Students' Construction of Meanings about the Co-ordination of the Two Epistemological Perspectives on Distribution

Abstract

The importance of the connection between theoretical frequencies and observed relative frequencies in pedagogy is advocated by various probabilistic researchers. This study examines an associated area of importance to mathematical education. Little is known about the process by which the co-ordination of the data-centric and modelling perspectives on distribution might be achieved. The focus of this paper is on variation in students' (aged 14 to 15 years) evolving meanings about the co-ordination of two distinct epistemological perspectives on distribution. Extracts from two case studies illustrate students' construction of two interpretations for the two perspectives on distribution through their attempts to transform, directly or indirectly, the specific modelling distribution, and observing how that changes a graph/histogram of the actual outcomes. This is done by using on-screen control mechanisms to change the way that the computer generates the data within a carefully designed computer simulation.