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Gerd Brandell
Centre for Mathematical Sciences, Lund University, Sweden
A traditional calculus course was reformed in 2003 by integrating the use of Maple. The course is compulsory for all engineering students in the university and the reform was carried out in one of the programs, Environmental Engineering, with 50-60 students every year. The course is given during the second year and its content is calculus for functions of several variables. The use of the mathematical software is not for special laboratory sessions but as an every-day tool throughout the whole course. All students have access to Maple on a personal laptop. Students bring their laptops during lectures, lessons and while studying out of class.
Maple is used for interactive visualisation and easy computations. Visualisations and interactive views are invaluable, considering how difficult it is to sketch such objects as graphs of functions of two variables or direction fields with paper and pencil and how crucial the geometric aspects are. Solving exercises often lead to time-consuming computations involving differentiation and integration. Students who are not fluent with managing algebraic simplifications or finding derivatives and primitive functions will spend a lot of time doing these exercises, without necessarily advancing their knowledge or understanding in calculus.
The use of Maple is autonomous in the sense that it is up to the student in what situations and to what extent he/she will use Maple. Hence, a student may accommodate the integration of Maple into the course to his or her personal learning goals. These may include more or less of computer skills. However during the first week of the course a brief introduction to Maple is presented and all students are required to practice some basic Maple. Successively relevant - but relatively few - Maple commands are introduced. Maple is allowed as a tool during the written examination.
The object of the Maple integration is not just to facilitate the students’ learning of mathematics but also to let them experience a professional mathematical software of a kind that most of them will encounter during their continued studies and future careers. One important goal is to illustrate the limitations of the mathematical software.
The course has been well received and attendance has been high. The results of the course will be presented and possible challenges will be discussed.