Abstract:

Active learning is generally defined as any instructional method that engages students in the learning process. The core elements of active learning are student activity and engagement in the learning process within the classroom. In short, active learning requires students to do meaningful learning activities and think about what they are doing. Strong evidences of the effectiveness of using active learning techniques can be found in the literature.

We present the GLP-Tool, a good example of an active learning technical tool to explore the fundamental concepts of Linear Programming (LP).

When introducing the subject of linear programming it is rather useful to present the graphical method for solving a two-variable linear program as it provides valuable insights about the general nature of multivariable linear programming models. The graphical method illustrates numerous aspects of the more complex, algebra-based, solution algorithm - the simplex method. Graphically solving a linear program provides students with intuitive visual aids to facilitate their understanding of many LP concepts. Nonetheless, without a dynamic tool, it is not easy to show students what happens in a (two-variable) LP problem instance as constraint boundary lines and objective-value lines move around on a graphic.

The GLP-Tool is a dynamic, interactive, visual application and was implemented using the computer algebra system Mathematica. It allows the user to dynamically explore and solve two-variable linear programming problems with user-defined objective functions and constraint sets. All the GLP-Tool functionalities are represented analytically and graphically and updated in real time. The interactive, dynamic, analytical, and graphical features of the GLP-Tool make this application a powerful tool for teaching LP both in undergraduate and high school courses. It can be used both by teachers to graphically illustrate fundamental concepts and by students to experiment with changes within a graphical representation of a linear program instance, facilitating their understanding of numerous LP concepts.

We believe that this new GLP-Tool is an important contribution to the improvement of the teaching-and-learning process of LP precisely by providing teachers and students alike with an active learning technical tool to explore fundamental concepts of the subject.

We intend to make the GLP-Tool available online to the general public, via the Wolfram Demonstrations Project website.

Keywords:

Educational software, graphical linear programming, interactive graphical visualization, Wolfram Mathematica.