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Abstract:
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In calculus-based statistics courses, the expected value of a random variable (EVORV) is discussed in relation to the mathematical notion that underlies this statistical concept. In this study, we examine how students learn about EVORV in connection with its semiotic and lexical features, the mathematical notions that underlie it, and its computational aspect. The participants in this qualitative study, which was conducted via surveys and interviews, were eight students enrolled in a calculus-based university statistics course. The results suggest that while the students in general had the computational accuracy to correctly calculate EVORV, they struggled to understand the notion, and in particular to make sense of the term "random" as in random variable and the symbol "E(X)" in the mathematical context. The study provides a basis for understanding the potential challenges to students' learning of EVORV and other similar/related statistics topics, which may emerge from the semiotic and lexical ambiguities inherent in terms and symbols used in statistics.
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