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.     

Decreasing “obscene” language of behaviorally disordered children through the use of a DRL schedule

The purpose of the present study was to determine the value of DRL schedules in reducing the behavior of a group of behaviorally disordered children. During the DRL procedure, reinforcement was made available for inappropriate language that was less than a prescribed limit for each day. When the DRL limit was successively decreased across weeks, the behavior of the students systematically decreased. Data indicated that reinforcing low rates of behavior may be an effective alternative to the use of aversive contingencies to reduce the misbehavior of such children.     

The Status of Genetics Curriculum in Higher Education in the United States: Goals and Assessment

We review the state of genetics instruction in the United States through the lens of backward design, with particular attention to the goals and assessments that inform curricular practice. An analysis of syllabi and leading textbooks indicates that genetics instruction focuses most strongly on foundations of DNA and Mendelian genetics. At the same time, a survey of faculty indicates that other concepts, such as the application of genetics to society or the environment, are viewed as equally or even more important than foundation concepts. This disconnect suggests a need for more explicit goal setting prior to curriculum development. We also review the relationship between concept inventories, multiple-choice tests measuring conceptual understanding, and curricular goals. Existing concept inventories offer a strong foundation on which to build community-developed concept assessments of genetics knowledge. Concept assessments such as these would allow the genetics education community to test hypotheses of curricular change.