Virtual On line
June 22, 2020
June 22, 2020
June 26, 2021
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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