Reasoning and Proof Vol.2-403 TRACING MIDDLE-SCHOOL STUDENTS ’ ARGUMENTS

The purpose of this paper is to deepen our understanding of how group discussion of middle-school aged urban students can facilitate the learning of mathematics. We illustrate how student challenges and counterarguments can lead them toward investigating the deep, underlying mathematical structure involved in the situation that they are investigating and the arguments that they are making. In particular, we investigated how students made judgments about fairness of dice by running computer simulations of die tosses. Our analysis revealed that although students initially offered unsophisticated justifications for their judgments on which dice were fair, challenges to students ' justifications led to a lively debate on important mathematical principles such as the importance of sample size