RUME 25
2023
Omaha, Nebraska
Students’ Inferences Using a Conditional Statement in Probability: The Relationship between Independence and Covariance of Random Variables
Page: 702
The purpose of this study was to investigate how students in a probability course interpret a theorem and how they apply the theorem when asked to determine whether two random variables are independent given the value of the variables’ covariance. We considered how responses of students with prior training in logic compare to other students, as the theorem is a conditional statement. We used a quasi-experimental design to investigate the impact of two instructional treatments, using isomorphic colloquial statements and using Euler diagrams. Participants largely gave conventional truth values for variants of the conditional statement prior to instruction, but many of them used the converse and/or did not use the contrapositive when given covariance values and asked to determine whether two variables were independent. Our results do not consistently show a significant difference in students’ choices based on their prior logic training or either treatment.