Exploring Foundation Concepts in Introductory Statistics Using Dynamic Data Points

Abstract

This paper analyses introductory statistics students’ verbal and gestural expressions as they interacted with a dynamic sketch (DS), designed using Sketchpad software. The DS involves data points built on the number line whose values change as the points are dragged along the number line. The study is framed on aggregate reasoning with quantitative data, but it also draws on the Vygotskian social cultural and historical perspectives of learning, particularly, how cultural artefacts including language support learning. Three concepts, namely, data distribution, the mean and standard deviation were analyzed in the study. Tasks were designed such that students first talked about their informal understanding of the three foundation concepts before interacting with the DS; then they interacted with the DS and discussed the connections among the three concepts during the tasks and after the tasks. Analysis of students’ verbal, gestural and other expressions suggest firstly, that the dynamic sketch mediated the informal meaning of data variability for them, particularly the meaning of standard deviation, which before, most students only recalled through a formula. Secondly, the interactions with the DS drew students’ attention away from focusing on formulas and calculations, which were clearly evident in their statements before interacting with the DS, to investigating the connections among concepts. These findings support previous studies that have proposed that the use of dynamic computing tools strongly support students’ understanding of abstract mathematical concepts. Implications for the teaching and learning introductory statistics are discussed.