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>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
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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.
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机译：通过定性案例研究，该研究调查了三个四年级学习者数学学习倾向的性质。它进一步探讨了这些倾向在他们随时间参加课后数学俱乐部每周活动的背景下如何演变。这项研究具有特别重要的意义，它借鉴了Kilpatrick，Swafford和Findell（2001）和Carr＆Claxton（2002）的处置框架，并指出了可以有效地将这些框架整合在一起以提供更丰富的学习倾向图片的方式。 Kilpatrick，Swafford和Findell（2001）的数学熟练度框架涉及五个相互关联的环节，其中生产性配置为第五环节，并且研究不足（Graven，2012年）。这条线被定义为“倾向于在数学上看到意义，认为它既有用又有价值，相信学习数学的努力会有所收获，并且将自己视为数学的有效学习者和行为者”（Kilpatrick， Swafford和Findell，2001年，第131页）。 Carr＆Claxton（2002）同样认为学习倾向的重要性，并指出韧性，嬉戏性和机智作为三个关键指标的重要性。这项研究通过问卷调查和有关学生学习倾向的访谈数据，概述了三个案例研究学习者的发现。访谈向学习者询问了各种问题，例如，完成句子“ Maths is ...”，描述一个有效的数学学习者，并说出如果您不知道答案的话该怎么做。该工具最初是通过口头管理的，要求学习者写下答案（2012年5月），一年后，由俱乐部主持人作为面试（2013年5月）进行管理。虽然由于学习者在2012年（书面）和2013年（口头）回答的方式不同而存在比较的局限性，但回答在某些方面的变化性质在一定程度上表明了向倾向于越来越有生产力的倾向的转变的迹象。此外，研究还分析了五个月期间几个俱乐部会议的详细录像记录。研究结果提出了扩展性格框架的方法，并且学习者限制了性格，尤其是在跨时间的理性和机智方面。研究结果还表明，随着时间的推移，性格会发生变化，尤其是在看到稳定的努力获得回报的方面。
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