Students' Understanding Of Variability In A Probability Environment

The concept of statistical variation in a probability distribution is closely connected to the concept of sample space in a probability task. One must have some sense of the possible outcomes in a probability task in order to predict the likely variation range that will occur during repeated trials of that probability task. A survey version of a NAEP probability task was given to 652 mathematics students in grades 6 - 12 to obtain information on students' understanding of the sample space. Subsequently 28 students from grades 8-12 were given an interview version that included a simulation of the task. Survey results indicate that a higher percentage of students taking advanced mathematics correctly answered the probability task than was predicted by the NAEP data. Results of the interviews suggest that students who at first thought incorrectly about the probability task were likely to change their minds after seeing the variation in results of sets of repeated trials of the task.