Preservice elementary teachers' thinking about situations involving probability

The focus of this study was how preservice elementary teachers think about situations involving fundamental concepts of probability. Specifically, this study examined how preservice elementary teachers think about situations involving simple probability, the law of large numbers, compound events, and conditional probability. The goal of the study was to provide mathematics teacher educators with information about some of the conceptions and misconceptions that preservice elementary teachers may have when they begin to study probability as part of their preservice elementary coursework. Twenty-four preservice elementary teachers who had not yet studied probability as part of their preservice elementary mathematics coursework were interviewed using a task-based interview. The results indicated that many of them did not have an adequate understanding of the basic concepts necessary for a meaningful understanding of probability. One third of the participants either did not know the meaning of probability or gave an inadequate response when asked to evaluate a simple probabilistic event with equally likely outcomes. More than three-fourths of the participants did not have an adequate understanding of theoretical probability, experimental probability, and/or the law of large numbers. When participants were asked mathematically equivalent questions about the probability of compound events, their responses were often inconsistent and very sensitive to the framing of the questions. Participants could often be seen to be using reasoning that would have been appropriate for a different situation but was inappropriate for the task at hand. The results of this study suggest that mathematics teacher educators need to provide preservice elementary teachers with instruction and experiences that will enable them to develop a meaningful understanding of the basic concepts of probability.