Middle school and high school students' probabilistic reasoning on coin tasks

This article describes a subset of results from a larger study (Rubel, 2002) that explored middle school and high school students' probabilistic reasoning abilities across a variety of probabilistic contexts and constructs. Students in grades 5, 7, 9, and 11 at an urban, private school for boys (n = 173) completed a Probability Inventory, comprising adapted tasks from the research literature, which required students to provide answers as well as justifications of their responses. Supplemental clinical interviews were conducted with 33 students to provide further detail about their reasoning. This article focuses specifically on the probabilistic constructs of compound events and independence in the context of coin tossing. Analyses of justifications of correct and incorrect answers are provided, offering insight into students' strategies, reasoning, and underlying cognitive models. A belief framework is supported by the results of this study. Potential implications for research and instruction are also discussed.