CONCEPTUAL ISSUES IN QUANTIFYING EXPECTATION: INSIGHTS FROM STUDENTS' EXPERIENCES IN DESIGNING SAMPLING SIMULATIONS IN A COMPUTER MICROWORLD

摘要

We report on part of a classroom teaching experiment that engaged a group of high school students in designing and running sampling simulation in a computer micro world. The simulation design activities provided a vehicle for engaging students with informal hypothesis testing and for fostering their (re)construal of contextualized situations as probabilistic experiments--that is, as a scheme of interconnected ideas involving an imagined population, a sample drawn from it, and repeated sampling as an imagistic basis for quantifying one's expectation of particular sampling outcomes under an assumption about the composition of the sampled population. Our report highlights challenges that students experienced and that shed light on aspects of quantifying one's expectation that a random sampling process will produce a particular type of outcome.