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.

Tow Takes on the Critical

This important volume on the critical pedagogical approach addresses such topics as critical multiculturalism, gender and language learning, and popular culture. Critical pedagogies are instructional approaches aimed at transforming existing social relations in the interest of greater equity in schools and communities. This paperback edition on the pedagogical approach addresses such topics as critical multiculturalism, gender and language learning, and popular culture. Committed to language education that contributes to social justice - and the political, economic, and sociocultural changes such justice requires - the contributors explore the meaning of creating equitable and critical instructional practices, by exploring diverse representations of knowledge. In addition, recommendations are made for further research, teacher education, and critical testing. Graduate students and researchers in TESOL, applied linguistics, and education will find this volume a thought-provoking and comprehensive presentation of theory and practice in this important new area of scholarship.

Primary students' success on the structured number line

Number lines are part of our everyday life (e.g., thermometers, kitchen scales) and are frequently used in primary mathematics as instructional aids, in texts and for assessment purposes on mathematics tests. There are two major types of number lines; structured number lines, which are the focus of this paper, and empty number lines. Structured number lines represent mathematical information by the placement of marks on a horizontal or vertical line which has been marked into proportional segments (Figure 1). Empty number lines are blank lines which students can use for calculations (Figure 2) and are not discussed further here (see van den Heuvel-Panhuizen, 2008, on the role of empty number lines). In this article, we will focus on how students’ knowledge of the structured number line develops and how they become successful users of this mathematical tool.

Personalising teacher professional development : strategies enabling effective learning for educators of 21st century students

In the Knowledge Society, new demands are placed on teachers as they strive to empower young people to be global citizens, ready for the 21st century. Systemic shifts need to be made, however, to build capacity across the workforce to practise new ways of teaching and learning, including the personalisation of teacher professional development. This article argues new strategies and approaches for effective adult learning, including an individualised focus, context-based learning and an empowerment of teachers to develop their own personal learning networks. This article concludes with an analysis of the challenges facing professional development leaders in moving towards personalised teacher learning.

Preparing quality teachers : making learning visible

Teacher quality is recognised as a lynchpin for education reforms internationally, and both Federal and State governments in Australia have turned their attention to teacher education institutions: the starting point for preparing quality teachers. Changes to policy and shifts in expectations impact on Faculties of Education, despite the fact that little is known about what makes a quality teacher preparation program effective. New accountability measures, mandated Professional Standards, and proposals to test all graduates before registration, mean that teacher preparation programs need capacity for flexibility and responsiveness. The risk is that undergraduate degree programs can become ‘patchwork quilts’ with traces of the old and new stitched together, sometimes at the expense of coherence and integrity. This paper provides a roadmap used by one large Faculty of Education in Queensland for reforming and reconceptualising the curriculum for a 4-year undergraduate program, in response to new demands from government and the professional bodies.

Matching cognitive styles to computer-based instruction : an approach for enhanced learning in electrical engineering

An approach aimed at enhancing learning by matching individual students' preferred cognitive styles to computer-based instructional (CBI) material is presented. This approach was used in teaching some components of a third-year unit in an electrical engineering course at the Queensland University of Technology. Cognitive style characteristics of perceiving and processing information were considered. The bimodal nature of cognitive styles (analytic/imager, analytic/verbalizer, wholist/imager and wholist/verbalizer) was examined in order to assess the full ramification of cognitive styles on learning. In a quasi-experimental format, students' cognitive styles were analysed by cognitive style analysis (CSA) software. On the basis of the CSA results the system defaulted students to either matched or mismatched CBI material. The consistently better performance by the matched group suggests potential for further investigations where the limitations cited in this paper are eliminated. Analysing the differences between cognitive styles on individual test tasks also suggests that certain test tasks may better suit certain cognitive styles.

