresses the development of both abstract mathematical and applied physical competence in a physics intervention course in a Finnish university. The focus is on the key mathematical concept of vectors, which is covered in introductory physics courses and considered highly difficult, as students tend to acquire misconceptions of the topic and struggle to apply the mathematical construct in the physical context. The pre- and post-test results show that most of the learning outcomes during the intervention course were related to improved applied physical competence. Furthermore, common misconceptions regarding vectors are identified. Analysing the joint development of mathematical and physical competencies supports the assumption that the improvement of applied physical competence depends on some foundational level of mathematical understanding. Furthermore, the students’ prevailing misconceptions and only modest overall improvement of their physics understanding highlights the need for more deliberate teaching practices.