Abstract
Abstract This paper presents ‘expert opinions’ on what should be taught in a first-year linear algebra course at university; the aim is to gain a generic picture and general guiding principles for such a course. Drawing on a Delphi method, 14 university professors—called ‘experts’ in this study—addressed the following questions: What should be on a first-year linear algebra undergraduate course for engineering and/or mathematics students? How could such courses be taught? What tools (if any) are essential to these two groups of students? The results of the investigation, these experts’ opinions, mainly concern what should be in a linear algebra course (e.g. problem-solving and applications) and what students should be able to do. The experts also emphasized that certain theoretical aspects (e.g. proofs, abstract structures, definitions and relationships) were more important to mathematics students. There was no real consensus among the experts on teaching methods or the use of digital tools, but this lack of consensus is interesting in itself. The results are discussed in relation to extant research.
Highlights
Students commonly see linear algebra courses at university level as difficult mathematics courses
Drawing on a Delphi method, 14 university professors—called ‘experts’ in this study—addressed the following questions: What should be on a first-year linear algebra undergraduate course for engineering and/or mathematics students? How could such courses be taught? What tools are essential to these two groups of students? The results of the investigation, these experts’ opinions, mainly concern what should be in a linear algebra course and what students should be able to do
The questionnaire had five questions: Q1 What is important to teach in a first course in linear algebra? Q2 Are there methods of teaching that are suited or not suited to linear algebra? Q3 Are there specific tools that should or should not be used in the study of linear algebra? Q4 Do any of your answers to (1) to (3) vary according to whether the students are studying engineering or mathematics? If so, how? Q5 Do you have any further comments?2 The responses were analysed using thematic analysis (Braun & Clarke, 2006)
Summary
Students commonly see linear algebra courses at university level as difficult mathematics courses. Courses in linear algebra may take different directions according to the focus to which the content is applied, pure and formal or more applicable This makes it relevant to ask what a course in linear algebra should be about, what views there are among teachers of such courses, what content is essential to include and whether the answers to these questions vary depending on whether the students are studying mathematics or engineering. This is the motivation for the present investigation. We seek to gain a generic picture and general guiding principles by drawing on
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