A Novel Web-based Support Tool for Learning Random Variables

In probability and statistics, a random variable is a function that assigns a number to each outcome of a random experiment. Random variables have various applications in different scientific and engineering fields including health-care, genetics, communication, engineering management, etc. There is an inherent complexity in learning random variables and their distribution models. We have identified two issues that contribute the most to the difficulty students experience: 1) the complexity of the mathematical logic behind the probability theory and 2) lack of motivation to attempt and explore more problems due partly to the static nature of textbook problems. Therefore, our objectives were to enhance students' understanding of random variables and to increase motivation for learning by developing an interactive web-based tool. We have developed a novel e-learning module to assist students in exploring three types of random variables, namely Poisson, Exponential, and Erlang, that differs from the current available resources. We assessed the effectiveness of the module by measuring the change in cognitive and affective behavior of students. We utilized independent diagnostic measures, a homework assignment, a quiz and a question on the final that exclusively cover the three mentioned families of random variables to assess the changes in the cognitive behavior. The treatment group had a superior performance in all measures. The Mann-Whitney U-test analysis shows that the improved performance on the quiz and the final was statistically significant. We also developed a survey to evaluate the students' affective behavior by measuring their motivation for learning and their perceptions of effectiveness of the module. A majority of students (82%) enjoyed doing the web module problems more than the textbook problems. Students agree (91%) that they would explore the web module problems beyond what they are asked to and 86% feel that web module was more motivating than the textbook.