An approach for the effective integration of Computer Algebra in an Undergraduate Calculus and Linear Algebra Course

In this paper we describe an approach for an effective integration of computer algebra systems in an elementary calculus and linear algebra course. In our mathematics courses at Wageningen University, an education and research centre for the biological, environmental, agrotechnical and social sciences, we have noted that students often show a lack of conceptual understanding while using computer algebra systems. A reason for this seems to be that the students do not establish a right link between the computer algebra techniques and their mental approach of mathematics. We have composed a framework that aims at establishing such a link. Because the students have developed their mathematical way of thinking in close relation with paper-and-pencil methods, this framework is based on an integration of computer algebra and paper-and-pencil techniques. We have used this framework for the set-up of an elementary calculus and linear algebra course for first year students in social sciences. We first describe this framework, which is made up of several steps. In these steps the use of paper-and-pencil and computer algebra alternate and reinforce each other. Next we show how we worked out this approach for an example from calculus: the determination of the stationary points and extremes of functions of two variables. In this example also the graphic facilities of the computer algebra system are exploited. The last part of the example is an application on maximising the profit of a production process, both without and with constraints