Abstract
The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasize the development of mathematical abilities primarily associated with modelling and interpreting, which aren´t limited only to calculus abilities. Considering this, an instructional design was elaborated based on mathematic modelling and emerging heuristic models for the construction of specific linear algebra concepts: span and spanning set. This was applied to first year engineering students. Results suggest that this type of instructional design contributes to the construction of these mathematical concepts and can also favour first year engineering students understanding of key linear algebra concepts and potentiate the development of higher order skills.
Highlights
Linear algebra is among the subjects first taken by students in the engineering area and is considered one of the fundamentals in the field
The main contribution of this study is to provide a first approximation of the use of mathematical modelling and the emerging models for learning about spanning set and span for engineering students, since currently no studies exist on this subject, which makes this research innovative and original
The students, through the creation of a password generator, put their previous vector concepts into use, which helped them connect these with the following task that sought a first approximation on spanning set and span
Summary
Linear algebra is among the subjects first taken by students in the engineering area and is considered one of the fundamentals in the field. This is due in part to the essential role it plays later on in the development of other subjects, given its unifying and generalizing nature (Dorier, 2002). Despite its relevance, teaching linear algebra at university level is considered a frustrating experience both for teachers and students (Hillel, 2000), and independently of how it is taught, it is a hard subject for students both cognitively and conceptually (Dorier & Sierpinska, 2001).
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