Misconceptions of probability: An experiment with a small-group, activity-based, model building approach to introductory probability at the college level

Summary

The day-by-day observations made by the experimenter during one of the activity-based classes indicate that college students can learn to discover some elementary probability models and formulas for themselves while working on probability experiments in small groups. Furthermore, the effects of sample size upon measures of central tendency and variability can be learned by students working on activities such as those developed for the experimental course in this study. Making guesses for the probability of events and checking guesses with a hand-held calculator seems to help college students to be more cautious about probability estimates, and helps to make them aware about some of their own misconceptions about probability. Small-group problem solving, keeping a log of all class work and activities, and investigating the misuses of statistics all appeared to have a positive effect upon college students' attitudes towards mathematics, as indicated in the questionnaires filled out by the subjects in the experimental sections.

The present results of this study support the hypotheses of Kahneman and Tversky [10, 12] which claimed that combinatorially naive college students rely upon availability and representativeness to estimate the likelihood of events. Kahneman and Tversky were skeptical about the possibility of helping students to overcome their reliance upon availability and representativeness. The results on the posttest in this study suggest that the manner in which college students learn probability makes a difference in their ability to overcome misconceptions that arise from availability and representativeness. Mere exposure to probability concepts is not sufficient to overcome certain misconceptions of probability. Fischbein [9] notes that the “synthesis between the necessary and the possible-which is the basis of probabilistic thinking-does not in fact take place spontaneously ....” He claims that science education emphasizes only the deterministic aspect, and neglects the study of uncertainty. Thus peoples' intuition of probabilistic thinking is distorted by science education's emphasis on the necessary, and neglect of the possible. This experiment suggests that the course methodology and the teaching model used in an elementary probability course can help develop peoples' intuition for probabilistic thinking. A course in which students carry out experiments, work through activities to build their own probability models, and discover counting principles for themselves can help students to overcome their misconceptions about probability, and can help restore the synthesis between the necessary and the possible which is essential to probabilistic thinking.