Mathematical modelling routes supported by technology in the learning of linear algebra: a study with Costa Rican undergraduate students - Ramírez Montes, Guillermo Enrique (2021)
Mathematical modelling is a significant and productive context for teaching linear algebra, favoring students’ learning of concepts and modelling competencies, often neglected in undergraduate mathematics. This study aims to characterize the modelling routes performed and the competencies put into practice by Costa Rican undergraduate students in a linear algebra course, when solving a mathematical modelling task involving the concepts of spanning set and basis of a vector subspace, using the Excel spreadsheet. Data collection included participant observation of the students’ discussions, their written work on the task, and the Excel files produced. The analysis reveals incomplete and complete modelling routes performed by the students, in which they used the concepts of linear combination, span, standard and non-standard basis to build models. The use of technology influenced the way students obtained mathematical and/or real results from their mathematical model. In complete modelling routes, the computer model has driven several transitions within the modelling cycle, namely between computational, mathematical, and real results, enhancing the modelling processes. In addition, the spreadsheet performed two main functions, calculating and simulating, allowing the groups who used it to assess the effectiveness of their mathematical and computer models and validate them against the real situation.