The role of the geometric concepts in the learning of the simplex method

Abstract

Linear programming constitutes university students’ first approach to numerical optimization. The involved concepts require a high level of abstraction. It is thus important to understand how they are constructed. This study presents the results obtained from the use of an APOS Theory based didactical model together with a simple modeling problem to teach the elementary linear programing concepts starting from the basic problem and finishing with the simplex algorithm to students in their first Linear Algebra course. Results show that this didactic approach fosters a meaningful construction of the geometrical model and of its relation to the simplex algorithm steps. These constructions play an important role in the understanding of the concepts involved in the formalization of this algorithm. This study contributes to the literature in studying a topic, linear programming, which has received very little attention from researchers, although it is part of many linear algebra courses at the university level. Moreover, results show that students understand the concepts involved in the simplex algorithm.