Maths lecturers in denial about their own maths practice? A case of teaching matrix operations to undergraduate students

Abstract

This case study provides evidence of an apparent disparity in the way that certain mathematics topics are taught compared to the way that they are used in professional practice. In particular, we focus on the topic of matrices by comparing sources from published research articles against typical undergraduate textbooks and lecture notes. Our results show that the most important operation when using matrices in research is that of matrix multiplication, with 33 of the 40 publications which we surveyed utilising this as the most prominent operation and the remainder of the publications instead opting not to use matrix multiplication at all rather than offering weighting to alternative operations. This is in contrast to the way in which matrices are taught, with very few of these teaching sources highlighting that matrix multiplication is the most important operation for mathematicians. We discuss the implications of this discrepancy and offer an insight as to why it can be beneficial to consider the professional uses of such topics when teaching mathematics to undergraduate students.