2023 ASEE Annual Conference & Exposition

Probability is a fundamental course for students in both electrical and computer engineering majors. This course serves as an introduction to probabilities and statistics, as well as their applications to engineering problems. Most students consider probability and statistics a hard subject, partly because it requires a combination of math theory and real world thinking, often not in a very intuitive way. It is also challenging for students to apply the theory to problem solving, especially on how to interpret what is given in a scenario, identify the goal, and connect the two using probability tools.

The probability course in the ECE department at Purdue University Fort Wayne is scheduled in a face-to-face setting except in the spring 2020 semester when campus was closed for COVID. There has been a noticeable decrease in student motivation to attend lectures, interact with faculty and peer students, and seek academic assistance. This especially affects the quality of learning for those at risk. Didactic lecture is still the most commonly used method in teaching probability courses. During lectures, to illustrate the application of probability in real-life and engineering scenarios, the instructor would spend a moderate amount of time demonstrating the step-by-step problem solving process. Due to the lecture time limit, however, students often do not get sufficient time themselves to inspect the problem setting, interpret the problem through the lens of probability theory, and take an active role in their learning.

This paper summarizes the effort of a probability course instructor in spring 2022 and spring 2023 semesters to actively involve students in their own learning process and enhance the teaching and learning effectiveness. More than half of the students enrolled in this course are working either full time or half time. Therefore, the goal is to design materials and strategies to efficiently engage them before, during, and after lecture, but not overwhelm them with too much workload. The strategies explored include the following:

• Encouraging participation and feedback: Participation credits are added encompassing both before-lecture online quizzes and lecture attendance. The requirement of lecture attendance encourages students’ presence and interaction in the classroom. The instructor can directly observe students’ understanding and struggles during class. The online quizzes engage students before and after each lecture with relevant problems. Each quiz also provides an opportunity for students to leave feedback.

• Adding online quizzes for better preparation and review: These online quizzes focus on timely review past learning and preparation of new learning. Questions are designed to allow students to think through some in-class illustrative problem before lecture. Students attempt to interpret the probabilities and identify the goal. This way they will come more prepared and better understand why the instructor chooses a certain approach in solving the problem. In addition, the instructor will be aware of the common mistakes and misunderstandings, and can better elaborate the reasoning behind the steps. Besides questions to preview in-class problems, review questions are also included to help students timely assess their previous learning.

• Adding instructional resources to support learning: An important concept in probability theory is distribution of random variables, especially how different parameter values would change the distribution, and how additional knowledge about a random variable would affect its probability metrics. All these can be depicted through configurable figures or animations. For this purpose, interactive documents such as MATLAB live scripts are written to allow students vary certain parameters and observe their effects on probability features instantly. In addition, the instructor recorded short instructional videos in spring 2020 for virtual teaching during COVID. These videos are used as optional review resources and released after corresponding lectures. Furthermore, to enhance self-learning, questions are embedded in these short videos to stimulate learning and self-assessment.

The detailed design and implementation of the above-mentioned pedagogical strategies are explained. The effectiveness of these strategies is assessed through student participation and performance data over both semesters. Ideas for further improvement are discussed as well. These strategies can be tailored to other engineering courses.