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Session: 3565

Using the History of Calculus as an Aid for Teaching Dynamics

Maximo J. Ortega

Purdue University

Introduction

Nowadays, Calculus teaching has become a real challenge. Experiences in the classroom show that students consider Calculus a never-ending succession of techniques or, as they usually say, “recipes”. Most of the problems presented do not have any “real” meaning for them. 1,2 Frequently the teacher introduces these problems by using Geometry. 3,4,5 This approach is sometimes very useful, however its scope is rather limited to some very specific applications. Geometry alone cannot represent the importance of Calculus in the development of Science and Technology. The student may learn the methodology, remember the formula, and find the tangent equation or any other task assigned by his teacher. But sooner or later, the student will ask the question, “what am I going to do with this?” Freudenthal mentions that a considerable amount of research has been done about the learning process but most of this research has been more lab-oriented than classroom-oriented. Very little is known about how an individual applies what he or she has learned. This knowledge is the key to understanding why many people never successfully apply their theoretical knowledge 6.

In summary, there is a lot of controversy about the way Calculus should be taught. Without disregarding other possible deficiencies, it can be considered that one of the main issues is the deep disassociation between the mathematical models being taught and the causes that motivated the creation of these models. This motivation is something that many students do not perceive at all. Cantoral et al. pointed out that it is important to understand the circumstances that allowed the building of the knowledge, instead of merely knowing the circumstances that facilitated its evolution 7. Attention must be focused on the initial stages of an idea. These initial stages always involve intuition and every day experiences but with the development of theoretic formulations the idea evolves into the base argument of theoretic results. This evolutionary process eventually conceals the original meaning. Sometimes, theoretic results are shown in the classroom while the original idea is ignored.

Another issue that emphasizes the importance of new teaching approaches is the fact that most students find it very difficult to apply their knowledge of Calculus in other courses. When faced with a problem that requires them to find a derivative or calculate an integral, many students “Proceedings of the 2002 American Society for Engineering Education Annual Conference & Exposition Copyright Ó 2002, American Society for Engineering Education”

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Ortega, M. (2002, June), Using The History Of Calculus As An Aid For Teaching A Dynamics Course Paper presented at 2002 Annual Conference, Montreal, Canada. 10.18260/1-2--10986