Student and expert perceptions of the role of mathematics within physics

Abstract

Students' perceptions of the role of mathematics within physics were examined. I propose that the identification of physics as a science based ultimately on experiment is a threshold concept: transformation from a naïve view that physics is based upon mathematics to an expert view that physics is based on experiment is difficult for students. Seven students taking first-year university physics were interviewed in two focus groups; nine practising physicists from academia and industry (considered as experts) were interviewed as six individuals plus one focus group of three participants. Of particular interest was the 'expert' view emphasizing the conceptual nature of physics. This was a threshold in understanding that had not been crossed by students. Rather, students viewed mathematics and physics as being more strongly connected than did practising physicists; specifically that 'maths explains physics'. Experts consider this view as holding back a student's understanding of the subject and preventing them from becoming effective physicists. It is troublesome to students because they are less able to identify the relevant concepts before trying to tackle a problem with mathematics, making their approach less likely to be effective, however, both groups (physicists and students) identified physics as belonging to 'the real world' and that mathematics shows how physical entities can be combined or related, indicating student responses are not completely naïve. Opinions on how best to teach mathematical concepts in physics varied considerably across participants.