An investigation into the nature of grade 4 learners’ evolving mathematics learning dispositions : a case study of 3 learners participating in an after school mathematics club

Through a qualitative case study approach this research investigated the nature of three Grade 4 learners’ mathematical learning dispositions. It further explored how these dispositions evolve within the context of their participation in a weekly after school mathematics club over time. Of particular significance the research drew on the dispositional frameworks of Kilpatrick, Swafford and Findell’s (2001) and Carr & Claxton (2002) and pointed to ways in which these framework can be usefully brought together to provide a richer picture of learning dispositions. Kilpatrick, Swafford and Findell’s (2001) framework of mathematical proficiency involves five interrelated strands of which productive disposition is the fifth strand and largely underresearched (Graven, 2012). This strand is defined as ‘the tendency to see sense in mathematics, to perceive it as both useful and worthwhile, to believe that steady effort in learning mathematics pays off, and to see oneself as an effective learner and doer of mathematics’ (Kilpatrick, Swafford and Findell, 2001, p. 131). Carr & Claxton (2002) similarly argue for the importance of learning dispositions and point to the importance of resilience, playfulness and resourcefulness as three key indicators. The research outlines findings of the three case study learners in terms of data obtained from a questionnaire and interview about students’ learning dispositions. The interview asked learners various questions including for example, complete the sentence ‘Maths is…’, describe an effective learner of mathematics and say what you do if you don’t know an answer. The instrument was first administered orally and learners were asked to write their answers (in May 2012) and a year later it was administered as an interview by the club facilitator (in May 2013). While there is the limitation of comparison due to the different ways in which learners responded in 2012 (written) and 2013 (oral) the shifting nature of responses in certain respects provides some indication of shifts towards increasingly productive dispositions. Additionally the research analysed detailed transcripts of video recordings of several club sessions over a five-month period. Findings suggest ways of extending dispositional frameworks and that learners have restricted dispositions particularly in terms of sense making and resourcefulness across time. The findings also suggest shifts in dispositions over time especially in terms of seeing steady effort as paying off