On Teaching and Learning the Concept of Derivative in Visual and Intuitive Ways

Daniel Raviv; Juan David Yepes

Download Paper | Permalink

Conference: ASEE Southeast Section Conference
Location: Arlington, Virginia
Publication Date: March 12, 2023
Start Date: March 12, 2023
End Date: March 14, 2023
Conference Session: Mathematics and Material Science
Tagged Topic: Professional Engineering Education Papers
Page Count: 16
DOI: 10.18260/1-2--45030
Permanent URL: https://peer.asee.org/45030
Download Count: 58

Request a correction

Paper Authors

biography

Daniel Raviv Florida Atlantic University

visit author page

Dr. Raviv is a Professor of Computer & Electrical Engineering and Computer Science at Florida Atlantic University. In December 2009 he was named Assistant Provost for Innovation and Entrepreneurship.

With more than 30 years of combined experience in the high-tech industry, government and academia Dr. Raviv developed fundamentally different approaches to “out-of-the-box” thinking and a breakthrough methodology known as “Eight Keys to Innovation.” He has been sharing his contributions with professionals in businesses, academia and institutes nationally and internationally. He was a visiting professor at the University of Maryland (at Mtech, Maryland Technology Enterprise Institute) and at Johns Hopkins University (at the Center for Leadership Education) where he researched and delivered processes for creative & innovative problem solving.

For his unique contributions he received the prestigious Distinguished Teacher of the Year Award, the Faculty Talon Award, the University Researcher of the Year AEA Abacus Award, and the President’s Leadership Award. Dr. Raviv has published in the areas of vision-based driver-less cars, innovative thinking, and teaching innovatively. He is a co-holder of a Guinness World Record. He is a co-author of five books on innovative thinking and teaching innovatively.

Dr. Daniel Raviv received his Ph.D. degree from Case Western Reserve University in 1987 and M.Sc. and B.Sc. degrees from the Technion, Israel Institute of Technology in 1982 and 1980, respectively.

visit author page

author page

Juan David Yepes

Download Paper | Permalink

Abstract

Calculus is a basis for advanced mathematics for many university students and in particular for engineering students. Calculus courses introduce many important concepts and ideas that are not only applicable to STEM fields, but also play a role in day-to-day life. We have observed that many engineering students struggle with basic concepts in calculus due to its daunting deviation from topics found in earlier math courses and the disconnect to real-life examples. This is due in part to the current structure of curricula that follow a more traditional “textbook” structure by relying on equations and graphs without building the intuition behind the topics. This paper focuses on easing the process of introducing an early topic in calculus known as the derivative through visual and intuitive examples that relate to day-to-day life experiences. Such examples are chosen because they provide an initial grounding for this concept in mathematics. An introduction where the concept is relatable can provide a general sense of the idea behind derivative, on top of which students can expand their knowledge with more formal textbook definitions. Examples used in this paper include topics such as 1) different slopes as experienced when traveling up and down hills, 2) rates of losing calories during running, walking, sitting, and sleeping, 3) rates of filling out water in a bucket, 4) basic rate of change as related to filling out and using gas in a vehicle, 5) phone charging and discharging at different rates, and 6) a visual introduction to the formal definition of derivatives using graphs. This paper is a work in progress. Additionally, it is not meant as a replacement for traditional teaching methods and is rather meant as supplemental material to enrich the students’ understanding the concept of derivatives. Examples and exercises presented in this paper have been shared with students to gauge the effectiveness of this teaching and learning method. A questionnaire was then given to 41 engineering students in two different classes where a majority of the responses deemed such a method of instruction to be “very important” (the highest of five categories) and engaging. Furthermore, this paper is an expansion of the current effort aimed at introducing mathematical concepts in more intuitive and visual ways. Other concepts that have been explored with such a method include explaining normal distributions, continuity, limit, inverse function, integrals, and first order equations. Previous assessments of this teaching style have shown that this method for teaching and learning is received very positively by students.

Citation
Format

Raviv, D., & Yepes, J. D. (2023, March), On Teaching and Learning the Concept of Derivative in Visual and Intuitive Ways Paper presented at ASEE Southeast Section Conference, Arlington, Virginia. 10.18260/1-2--45030

TY - CPAPER
AB - Calculus is a basis for advanced mathematics for many university students and in particular for engineering students. Calculus courses introduce many important concepts and ideas that are not only applicable to STEM fields, but also play a role in day-to-day life. We have observed that many engineering students struggle with basic concepts in calculus due to its daunting deviation from topics found in earlier math courses and the disconnect to real-life examples. This is due in part to the current structure of curricula that follow a more traditional “textbook” structure by relying on equations and graphs without building the intuition behind the topics.
This paper focuses on easing the process of introducing an early topic in calculus known as the derivative through visual and intuitive examples that relate to day-to-day life experiences. Such examples are chosen because they provide an initial grounding for this concept in mathematics. An introduction where the concept is relatable can provide a general sense of the idea behind derivative, on top of which students can expand their knowledge with more formal textbook definitions. Examples used in this paper include topics such as 1) different slopes as experienced when traveling up and down hills, 2) rates of losing calories during running, walking, sitting, and sleeping, 3) rates of filling out water in a bucket, 4) basic rate of change as related to filling out and using gas in a vehicle, 5) phone charging and discharging at different rates, and 6) a visual introduction to the formal definition of derivatives using graphs.
This paper is a work in progress. Additionally, it is not meant as a replacement for traditional teaching methods and is rather meant as supplemental material to enrich the students’ understanding the concept of derivatives. Examples and exercises presented in this paper have been shared with students to gauge the effectiveness of this teaching and learning method. A questionnaire was then given to 41 engineering students in two different classes where a majority of the responses deemed such a method of instruction to be “very important” (the highest of five categories) and engaging. Furthermore, this paper is an expansion of the current effort aimed at introducing mathematical concepts in more intuitive and visual ways. Other concepts that have been explored with such a method include explaining normal distributions, continuity, limit, inverse function, integrals, and first order equations. Previous assessments of this teaching style have shown that this method for teaching and learning is received very positively by students.

AU - Daniel Raviv
AU - Juan David Yepes
CY - Arlington, Virginia
DA - 2023/03/12
PB - ASEE Conferences
TI - On Teaching and Learning the Concept of Derivative in Visual and Intuitive Ways
UR - https://peer.asee.org/45030
DO - 10.18260/1-2--45030
ER -