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Using Time-based Experiences for Explaining the Concept of Discontinuity

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2020 ASEE Virtual Annual Conference Content Access


Virtual On line

Publication Date

June 22, 2020

Start Date

June 22, 2020

End Date

June 26, 2021

Conference Session

Mathematics Division Technical Session 2: Poster Presentations

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Daniel Raviv Florida Atlantic University

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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 25 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. Most recently 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 driverless cars, green innovation, and innovative thinking. He is a co-holder of a Guinness World Record. His new book is titled: "Everyone Loves Speed Bumps, Don't You? A Guide to Innovative Thinking."

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.

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Many instructors have observed that today’s students learn differently: less textbook-reliance and more dependence on web-based explanations, short videos, animations, and demonstrations. When it comes to concept comprehension, students repeatedly ask for more hands-on, experiential, visual, intuitive, fun, and tech-based information. Clearly, basic concepts should be introduced in easy-to-comprehend, visual, and intuitive ways. This is even more relevant in math courses that are usually taught with little or no connection to real life.

This paper focuses on introducing one math concept, namely the concept of discontinuity, by linking it to daily, experience-based and relevant analogy-based examples, to be introduced prior to digging into purely mathematical explanations and proofs.

The paper uses examples that are related to time. These include: (a) time regions, e.g., time zones, daylight saving time, and the International Date Line, (b) devices that use discontinuity to operate, e.g., A/C control, ABS, digital clock, mechanical school bell, digital-to-analog converter, stroboscope and zoetrope, animation video, (c) activities, such as popping a balloon, “exploding” rubber watermelon, flipping coin on a bottle, flipping an animation book, and (d) experiences that can illustrate potential loss of information due to discontinuity, e.g., the famous “Heidi” football story, and of course the effect of discontinuous sensing while texting during driving.

We also use anecdotes and stories that can help connect the students to the topic. These include, for example the SAMOA new time zone and the “lost” day, and Jules Verne story (Around the world in 80 days). These ideas are shared so that instructors can use them to enhance understanding of discontinuity and to show its relevance. It is not meant to suggest competition, modifications or replacement of existing textbooks or pedagogical methodologies. We refer to the material in this paper as “work in progress.” When we used the above examples (and many other examples) in some engineering classes, students have demonstrated better understanding of this and other basic concepts, and commended the approach. Even though there was no official assessment, based on similar experience that was gained and assessed by the author multiple times in other engineering related subjects (Control Systems, Digital Signal Processing, Computer Algorithms, Algebra, Calculus, and even Physics Laws of Motion), there is a reason to believe that the approach has a promising potential.

Raviv, D. (2020, June), Using Time-based Experiences for Explaining the Concept of Discontinuity Paper presented at 2020 ASEE Virtual Annual Conference Content Access, Virtual On line . 10.18260/1-2--35476

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