RUME 26
2024
Omaha, Nebraska
Student Interpretations of Conditional Statements in Probability: The Cases of Byron and Sophie
Page: 1133
Students often have to interpret conditional statements in mathematics classes without prior training in logic. In a previous study, we investigated how students interpreted variants of the conditional statement: If two random variables are independent, their covariance is 0. The purpose of the current study is to explore surprising results and apparent inconsistencies in student interpretations using clinical interviews after a lecture introducing the conditional statement. In this paper we contrast the experiences of two students, Byron and Sophie. Preliminary results suggest that Byron relies both on his logic training and his domain knowledge to solve problems about independence and covariance. Sophie’s incorrect domain knowledge led to her reversing the implication. Once this was resolved, she was not confident in assigning truth values to statement variants. We discuss teaching implications that arise from issues of both mathematical efficiency and accuracy in presenting this theorem.