Abstract
This paper explores and promotes the notion of ‘procept’ in an undergraduate mathematics course in Linear Algebra for first year pure and engineering students. On the basis of students’ preference for procedural to conceptual solutions to mathematical problems, this paper augments the role of certain concepts in pure and applied mathematics, particularly in the problem‐solving approaches at the undergraduate level by providing novel solutions to problems solved in the usual traditional manner. The development of the concept of ‘procept’ and its applicability to mathematics teaching and learning is important to mathematics education research and tertiary pure and applied mathematics didactics in South Africa, welcoming the amalgamation of the theories developed at pre‐tertiary level mathematics with theorems and proof at the undergraduate level.
Highlights
The novelty of this paper is twofold. It transcends the boundaries between elementary mathematics education research and tertiary pure and applied mathematics didactics, welcoming the amalgamation of the theories developed at pre-tertiary level mathematics education with an approach to teaching theorems and proof at the undergraduate level
It augments the role of certain concepts in pure and applied mathematics, in the problem-solving approaches at the undergraduate level by providing novel solutions to problems solved in the usual traditional manner
Concluding remarks In South Africa, the general perception is that secondary school teaching of mathematics tends to be fairly procedural and that students that enter university are better equipped to deal with procedural problems than with conceptual problems (Engelbrecht, Harding, & Potgieter, 2005)
Summary
This paper explores and promotes the notion of ‘procept’ in an undergraduate mathematics course in Linear Algebra for first year pure and engineering students. The paper explores and promotes the notion of procept in an undergraduate mathematics context which emanated from the teaching unit of skew lines in 3-dimensional space,. It augments the role of certain concepts in pure and applied mathematics, in the problem-solving approaches at the undergraduate level by providing novel solutions to problems solved in the usual traditional manner. The classical approach in determining whether two non-parallel lines in are skew is to equate their parametric equations and solve the resultant system of equations by Gaussian elimination This procedural approach to solving such a problem has always been the traditional computational mode of instruction in an undergraduate level Linear Algebra course. Of , , represents the area under (for positive ) or the work done by a force in moving an object from to
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