Learners' shifting perceptions of randomness.

Johnston-Wilder, Peter (2006). Learners' shifting perceptions of randomness. PhD thesis The Open University.

DOI: https://doi.org/10.21954/ou.ro.0000f66b

Abstract

This is a phenomenographic study of learners’ perceptions of randomness. Underpinning the study is a sense of randomness as a dynamic process, in which events emerge unpredictably from a generating process, into the determined past, through the curtain separating past from future. Previous research into perceptions of randomness has often used tasks in which people are asked to recognise randomness in a given sequence of outcomes. Other research has asked people to make up sequences of random outcomes. Such tasks do not carry the sense of randomness as dynamic.

Interview tasks in this study were designed to present the dynamic sense of randomness using outcomes from random generators such as dice, coins and sampling bags in situ. Interviewees were invited to talk about their experiences of making sense of the emerging sequence of outcomes.

The analysis of the interview transcripts addressed two related questions:

• What do learners believe about randomness?

• To what situations and circumstances do learners consider randomness to be an appropriate model?

The first question encompasses learners’ expectations of a random generator and the methods, strategies and heuristics by which learners discern what is random from what is not. Drawing on local and global meanings of randomness identified by Pratt (1998), the thesis argues that learners’ perspectives on randomness shift rapidly and frequently between the local and global as the learners seek to interpret the observed outcomes. Learners’ interpretations of and beliefs about randomness are found to have significant impact upon the kinds of situations to which learners are able and willing to apply the model of randomness.