Using Time-based Experiences for Explaining the Concept of Discontinuity
2020 ASEE Virtual Annual Conference Content Access Proceedings
This paper is about real-life, experience-based examples that can help instructors teach, and students understand, the concept of discontinuity. There are, of course, sophisticated examples such as energy levels of electrons and phase transitions where a quantity changes discontinuously. However, there is a need for visualizing the concept in a more fundamental way using examples that are outside the mathematical domain so that students can comprehend the idea prior to delving into purely
... atical proofs and explanations of the different types of discontinuity. This is particularly true since the new generation of students comprehend material in more visual, intuitive, and engaging ways, while at the same time most textbooks pay little attention to connecting the concept to reality. The paper focuses on two sets of examples: 1. Examples that are unrelated to time. These include (a) discontinuity in space, for example water levels at different sides of the locks in Panama Canal, sharp change in elevation of sidewalks (known as curbs), length of unused paper towel or toilet paper, change in brightness level from light to shadow and between intensity level of pixels in a digital image, (b) numerical displays, such as an abrupt change in the numerical display of an elevator's floor, change in digital display of radio frequencies, (c) switch-based devices such as light switches, (d) audio frequencies, such as audio frequencies of piano keys, and (e) cartoon-based and non-STEM examples of discontinuity. 2. 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 operate based on using discontinuously, e.g., A/C control, ABS, digital clock, stroboscope and Zoetrope, and animation videos, (c) activities, such as "exploding" rubber watermelon, flip book, and (d) experiences that can illustrate potential loss of information due to discontinuity, e.g., the "Heidi" football story, and of course discontinuous sensing while texting and driving. We 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's story Around the World in 80 Days. We refer to the material in this paper as a work in progress. It has not yet been tested in a classroom setting. However, we intend to assess the effectiveness of the ideas in the near future. In the past, when we used visual and intuitive examples, students have demonstrated clearer understanding of difficult concepts. Based on similar experiences that were gained and assessed multiple times by the author in other engineering related subjects (Control Systems, Digital Signal Processing, Computer Algorithms, Mechanical engineering, Calculus, and Physics), it is believed that the approach has great potential. In addition, the information and ideas for enhancing teaching and learning are not meant to replace existing textbooks or other teaching tools. They should be viewed as supplemental to existing, well established and tested educational material. I.