Individual differences in learning from worked examples by senior secondary mathematics students

The primary purpose of this research was to examine individual differences in learning from worked examples. By integrating cognitive style theory and cognitive load theory, it was hypothesised that an interaction existed between individual cognitive style and the structure and presentation of worked examples in their effect upon subsequent student problem solving. In particular, it was hypothesised that Analytic-Verbalisers, Analytic-Imagers, and Wholist-lmagers would perform better on a posttest after learning from structured-pictorial worked examples than after learning from unstructured worked examples. For Analytic-Verbalisers it was reasoned that the cognitive effort required to impose structure on unstructured worked examples would hinder learning. Alternatively, it was expected that Wholist-Verbalisers would display superior performances after learning from unstructured worked examples than after learning from structured-pictorial worked examples. The images of the structured-pictorial format, incongruent with the Wholist-Verbaliser style, would be expected to split attention between the text and the diagrams. The information contained in the images would also be a source of redundancy and not easily ignored in the integrated structured-pictorial format. Despite a number of authors having emphasised the need to include individual differences as a fundamental component of problem solving within domainspecific subjects such as mathematics, few studies have attempted to investigate a relationship between mathematical or science instructional method, cognitive style, and problem solving. Cognitive style theory proposes that the structure and presentation of learning material is likely to affect each of the four cognitive styles differently. No study could be found which has used Riding's (1997) model of cognitive style as a framework for examining the interaction between the structural presentation of worked examples and an individual's cognitive style. 269 Year 12 Mathematics B students from five urban and rural secondary schools in Queensland, Australia participated in the main study. A factorial (three treatments by four cognitive styles) between-subjects multivariate analysis of variance indicated a statistically significant interaction. As the difficulty of the posttest components increased, the empirical evidence supporting the research hypotheses became more pronounced. The rigour of the study's theoretical framework was further tested by the construction of a measure of instructional efficiency, based on an index of cognitive load, and the construction of a measure of problem-solving efficiency, based on problem-solving time. The consistent empirical evidence within this study that learning from worked examples is affected by an interaction of cognitive style and the structure and presentation of the worked examples emphasises the need to consider individual differences among senior secondary mathematics students to enhance educational opportunities. Implications for teaching and learning are discussed and recommendations for further research are outlined.

Narrative on a doctoral narrative : reflections on postgraduate study and pedagogy

This paper explores the stages of one student’s intellectual journey through a Doctor of Philosophy program of study in an Australian university. It outlines the theoretical and methodological insights made as she came to understand that data was discourse, entailing a politics and position of power that ran contrary to the aims of the study that the student was undertaking in and on her own community. The article is a reflective narrative produced from the experience of having to come to terms with some of the personal and professional tensions and contradictions that postgraduate study can, and maybe should, engender if it is to be any of real value.

Integrating a sustainable academic career around scholarly learning and teaching activities

To be scholarly in learning and teaching is rigorous academic work. It demands: currency and command of both discipline subject matter and educational theory; inquiring, methodical, and reflective approaches; the collection, evaluation and documentation of evidence of learning and teaching efficacy; and, optimally, entails participation in and communication among a community of teaching professionals. This chapter examines the author’s own practice in this regard to explicate the ‘how’ and ‘why’ of scholarly and scholarship approaches, as much as the ‘what’ and ‘where’ of that endeavour. In doing so, this meta‐analysis is made ‘community property’, in the same way that Shulman (1993: 6) exhorted we ‘change the status of teaching from private to community property’ so that teaching might be more greatly valued in the academy.