This study examined the problem-solving behavior of four students from an urban, middle school as they used computer simulation software to solve probability tasks, by generating and interpreting computer data and representations to make decisions about fairness and adequacy of sample size. The questions that guided the study were: (1) How are data generated by the students from computer simulations interpreted with respect to (a) fairness and (b) significance of sample size? (2) What decisions about fairness and adequacy of sample size do students make on the basis of evidence that they collect? and (3) How are student ideas influenced, if at all, by their computer-generated representations and others?

The students were video-taped during five sessions which occurred on two days of a summer institute, a component of the Informal Mathematical Learning (IML) Project at Rutgers University. Data consisted of discussions between and among students as they worked in pairs on the task, conversations between students and researchers, screen-shots of computer representations that students selected and discussed, and students’ written work recorded on CDs. These were analyzed using the Powell, Francisco & Maher (2003) model for investigating the development of mathematical knowledge using video data.

Analysis of the data revealed that the simulation software, together with social interaction, resulted in students' making and testing conjectures about a sophisticated concept, the Law of Large Numbers. The type of representations that were chosen by students also influenced their arguments. The students agreed that fair dice have a uniform frequency distribution; however, they also agreed that a fair die could have an outcome that alternated between having the highest and then lowest frequencies in two separate experiments.

This study contributes to the data base that documents the building of mathematical ideas as students work on investigations in supportive environments, and addresses a gap in the probability education literature for studies of middle-school students using simulation software to generate data and representations that support their claims.