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.

This paper addresses the need identified by Graham Jones for more research related to the connections made by students in the middle years 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 five 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.