Building a connection between experimental and theoretical aspects of probability

Abstract

This paper addresses a question identified by Graham Jones: what are the connections made by students in the middle years of schooling between classical and frequentist orientations to probability? It does so based on two extended lessons with a class of Grade 5/6 students and in-depth interviews with eight students from the class. The Model 1 version of the software TinkerPlots was used in both settings to simulate increasingly large samples of random events. The aim was to document the students' understanding of probability on a continuum from experimental to theoretical, including consideration of the interaction of manipulatives, the simulator, and the law of large numbers. A cognitive developmental model was used to assess students' understanding and recommendations are made for classroom interventions. © 2009 by GOKKUSAGI.