Gifted students’ understanding of statistics: analysis of data arising from a small group teaching experiment

Abstract

The principal objective of the study was to gain insight into cognitive processes related to three gifted students’ understanding of data. Small group teaching experiment methodology was used to uncover students’ understanding of the notion of distribution and consisted of a clinical interview phase, teaching phase and analysis phase. Fifteen teaching episodes followed the initial clinical interview and involved students working together on a variety of mathematical activities. The study examined how students organized data, described and indexed distributions of data, in addition to investigating their conceptualization of the mean. Results suggest that (a) modes and ranges were the most salient features of distributions, (b) typical values were generally located in clusters of data, (c) the mean was not utilized in the constructed measures of typicality, and (d) students had a relatively sophisticated understanding of samples and populations. Implications for curricular treatment of statistics for gifted students are discussed.