2024 ASEE Annual Conference & Exposition

In today's educational landscape, students increasingly seek to grasp basic understanding of mathematical concepts. It is imperative that teaching approaches evolve to meet this demand, especially in the realm of mathematics where there is a gap between understanding the theory and applying its relevant techniques. This paper focuses on addressing the challenges students face when learning calculus, particularly the L'Hôpital's Rule. While students may learn how to apply it, many lack a fundamental understanding of its origins, missing the crucial "why" behind its application.

The primary objective of this paper is to deepen students' understanding of L'Hôpital's Rule by incorporating visualization and intuition techniques with mathematical approaches. We explore the background of L'Hôpital's Rule and present three different ways to explain the essence of the rule by: a) zooming in on the intersection of two functions, b) employing the Taylor Series, and c) utilizing Infinitesimal Calculus. By using these approaches, it becomes easier to grasp the essence of L'Hôpital's Rule, which is about comparing how fast two functions change as they approach a particular point. Moreover, to provide a comprehensive perspective we share some practical textbook examples that highlight the applications of L'Hôpital's Rule.

To assess the effectiveness of the new approach for learning L’Hopital Rule we conducted an in-class anonymous questionnaire. 58 students responded. The results clearly show that understanding the concept of L’Hopital Rule is either important or very important to students. Most of them praised the visualization and intuition approach for teaching the rule. Even though we have not used activities and exercises, students felt that more hands-on activities and in-class exercises could be very helpful as well. In general, they like traditional presentations, but not as excited as we thought about power point presentations. Surprisingly most of them prefer not to read textbooks but rather to be taught. Overall, our assessment reveals that students greatly preferred visualizations as an additional learning method. This approach not only enhances their comprehension of L’Hopital Rule but also underscores their preference for a visual learning experience. The results are consistent with our multi-year experience in evaluating similar methods across various engineering related subjects like Control Systems, Digital signal Processing, Computer Algorithms, and Physics.

It is important to note that this work should be considered work in progress. It is not intended to replace traditional textbook chapters but rather to serve as an invaluable add-on resource. Our goal is to assist educators in teaching and empower students in learning complex mathematical concepts in a more engaging and meaningful manner.