Análisis del aprendizaje de conceptos y técnicas de Álgebra lineal en primercurso de una ingeniería multidisciplinar

Resum

The aim of this work is to analyze Linear Algebra concepts and techniques learning in the context of a first year mathematical subject, “Matemáticas 1”, in a multidisciplinary engineering degree, “Grado en Tecnologías de la Información para la Salud” (Degree on Information Technology for Health Sciences) in the “Escuela Politécnica Superior de la Universidad de Alicante” (University of Alicante Polytechnic School). First, the context of the research is described and analyzed, with respect to the objectives of the subject, not only regarding Linear Algebra contents but also its role as the first subject of Mathematics that students are exposed to in the degree, especially considering the role of the subject in normalizing general mathematical skills, use of symbolic language and formal reasoning,and the introduction of basic concepts about algorithms and computation. Next, some specific aspects of Linear Algebra teaching are discussed, in relation with the available didactic literature, with especial attention to the possible epistemological obstacles, specific or especially relevant, pointed out by different authors (formalism, different levels of representation and reasoning, etc…). General basicmathematical capacities (modelling, generalization, etc…) and specific topics, particularly relevant for Algebra teaching (formalism, abstraction, linearity, etc…) were defined as factors to be consideredin the analysis. We analysed the effect of the student prior education, which was very heterogeneous, including students that had not taken any course in Mathematics in the last years of secondary educationtogether with a majority of students that had taken subjects in Mathematics that included the basic content of Linear Algebra. The methodological approach was based on a variety of multivariateanalyses of the students’ responses to a wide range of questions, exercises and computer lab activities completed during the academic years 2015-2016 and 2016-2017. As a reference of the conceptsand skills/techniques that the students could have acquired during their pre-university education, we analyzed the results of similar tests on specific contents of Linear Algebra and related topics, in pre-university Mathematics courses, carried out in a high school in San Vicente del Raspeig (IES San Vicente). The analyzed questions, exercises and computer lab activities were evaluated, in a posterioranalysis, in order to identify and weight the different dimensions of general mathematical and specific Linear Algebra competences that characterized them. As a particular aspect of the research, weanalysed the relation between the results corresponding to computer lab activities, where a computer algebra system was used, and the results of questions and exercises. This way, even although the typeof analysis does not allow to infer causal effects, we aimed to identify the concepts and techniques were computer lab activities could be more relevant. Overall, the results from this work provide a baseline for discussing the various aspects considered in the research and identifying changes and adaptations in the teaching approach that could facilitate and foster a meaningful learning of key concepts and techniques, which in turn should also result in a higher efficiency of the subject.