Appears in:
Pages: 3546-3552
Publication year: 2018
ISBN: 978-84-697-9480-7
ISSN: 2340-1079
doi: 10.21125/inted.2018.0681

Conference name: 12th International Technology, Education and Development Conference
Dates: 5-7 March, 2018
Location: Valencia, Spain

# VISUAL AND INTUITIVE EXPLANATIONS OF BASIC MATHEMATICAL CONCEPTS

D. Raviv

Florida Atlantic University (UNITED STATES)
Today’s students are exposed to information presented in visual, intuitive and concise ways. They expect explanations for why a subject is important and relevant, as well as for its potential use. In order to adapt to students’ learning preferences and styles, efforts must be made to further modify teaching methods to include relevance of the material to daily life experiences. The material should also be presented in easy to comprehend, visual, and intuitive ways. This is most relevant in math courses that are usually taught with little or no connection to other disciplines such as engineering.

This paper focuses on introducing basic math concepts by linking them to daily experiences using relevant analogy-based examples, prior to delving into purely mathematical explanations and proofs.

The paper shows tangible physical explanations of concepts in calculus, specifically on topics such as:
(a) Integration and differentiation. To explain the concepts and the relations between them it uses
(1) relations between steering wheel angle of a car and the physical angle of the car in world coordinates,
(2) relations between water flow and its accumulation in a container,
(3) elevator motion (i.e., the relations between position, velocity, acceleration and jerk), and
(4) calories as function of time and calories rate-of-change during running, walking, sitting, and sleeping.
(b) First order differential equation, time constant of first order system, and the understanding of initial conditions. Based on accumulated teaching experience, helpful examples are:
(1) charging battery of a mobile phone at different initial charging values and at different stages of the battery’s life,
(2) cooling rate of coffee which is proportional to the difference between the coffee and the room temperatures, and
(3) behavior of car’s shock absorbers.

Diffusion, i.e., when molecules from a region of high concentration move to a region of lower concentration, is another great example for exponential, first-order-based change. There are of course many other examples, but not all of them are as impactful (e.g., radioactive decay and carbon dating). These ideas are shared so that instructors can use them to enhance understanding of engineering-related math concepts, and to show their relevance.

We refer to this approach as “work in progress.” When using the above examples (and many other examples), students have demonstrated better, clearer understanding of difficult concepts, and praised the approach. Even though this was not an 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, and Computer Algorithms, and even Physics Laws of Motion), it is believed that the approach has a great potential.
@InProceedings{RAVIV2018VIS,
author = {Raviv, D.},
title = {VISUAL AND INTUITIVE EXPLANATIONS OF BASIC MATHEMATICAL CONCEPTS},
series = {12th International Technology, Education and Development Conference},
booktitle = {INTED2018 Proceedings},
isbn = {978-84-697-9480-7},
issn = {2340-1079},
doi = {10.21125/inted.2018.0681},
url = {http://dx.doi.org/10.21125/inted.2018.0681},
publisher = {IATED},
location = {Valencia, Spain},
month = {5-7 March, 2018},
year = {2018},
pages = {3546-3552}}
TY - CONF
AU - D. Raviv
TI - VISUAL AND INTUITIVE EXPLANATIONS OF BASIC MATHEMATICAL CONCEPTS
SN - 978-84-697-9480-7/2340-1079
DO - 10.21125/inted.2018.0681
PY - 2018
Y1 - 5-7 March, 2018
CI - Valencia, Spain
JO - 12th International Technology, Education and Development Conference
JA - INTED2018 Proceedings
SP - 3546
EP - 3552
ER -
D. Raviv (2018) VISUAL AND INTUITIVE EXPLANATIONS OF BASIC MATHEMATICAL CONCEPTS, INTED2018 Proceedings, pp. 3546-3552.
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