A Preliminary Genetic Decomposition of Probabilistic Independence

Abstract

The purpose of this research is to construct a preliminary genetic decomposition delineating the mental constructions underlying probabilistic independence. This delineation will be considered within the framework of APOS theory. While the use of the term independence in probability is often conflated with causation, the technical definition relies instead upon an understanding of conditional probability. I hypothesize that the concept of independence is only fully available to students with a schema conception of probability. I offer additional hypotheses, supported by literature and anecdotal teaching experience, regarding students’ quantification of probability and construction of combinatorial reasoning.