An introductory probability unit designed to counter representativeness misunderstandings.

The primary purpose of this study was to test how well a new basic probability unit could overcome students' representativeness misconceptions. Representativeness, a way of thinking about probability in which strong weight is given to one or two aspects of a problem to the diminution or exclusion of other aspects, is often the source of misunderstandings. The study focused on two particular kinds of representativeness, the "law" of small numbers (in which the theory of large numbers is applied to small number situations) and the conjunction effect (in which the conjunction of two events is seen as more probable than one of the events), as well as on general representativeness understandings. The treatment group of 103 students, enrolled in four sections of a college survey mathematics course, used an experimental introductory probability unit. The control group of 84 students, enrolled in two sections of the same course, used the probability unit of the course's regular text. All students took pretests and posttests of representativeness understanding. The 10 class hour experimental unit employed all of the following techniques: sensitivity to issues of communication; conflict confrontation; simulations with a priori predictions compared to simulation approximations; the spinner model; probability trees; tables (data, outcome, random number); and a definition of probability connecting probability to statistics. Paired t-tests confirmed improvement in the representativeness understanding of the treatment group (p =.0001) and of the control group (p =.004). A t-test showed that the improvement in the treatment group was greater than that of the control group (p =.0008). In an analysis of students' general probability learning, 26 students in one of the experimental sections served as the treatment group, and 92 students using the course's regular text served as the control group. Scores on the probability section of the course's final exam were covaried on pretest representativeness scores. Although the final exam was geared to the probability unit of the control group, ANCOVA showed no significant difference between the groups' performances. This study provides strong evidence that a unit such as the experimental one can, in the course of building a sound foundation of probability understanding, effectively combat representativeness misconceptions.PhDEducationUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/105070/1/9635489.pdfDescription of 9635489.pdf : Restricted to UM users only