As mathematicians, most of us believe that our subject is full of beauty and creativity. We use words such as "elegant" and "beautiful" to describe our favorite proofs, and we admire mathematical greats such as Gauss, Euler, and Ramanujan for their creative capacities -- not just their computational abilities.
As teachers of mathematics, however, we are all too aware of the misconceptions that many people seem to share about our discipline. We lament the facts that mathematicians are seen as "number crunchers" and that our subject is seen as a litany of formulae and procedures. This problem is exacerbated by the unfortunate reality that many of our students don't encounter the truly creative side of mathematics until they start proving theorems for themselves in upper level courses.
Reform efforts in recent years have placed a greater emphasis on ideas and concepts and have made some progress in allaying these student misconceptions. However, there is more to be done. Not only should we work harder to reveal the beauty of our field to a wider audience, but we need to assign coursework at the introductory level that will serve as motivation and inspiration to students.
To this end, I have designed and assigned computer-based calculus projects that involve elements of art and design. As a mathematician who started out as an artist -- my mother was an artist -- I have a propensity for the visual arts, and I have found that many of my students share this propensity. In Calculus II, my students design goblets and tiles. In Calculus III, they draw parametric pictures.
Students enjoy these projects, and they are willing to put in enormous amounts of time creating their own masterpieces. While these projects might not capture the same type of creativity involved in proving an elegant theorem, most students find the work rewarding, and they learn a lot of mathematics along the way.
In this article, I discuss the merits of using calculus projects that involve an element of design. I will highlight a few examples of such projects, including the accompanying module (Parametric Plots: A Creative Outlet), and then discuss the reasons why I think these projects work.
Published June, 2004