Perspectives and reflections on teaching linear algebra

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.

La formación de la capacidad matemática de los estudiantes a través de tareas orientadas a la competencia.

“…According to Alpers (2010), in linear algebra, we refer to tasks for application of algorithms of operations over matrices, finding matrix rank, calculating determinants of different orders, finding inverse matrix to the given one, constructing the orthogonal and normalized basis of space, investigating systems of linear equations for compatibility and definiteness and finding their solutions, reducing quadratic forms to canonical form, finding rank and basis of vector system, etc. One has to select and correctly apply algorithms, check or establish the correctness of an algorithm, and partially create one's algorithms, since the study of Rensaa et al, 2020).…”

Applying the Delphi method with early-career researchers to explore a gender-issues agenda in STEM education

“…Since the 1960s, the DM became better known publicly, and it has been used, developed, and adapted to various contexts and topics. For example, it has been used in STEM education to identify scientific competencies for citizenship (Gonzalez-Garcia et al, 2021), to gain consensus on how to teach linear algebra (Rensaa et al, 2020), or to develop an agenda for mathematical research cognition (Alcock et al, 2016). Consequently, its scope and definition have changed to accommodate various necessities, particularly relevant to this paper, its use in qualitative research (Brady, 2015).…”

Kepraktisan Soal Pemodelan Matematika Menggunakan Konteks Biaya Parkir

“…Siswa tampak lebih terbuka untuk menggunakan matematika secara praktis dan lebih tertarik untuk melihat penerapan matematika dalam masalah nyata (Rensaa et al, 2020). Pernyataan ini sangat mendukung pembelajaran pemodelan matematika.…”