The differential effect of two activity-based instructional treatments on subjects' concepts of probability was investigated. The concepts of interest were a classical/frequentist interpretation of probability and three misconceptions cited in the literature: law of averages, law of small numbers and availability. All subjects completed a workbook which presented a long-run frequency interpretation of probability. After completion of the workbook, subjects participated in a probability-matching activity where the task was to predict correctly the outcomes for 100 coin tosses of a fair coin. Half the subjects ( the No-Evaluation group) recorded only the outcome of each toss but not their guess. After the 100 tosses, No-Evaluation subjects were presented statements which pointed out congruities between the observed outcomes and the theory presented in the workbook. Evaluation subjects recorded both their guess and the outcome of each toss. In addition to the same statements presented to the No-Evaluation subjects, Evaluation subjects were asked questions which pointed out incongruitities between their recorded data and the three misconceptions. Evaluation subjects showed an increase in classical/frequentist responses from pretest to posttest. In contrast, No-Evaluation subjects showed an increase in law of averages responses with a consequent decrease in classical/ frequentist responses. These findings support the idea that misconceptions formed before or during instruction can be reinforced by experience with stochastic phenomena since subjects may be biased to attend information which confirms the misconceptions.
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education