Literature Index

The purpose of this chapter is to investigate issues concerning the nature and development of teachers' probability understanding. An outline of the central issues that affect teachers' efforts to facilitate students' probabilistic understanding is given. Then, I examine teachers' knowledge and beliefs about probability, their ability to teach probabilistic ideas, and lessons learned from programs in teacher education that have aimed at developing teachers' knowledge about probability.

This study focused on the relations between performance on a three-choice probability-learning task and conceptions of probability as outlined by Piaget concerning mixture, normal distribution, random selection, odds estimation, and permutations. The probability-learning task and four Piagetian tasks were administered randomly to 100 male and 100 female, middle SES, average IQ children in three age groups (5 to 6, 8 to 9, and 11 to 12 years old) from different schools. Half the children were from Middle Eastern backgrounds, and half were from European or American backgrounds. As predicted, developmental level of probability thinking was related to performance on the probability-learning task. The more advanced the child's probability thinking, the higher his or her level of maximization and hypothesis formulation and testing and the lower his or her level of systematically patterned responses. The results suggest that the probability-learning and Piagetian tasks assess similar cognitive skills and that performance on the probability-learning task reflects a variety of probability concepts.

The authors state that athletics in general can be used to demonstrate probabilistic concepts and that these may be reinforced due to the motivational aspects of the examples. In this article, the planification of the NCAA Regional Basketball tournaments is examined as a probability problem (e.g. what is the probability of team #3 winning the regionals?). In calculating the probability of any team winning, the students must: 1) evaluate the probability of each game played; 2) assume independence of each contest; and 3) incorporate the relative strength of each team in the model. Three probability models are considered, the third being the most adequate. It seems to provide a good fit to the data and is considered interesting to students without requiring a strong mathematical background. The key point in this article is that these models demonstrate the multiplication principle and the additive property of mutually exclusive events in addition to the motivation provided by the topic itself.

The teaching of probability theory has been steadily declining in introductory statistics courses as students have difficulty with handling the rules of probability. In this article, we give a data-driven approach, based on two-way tables, which helps students to become familiar with using the usual rules but without the formal structure.