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

Probability and Statistics is a pervasive topic in many careers. Engineers, medical professionals, and other specialists use Statistics to analyze data and determine courses of action. People utilize the basic concepts of probability to make decisions in their everyday lives. Despite this, many students struggle with Probability and Statistics in classroom settings. The equations and mathematics can be overwhelming or frustrating, partially because lessons are not visual or intuitive enough and are often missing the connection to daily, real-world experiences. This paper focuses on a visual, intuitive, example-based, and engaging approach to teaching a specific Probability and Statistics concept, namely the normal distribution. 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 more successful when introduced to equations and calculations associated with the topic. To teach this concept, the paper shares supplemental materials that can be introduced during class instruction prior to delving into mathematical details. The paper introduces this concept using (1) Examples, such as a Galton Board and flipping coins, (2) Visualizing basic concepts and some key concepts, (3) Real-life, experience-based examples such as height distribution, (4) A puzzle involving a multiple-choice exam, and (5) An in-class experiment of rolling a die. It should be noted that this paper is a work in progress. In addition, this method of teaching is meant to be supplemental and not to replace existing textbooks or other teaching and learning methodologies. The work in this paper has been presented to 21 students in a Probability and Statistics classroom setting. Following the presentation, it has been assessed and received very positive feedback. This visual, intuitive, and engaging approach to teaching and learning has also been tested in the past for topics in 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. In all of these cases, students commended the approach and found it to be very effective for learning.