A deep structure model of students' statistical misconceptions

The present study investigated a model used by non-mathematically oriented
students in solving problems in descriptive statistics. Analyses show that college students mistakenly assume that a set of means together with simple mean computation constitutes a mathematical group satisfying the four axioms of closure, associativity, identity, and inverse. This set of misconceptions is so deeply ingrained in a students' underlying knowledge base that mere exposure to a more advanced course in statistics is not sufficient to overcome those misconceptions. However, results of an experiment indicated that most students were able to acquire the appropriate schema of statistical concepts by engaging in diagnostic activities embedded within a feedback-corrective procedure.