Cognitive processes and strategies employed by children to learn spatial representations

Children often have difficulties in learning spatial representations. This study investigated the effect of four different instructional formats on learning outcomes and strategies used when dealing with spatial tasks such as assembly procedures. It was hypothesised that instructional material that imposed least extraneous cognitive load would facilitate enhanced learning. Forty secondary students were presented with four types of instruction; orthographic drawing, isometric drawing, physical model and, isometric and physical model together. The findings provide evidence to suggest that working from physical models caused least extraneous cognitive load compared to the isometric and orthographic groups. The model group took less time, had more correctly completed models, required fewer extra looks, spent less time studying the instruction and made fewer errors. Problem decomposition, forward working and attending to information in the foreground of the graphical representation strategies were analysed.

Personalizing the design of computer-based instruction to enhance learning

This paper reports two studies designed to investigate the effect on learning outcomes of matching individuals' preferred cognitive styles to computer-based instructional (CBI) material. Study 1 considered the styles individually as Verbalizer, Imager, Wholist and Analytic. Study 2 considered the bi-dimensional nature of cognitive styles in order to assess the full ramification of cognitive styles on learning: Analytic/Imager, Analytic/ Verbalizer, Wholist/Imager and the Wholist/Verbalizer. The mix of images and text, the nature of the text material, use of advance organizers and proximity of information to facilitate meaningful connections between various pieces of information were some of the considerations in the design of the CBI material. In a quasi-experimental format, students' cognitive styles were analysed by Cognitive Style Analysis (CSA) software. On the basis of the CSA result, the system defaulted students to either matched or mismatched CBI material by alternating between the two formats. The instructional material had a learning and a test phase. Learning outcome was tested on recall, labelling, explanation and problem-solving tasks. Comparison of the matched and mismatched instruction did not indicate significant difference between the groups, but the consistently better performance by the matched group suggests potential for further investigations where the limitations cited in this paper are eliminated. The result did indicate a significant difference between the four cognitive styles with the Wholist/Verbalizer group performing better then all other cognitive styles. Analysing the difference between cognitive styles on individual test tasks indicated significant difference on recall, labelling and explanation, suggesting that certain test tasks may suit certain cognitive styles.

Focus of attention and its impact on movement behaviour

Investigations into the relative effectiveness of either focusing on movement form (internal focus) or movement effects (external focus) have tended to dominate research on instructional constraints. However, rather than adopting a comparative approach to determine which focus of attention is more effective, analysis of the relative efficacy of each specific instruction focus during motor learning could be more relevant for both researchers and practitioners. Theoretical advances in the motor learning literature from a nonlinear dynamics perspective might explain the processes that underlie the effect of different attentional focus instructions. Referencing ideas and concepts from a current motor learning model, differential effects of either internal or external focus of instructions are examined. This paper also highlights some deficiencies in extant theory and research design on focus of attention which require further investigations.

Test and evaluation system for multi-protocol sampled value protection schemes

Proposed transmission smart grids will use a digital platform for the automation of substations operating at voltage levels of 110 kV and above. The IEC 61850 series of standards, released in parts over the last ten years, provide a specification for substation communications networks and systems. These standards, along with IEEE Std 1588-2008 Precision Time Protocol version 2 (PTPv2) for precision timing, are recommended by the both IEC Smart Grid Strategy Group and the NIST Framework and Roadmap for Smart Grid Interoperability Standards for substation automation. IEC 61850-8-1 and IEC 61850-9-2 provide an inter-operable solution to support multi-vendor digital process bus solutions, allowing for the removal of potentially lethal voltages and damaging currents from substation control rooms, a reduction in the amount of cabling required in substations, and facilitates the adoption of non-conventional instrument transformers (NCITs). IEC 61850, PTPv2 and Ethernet are three complementary protocol families that together define the future of sampled value digital process connections for smart substation automation. This paper describes a specific test and evaluation system that uses real time simulation, protection relays, PTPv2 time clocks and artificial network impairment that is being used to investigate technical impediments to the adoption of SV process bus systems by transmission utilities. Knowing the limits of a digital process bus, especially when sampled values and NCITs are included, will enable utilities to make informed decisions regarding the adoption of this technology.

