Looking at Linear Algebra Teaching Practices Through Multimodal Narratives

Looking at Linear Algebra Teaching Practices Through Multimodal Narratives

Cecília Costa (Universidade de Trás-os-Montes e Alto Douro, Portugal) and Ricardo Gonçalves (Instituto Politécnico do Cávado e do Ave, Portugal)
Copyright: © 2019 |Pages: 21
DOI: 10.4018/978-1-5225-8570-1.ch006
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There is a lack of research studies on teaching practices in higher education, which does not contribute to a greater and better reflection on the failure in some disciplines, namely in linear algebra. Multimodal narrative (MN) is a facilitator of research in this field. This chapter describes how the use of MN of linear algebra classes was done and allowed reflection on and modification of the practices. Formative situations are presented: 1) planned and successful, 2) planned and less achieved, 3) unexpected and successful, and 4) unexpected and less achieved. Two transversal aspects to the teaching sequence are also presented: use of technology and geometric approach. This study made it possible to recognize the MN's potential as a tool to “observe” and analyze linear algebra teaching practices in diverse aspects. It also shows that MN analysis allowed linear algebra teachers to promote their professional development regardless of the teacher's experience.
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During the 1960s, introductory linear algebra courses appeared for undergraduates, primarily intended for math and engineering majors (Uhlig, 2003). According to some researchers (Hillel, 2000; Kleiner, 2007; Tucker, 1993), linear algebra is the first full-fledged mathematical theory with which students have contact. It is traditionally taught through an axiomatic approach, which means starting from the axiomatic definition of vector space, followed by deduction of associated concepts and results.

Vector, vector space, linear transformation, system of linear equations and matrix are the basic concepts of linear algebra. All are abstract concepts (although some have a degree of abstraction greater than others), since they are secondary concepts, that is, concepts resulting from the action of the subject on other concepts, as happens with most mathematical concepts. This characteristic justifies part of the complexity attributed to mathematics and some of the difficulties presented by students. Next, an excerpt of a multimodal narrative (MN) (Multimodal Narrative Excerpt 1) is presented that is illustrative of the concept abstraction level of linear algebra and the students’ reaction to it.

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