A Visual and Engaging Approach to Teaching and Learning the Normal Distribution

Daniel Raviv; Daniel Ryan Barb

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Conference: 2020 ASEE Virtual Annual Conference Content Access
Location: Virtual On line
Publication Date: June 22, 2020
Start Date: June 22, 2020
End Date: June 26, 2021
Conference Session: Mathematics Division Technical Session 4: Assessing Success in Mathematics Education
Tagged Division: Mathematics
Page Count: 35
DOI: 10.18260/1-2--34082
Permanent URL: https://peer.asee.org/34082
Download Count: 1212

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Paper Authors

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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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biography

Daniel Ryan Barb Florida Atlantic University

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Daniel Barb is an undergraduate student studying Mechanical Engineering at Florida Atlantic University. He spent six years in the United States Navy working in a nuclear power plant aboard a fast attack submarine.

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Abstract

Probability and Statistics is a topic that is crucial for many careers. Engineers, medical professionals, data analysts, businesspeople, and many others use Statistics in analysis to determine courses of action. Additionally, most people utilize the basic concepts of probability to make decisions in their everyday lives. Based on many instructor’s experiences, it has been observed that students often struggle with concepts in Probability and Statistics. The equations and mathematics can be overwhelming and frustrating, partially because concepts are not intuitive and are often missing the connection to daily, real-world experiences. In addition, students learn differently, more visually, and they have short attention spans. To make them pay attention in class, the material and presentation methods should be clear, intuitive and engaging.

This paper focuses on a visual, example-based, and engaging step-by-step approach to teaching a specific Probability and Statistics concept, namely the normal distribution. To teach this topic, the paper shares supplemental materials that can be introduced during instruction. It introduces the concept using (1) An example of the Galton Board, (2) Daily, experience-based examples such as the distribution of shoe sizes, (3) Stories such as the Schlitz beer challenge to explain the binomial experiment, and (4) Puzzles such as a traffic puzzle examining the number of different paths for a car driving from one point to another in a grid. The point of this approach is to provide students with easy to understand examples that translate bookwork to real life and help in comprehension of the material. This more intuitive understanding allows them to be successful when later introduced to equations and calculations associated with the topic.

It should be noted that this paper is a work in progress. In addition, this method of teaching is meant to be supplemental in nature and not to replace existing textbooks or other teaching and learning methodologies. The work in this paper has not yet been shared with students in a classroom setting. However, we intend to perform classroom assessments in the near future. A similar visual, intuitive, and engaging approach has been conducted and assessed in classroom settings for the topics of Statics (explaining center of gravity), Calculus (explaining integration and explaining derivation by chain, product, and quotient rules), Differential Equations, Control Systems, Digital Signal Processing, Newton’s Laws of Motion, and Computer Algorithms. Based on our previous work, there is reason to believe in the effectiveness of this approach in the field of Statistics as well.

Citation
Format

Raviv, D., & Barb, D. R. (2020, June), A Visual and Engaging Approach to Teaching and Learning the Normal Distribution Paper presented at 2020 ASEE Virtual Annual Conference Content Access, Virtual On line . 10.18260/1-2--34082

TY - CPAPER
AB - Probability and Statistics is a topic that is crucial for many careers. Engineers, medical professionals, data analysts, businesspeople, and many others use Statistics in analysis to determine courses of action. Additionally, most people utilize the basic concepts of probability to make decisions in their everyday lives. Based on many instructor’s experiences, it has been observed that students often struggle with concepts in Probability and Statistics. The equations and mathematics can be overwhelming and frustrating, partially because concepts are not intuitive and are often missing the connection to daily, real-world experiences. In addition, students learn differently, more visually, and they have short attention spans. To make them pay attention in class, the material and presentation methods should be clear, intuitive and engaging.

This paper focuses on a visual, example-based, and engaging step-by-step approach to teaching a specific Probability and Statistics concept, namely the normal distribution. To teach this topic, the paper shares supplemental materials that can be introduced during instruction. It introduces the concept using (1) An example of the Galton Board, (2) Daily, experience-based examples such as the distribution of shoe sizes, (3) Stories such as the Schlitz beer challenge to explain the binomial experiment, and (4) Puzzles such as a traffic puzzle examining the number of different paths for a car driving from one point to another in a grid. The point of this approach is to provide students with easy to understand examples that translate bookwork to real life and help in comprehension of the material. This more intuitive understanding allows them to be successful when later introduced to equations and calculations associated with the topic.

It should be noted that this paper is a work in progress. In addition, this method of teaching is meant to be supplemental in nature and not to replace existing textbooks or other teaching and learning methodologies. The work in this paper has not yet been shared with students in a classroom setting. However, we intend to perform classroom assessments in the near future. A similar visual, intuitive, and engaging approach has been conducted and assessed in classroom settings for the topics of Statics (explaining center of gravity), Calculus (explaining integration and explaining derivation by chain, product, and quotient rules), Differential Equations, Control Systems, Digital Signal Processing, Newton’s Laws of Motion, and Computer Algorithms. Based on our previous work, there is reason to believe in the effectiveness of this approach in the field of Statistics as well.

AU - Daniel Raviv
AU - Daniel Ryan Barb
CY - Virtual On line
DA - 2020/06/22
PB - ASEE Conferences
TI - A Visual and Engaging Approach to Teaching and Learning the Normal Distribution
UR - https://peer.asee.org/34082
DO - 10.18260/1-2--34082
ER -