Leveraging R&D investment for the Australian built environment

This paper discusses a current research project building new understandings and knowledge relevant to R&D funding strategies in Australia. Building on a retrospective analysis of R&D trends and industry outcomes, an industry roadmap will be developed to inform R&D policies more attuned to future industry needs to improve research investment effectiveness. The project will also include analysis of research team formation and management (involving end users from public and private sectors together with research and knowledge institutions), and dissemination of outcomes and uptake in the Australian building and construction industry. The project will build on previous research extending open innovation system theory and network analysis and procurement, focused on R&D. Through the application of dynamic capabilities and strategic foresighting theory, an industry roadmap for future research investment will be developed, providing a stronger foundation for more targeted policy recommendations. This research will contribute to more effective construction processes in the future through more targeted research funding and more effective research partnerships between industry and researchers.

Leveraging R&D to advance digital modelling practice in Australian construction

This paper describes a lead project currently underway through Australia’s Sustainable Built Environment National Research Centre, evaluating impacts, diffusion mechanisms and uptake of R&D in the Australian building and construction industry. Building on a retrospective analysis of R&D trends and industry outcomes, a future-focused industry roadmap will be developed to inform R&D policies more attuned to future industry needs to improve investment effectiveness. In particular, this research will evaluate national R&D efforts to develop, test and implement advanced digital modelling technologies into the design/construction/asset management cycle. This research will build new understandings and knowledge relevant to R&D funding strategies, research team formation and management (with involvement from public and private sectors, and research and knowledge institutions), dissemination of outcomes and uptake. This is critical due to the disaggregated nature of the industry, intense competition, limited R&D investment; and new challenges (e.g. digital modelling, integrated project delivery, and the demand for packaged services). The evaluation of leading Australian and international efforts to integrate advanced digital modelling technologies into the design/construction/asset management cycle will be undertaken as one of three case studies. Employing the recently released Australian Guidelines for Digital Modelling developed with buildingSMART (International Alliance for Interoperability) and the Australian Institute of Architects, technical and business benefits across the supply chain will be highlighted as drivers for more integrated R&D efforts.

An investigation of the effect of individual cognitive preferences on learning through computer-based instruction

This paper reports a study investigating the effect of individual cognitive styles on learning through computer-based instruction. The study adopted a quasi-experimental design involving four groups which were presented with instructional material that either matched or mismatched with their preferred cognitive styles. Cognitive styles were measured by cognitive style assessment software (Riding, 1991). The instructional material was designed to cater for the four cognitive styles identified by Riding. Students' learning outcomes were measured by the time taken to perform test tasks and the number of marks scored. The results indicate no significant difference between the matched and mismatched groups on both time taken and scores on test tasks. However, there was significant difference between the four cognitive styles on test score. The Wholist/Verbaliser group performed better then all other groups. There was no significant difference between the other groups. An analysis of the performance on test task by each cognitive style showed significant difference between the groups on recall, labelling and explanation. Difference between the cognitive style groups did not reach significance level for problem-solving tasks. The findings of the study indicate a potential for cognitive style to influence learning outcomes measured by performance on test tasks.

Cognitive load and mental rotation : structuring orthographic projection for learning and problem solving

Cognitive load theory was used to generate a series of three experiments to investigate the effects of various worked example formats on learning orthographic projection. Experiments 1 and 2 investigated the benefits of presenting problems, conventional worked examples incorporating the final 2-D and 3-D representations only, and modified worked examples with several intermediate stages of rotation between the 2-D and 3-D representations. Modified worked examples proved superior to conventional worked examples without intermediate stages while conventional worked examples were, in turn, superior to problems. Experiment 3 investigated the consequences of varying the number and location of intermediate stages in the rotation trajectory and found three stages to be superior to one. A single intermediate stage was superior when nearer the 2-D than the 3-D end of the trajectory. It was concluded that (a) orthographic projection is learned best using worked examples with several intermediate stages and that (b) a linear relation between angle of rotation and problem difficulty did not hold for orthographic projection material. Cognitive load theory could be used to suggest the ideal location of the intermediate stages.