WIP: A Visual Approach to Teaching and Learning the Concept of Limit

Daniel Raviv

Download Paper | Permalink

Conference: 2022 ASEE Annual Conference & Exposition
Location: Minneapolis, MN
Publication Date: August 23, 2022
Start Date: June 26, 2022
End Date: June 29, 2022
Conference Session: Investigations Using Calculus Courses
Page Count: 25
DOI: 10.18260/1-2--40683
Permanent URL: https://peer.asee.org/40683
Download Count: 319

Paper Authors

biography

Daniel Raviv Florida Atlantic University

visit author page

Daniel Raviv received his B.Sc. and M.Sc. degrees from the Technion, and his Ph.D. from Case Western Reserve University in Cleveland, Ohio. He is a professor at Florida Atlantic University (FAU) where he is the Director of the Innovation and Entrepreneurship Lab. In the past he served as the assistant provost for innovation. Dr. Raviv taught at Johns Hopkins University, the Technion, and the University of Maryland, and was a visiting researcher at the National Institute of Standards and Technology (NIST) as part of a group that developed a vision-based driverless vehicle for the US Army (HUMVEE; 65 mph).
His related research work includes exploration of visual invariants that exist only during motion and can be used for real-time closed-loop control systems of cars and drones. He is also interested in teaching and learning innovative thinking, and how to teach innovatively. He is the author of five books: three on learning innovative thinking and two on teaching in visual, intuitive, and engaging ways.

visit author page

Download Paper | Permalink

Abstract

Abstract

A growing number of students have difficulties connecting mathematical principles to real life. In addition, as technology brings about a paradigm shift in the way people perceive and learn new information, students become more sidetracked, as their attention span has become shorter. They also prefer more visual and intuitive explanations of the material. This suggest that additional teaching methods should be explored to adjust to students' new styles of learning.

This paper describes several illustrative examples aimed at aiding in comprehension of the concept of limit. The idea is to introduce the topic in an intuitive and engaging manner before transitioning to conventional textbook material. Examples are drawn from (1) Art, using examples such as 2d perspective views and vanishing points in images, (2) Physics, using time-related examples such as the tendency towards equilibrium in nature, e.g., approaching temperature and pressure equilibria, (3) Engineering and Technology, using energy related examples such as charging the battery of a mobile phone, (4) Geometry, using images as obtained from two parallel mirrors, and fractals, and (5) Algebra and Calculus, using limit to explain the Golden Ratio, and the concepts of derivative and integration. The paper concludes with related math and engineering brain teasers.

The examples are designed to serve as a supplemental resource. The goal is to promote a basic level of intuitive comprehension prior to introducing further mathematical analysis. This will provide students with an easier transition, helping to reinforce intuition to achieve a higher level of success when learning difficult concepts. It is also designed to provide educators with additional material to help engage with students. The information presented is not meant to replace existing textbook chapters, or other teaching and learning methodologies.

This paper is a work in progress. To assess the validity of the proposed approach, the author introduced the concept of limit to students in a Calculus class followed by a detailed questionnaire, resulting in 29 responses. Summary of the results to multiple questions shows a very positive average response. This set of initial results indicates that the students preferred being introduced to the concept of limit visually and intuitively. They praised this approach and found it to be very effective for learning. There is good reason to believe that the approach has a promising potential.

Citation
Format

Raviv, D. (2022, August), WIP: A Visual Approach to Teaching and Learning the Concept of Limit Paper presented at 2022 ASEE Annual Conference & Exposition, Minneapolis, MN. 10.18260/1-2--40683

TY - CPAPER
AB - Abstract

A growing number of students have difficulties connecting mathematical principles to real life. In addition, as technology brings about a paradigm shift in the way people perceive and learn new information, students become more sidetracked, as their attention span has become shorter. They also prefer more visual and intuitive explanations of the material. This suggest that additional teaching methods should be explored to adjust to students' new styles of learning.

This paper describes several illustrative examples aimed at aiding in comprehension of the concept of limit. The idea is to introduce the topic in an intuitive and engaging manner before transitioning to conventional textbook material. Examples are drawn from (1) Art, using examples such as 2d perspective views and vanishing points in images, (2) Physics, using time-related examples such as the tendency towards equilibrium in nature, e.g., approaching temperature and pressure equilibria, (3) Engineering and Technology, using energy related examples such as charging the battery of a mobile phone, (4) Geometry, using images as obtained from two parallel mirrors, and fractals, and (5) Algebra and Calculus, using limit to explain the Golden Ratio, and the concepts of derivative and integration. The paper concludes with related math and engineering brain teasers.

The examples are designed to serve as a supplemental resource. The goal is to promote a basic level of intuitive comprehension prior to introducing further mathematical analysis. This will provide students with an easier transition, helping to reinforce intuition to achieve a higher level of success when learning difficult concepts. It is also designed to provide educators with additional material to help engage with students. The information presented is not meant to replace existing textbook chapters, or other teaching and learning methodologies.

This paper is a work in progress. To assess the validity of the proposed approach, the author introduced the concept of limit to students in a Calculus class followed by a detailed questionnaire, resulting in 29 responses. Summary of the results to multiple questions shows a very positive average response. This set of initial results indicates that the students preferred being introduced to the concept of limit visually and intuitively. They praised this approach and found it to be very effective for learning. There is good reason to believe that the approach has a promising potential.

AU - Daniel Raviv
CY - Minneapolis, MN
DA - 2022/08/23
PB - ASEE Conferences
TI - WIP: A Visual Approach to Teaching and Learning the Concept of Limit
UR - https://peer.asee.org/40683
DO - 10.18260/1-2--40683
ER -