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.

After the marketplace: evidence, social science and educational research

This paper is an essay on the state of Australian education that frames new directions for educational research. It outlines three challenges faced by Australian educators: highly spatialised poverty with particularly strong mediating effects on primary school education; the need for intellectual and critical depth in pedagogy, with a focus in the upper primary and middle years; and the need to reinvent senior schooling to address emergent pathways from school to work and civic life. It offers a narrative description of the dynamics of policy making in Australia and North America and argues for an evidence-based approach to social and educational policy – but one quite unlike current test and market-based approaches. Instead, it argues for a multidisciplinary approach to a broad range of empirical and case-based evidence that subjects these to critical, hermeneutic social sciences. Such an approach would join educational policy with educational research, and broader social, community and governmental action with the aim of reorganising and redistributing material, cultural and social resources.

Beyond a battery hen model? : a computer laboratory, micropolitics and educational change

This paper investigates what happened in one Australian primary school as part of the establishment, use and development of a computer laboratory over a period of two years. As part of a school renewal project, the computer lab was introduced as an ‘innovative’ way to improve the skills of teachers and children in information and communication technologies (ICT) and to lead to curriculum change. However, the way in which the lab was conceptualised and used worked against achieving these goals. The micropolitics of educational change and an input-output understanding of computers meant that change remained structural rather pedagogical or philosophical.