Learning Probability Through The Use Of A Collaborative, Inquiry-Based Simulation Environment

Abstract

In this paper we report on the Probability Inquiry Environment (PIE), which facilitates the development of probabilistic reasoning by making available collaborative inquiry activities and student-controlled simulations. These activities guide middle school students toward a deeper understanding of probability, a domain that is becoming increasingly important in the K-12 mathematics curricula of the United States but which is notoriously difficult to learn. A study is described in which middle school students who participated in the PIE curriculum significantly outperformed students who participated in the school’s traditional probability curriculum. We posit that this difference is due to the PIE curriculum fostering student collaboration as the students employ their existing intuitions as building blocks for formal knowledge. This provides evidence that a productive learning environment should not be based solely upon the logical structure of the target domain, but should also account for both students’ intuitive conceptions of a domain, as well as aspects of social interaction that shape students’ experiences. We then show the importance of intuitions and social interaction by analyzing a case study in which students articulated and revised their initial understandings of probability as they interacted with PIE-collaboratively making predictions, evaluating data, and interpreting representations.