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.

A novel winding structure in planar inductors to decrease the overall capacitive couplings

This paper presents a new method for winding configuration in planar magnetic elements with more than two layers. It has been proven by 3D Finite Element method and mathematical modeling that this suggested configuration results in reduction of the equivalent capacitive coupling in the planar inductor

What do IPAQ questions mean to older adults? Lessons from cognitive interviews

Background Most questionnaires used for physical activity (PA) surveillance have been developed for adults aged ≤65 years. Given the health benefits of PA for older adults and the aging of the population, it is important to include adults aged 65+ years in PA surveillance. However, few studies have examined how well older adults understand PA surveillance questionnaires. This study aimed to document older adults’ understanding of questions from the International PA Questionnaire (IPAQ), which is used worldwide for PA surveillance. Methods Participants were 41 community-dwelling adults aged 65-89 years. They each completed IPAQ in a face-to-face semi-structured interview, using the “think-aloud” method, in which they expressed their thoughts out loud as they answered IPAQ questions. Interviews were transcribed and coded according to a three-stage model: understanding the intent of the question; performing the primary task (conducting the mental operations required to formulate a response); and response formatting (mapping the response into pre-specified response options). Results Most difficulties occurred during the understanding and performing the primary task stages. Errors included recalling PA in an “average” week, not in the previous 7 days; including PA lasting ≤10 minutes/session; reporting the same PA twice or thrice; and including the total time of an activity for which only a part of that time was at the intensity specified in the question. Participants were unclear what activities fitted within a question’s scope and used a variety of strategies for determining the frequency and duration of their activities. Participants experienced more difficulties with the moderate-intensity PA and walking questions than with the vigorous-intensity PA questions. The sitting time question, particularly difficult for many participants, required the use of an answer strategy different from that used to answer questions about PA. Conclusions These findings indicate a need for caution in administering IPAQ to adults aged ≥65 years. Most errors resulted in over-reporting, although errors resulting in under-reporting were also noted. Given the nature of the errors made by participants, it is possible that similar errors occur when IPAQ is used in younger populations and that the errors identified could be minimized with small modifications to IPAQ.

Controller structure and design of firing angle controllers for (unit connected) HVDC systems

This paper investigates the control of a HVDC link, fed from an AC source through a controlled rectifier and feeding an AC line through a controlled inverter. The overall objective is to maintain maximum possible link voltage at the inverter while regulating the link current. In this paper the practical feedback design issues are investigated with a view of obtaining simple, robust designs that are easy to evaluate for safety and operability. The investigations are applicable to back-to-back links used for frequency decoupling and to long DC lines. The design issues discussed include: (i) a review of overall system dynamics to establish the time scale of different feedback loops and to highlight feedback design issues; (ii) the concept of using the inverter firing angle control to regulate link current when the rectifier firing angle controller saturates; and (iii) the design issues for the individual controllers including robust design for varying line conditions and the trade-off between controller complexity and the reduction of nonlinearity and disturbance effects