Undergraduate Students’ Learning of Linear Algebra Through Mathematical Modelling Routes

Abstract

Mathematical modelling has acquired relevance at all educational levels in the last decades since integrating this activity in instruction provides significant contexts for improving students' learning, including in linear algebra courses that have a notable presence in many undergraduate courses from different fields, including engineering and sciences. This paper reports a study aiming to characterize the distinct modelling routes performed by Costa Rican undergraduate students when solving a mathematical modelling task involving the concept of system of linear equations (SLE). In analysing those modelling routes, it was possible to identify their learning of linear algebra concepts and their modelling competencies as well as the associated difficulties that students faced. Data collection included participant observation, with audio recording of the students' discussions, their written work on the task and digital files of their work with technology. The results show that non-linear routes are associated with a greater mobilization of students' knowledge on SLE concepts and with their development of modelling competencies. The results also highlight the need to improve the students' competency of validating results, an important step that they did not take, and suggest the need to make technology relevant to the students' work on modelling tasks.

Advantages and challenges of using digital technologies in mathematical modelling education – a descriptive systematic literature review

“…Checking and validating solutions obtained is another important mathematical activity that can be supported by digital technology. These considerations clearly show that digital technology can prove useful in different phases of the modelling process (Greefrath, 2011;Ramirez-Montes et al, 2021;Frenken et al, 2022). Figure 2 shows different ways of applying digital technology (in italics) within a modelling process in Blum and Leiß's (2007) sevenstep modelling cycle.…”

“…However, the use of technology may introduce challenges to the modelling process; for instance, technical glitches may generate some problems such as outdated web links and errors in a technological system (Merck et al, 2021). Ramirez-Montes et al (2021) reported that technology may not always support students' skills to complete all stages of the modelling cycle as technology may restrict the extensive route of modelling with the acquisition of computational results. For example, technology can support students in measurement and calculation processes, but not in interpretation of the results.…”

Exploring New Fields for the Journal

“…Ramírez Montes et al (2021) focus their research on mathematical modeling, particularly involving the concept of solving a system of linear equations. They investigated the modeling competencies of undergraduate students in Costa Rica in linear algebra concepts.…”

Challenges in geometric modelling–A comparison of students’ mathematization with real objects, photos, and 3D models

“…Hernandez-Martinez & Vos, 2018). By looking at modelling tasks from different mathematics disciplines, several potentials for the development and training of mathematical thinking and acting can be recognized, too: Tasks require, for instance, discrete mathematics (e.g., Greefrath et al, 2022), algebraic structures (e.g., Ramírez-Montes et al, 2021) or geometric skills (e.g., A preliminary analysis of data concerning mathematical modelling was published in journal "Educational Studies in Mathematics" in March 2023. This paper extends this focus by providing a detailed analysis of encountered challenges.…”