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.
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