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.

Personal Epistemologies and Teaching

Over the last three decades, a growing body of research related to epistemic beliefs has been identified as a crucial for understanding teaching and learning (Yadav, Herron, & Samarapungavan, 2011). In particular, research related to beliefs about teaching, learning and knowledge has been considered important for understanding why teachers engage in certain approaches to pedagogy, curriculum and assessment in classrooms (Stromlo & Bråten, 2011). The beliefs held by teachers about knowledge and knowing, otherwise known as personal epistemology (Hofer, 2010), have been shown to influence other knowledge and beliefs (Schommer-Aikens, 2004). Five and Buehl (2012) indicated that because an individual’s understanding of reality is always seen through the lens of existing beliefs, the role of beliefs as a filter is particularly relevant in the context of teacher education. That is, if beliefs influence how individuals interpret new information and experiences, preservice and practicing teachers’ beliefs shape what and how they learn about teaching.” (p. 470-480). It is likely that such beliefs have an important relationship with teacher knowledge and practices...

Diversity in the Early Years: Intercultural Learning and Teaching

"New global contexts are presenting new challenges and new possibilities for young children and those around them. Climate change, armed conflict and poverty combine with new frontiers of discovery in science and technology to create a paradoxical picture of both threat and opportunity for our world and our children. On the one hand, children are experiencing unprecedented patterns of disparity and inequity; yet, on the other hand, they have seemingly limitless possibilities to engage with new technologies and social processes. Seismic shifts such as these are inviting new questions about the conditions that young children need to learn and thrive. Diversity in the Early Years: Intercultural Learning and Teaching explores significant aspects of working with children and adults from diverse backgrounds. It is a valuable resource for teaching early childhood pre-service teachers to raise awareness about issues of diversity - whether diversity of culture, language, education and/or gender - and for helping them to develop their own pedagogical approaches to working with diverse populations."--Publisher website