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.

Risk analysis in aquaculture: A step-by-step introduction with worked examples

This publication is based on materials covered and outputs generated during the Workshop on Risk Assessment Methodologies and Tools for Aquaculture in Sub-Saharan Africa, which was jointly held by WorldFish and FAO in Siavonga, Zambia on 28 June - 2 July 2010. The workshop was delivered as a training exercise to 17 participants from seven sub-Saharan countries and was designed to highlight current methodologies and tools available for environmental risk analysis in aquaculture development. A key focus of the workshop was to encourage participants to consider hypothetical but realistic scenarios and to discuss issues relevant to evaluating the environmental risks of a given activity or scenario. This publication presents selected scenarios from the workshop and the outcomes of the deliberative process as developed by the participants. This publication is factual but not comprehensive, therefore any statements or estimations of risk do not represent the actual risks arising from the described scenario. It is intended to serve as an easily readable introduction to risk analysis, highlighting worked examples that will provide guidance on how a risk analysis may be approached in a similar situation.

Effects of worked examples and algebra problem -solving skill on error and cognitive load

This study determined the levels of algebra problem solving skill at which worked examples promoted learning of further problem solving skill and reduction of cognitive load in college developmental algebra students. Problem solving skill was objectively measured as error production; cognitive load was subjectively measured as perceived mental effort. ^ Sixty-three Ss were pretested, received homework of worked examples or mass problem solving, and posttested. Univarate ANCOVA (covariate = previous grade) were performed on the practice and posttest data. The factors used in the analysis were practice strategy (worked examples vs. mass problem solving) and algebra problem solving skill (low vs. moderate vs. high). Students in the practice phase who studied worked examples exhibited (a) fewer errors and reduced cognitive load, at moderate skill; (b) neither fewer errors nor reduced cognitive load, at low skill; and (c) only reduced cognitive load, at high skill. In the posttest, only cognitive load was reduced. ^ The results suggested that worked examples be emphasized for developmental students with moderate problem solving skill. Areas for further research were discussed. ^

Testing After Worked Example Study Does Not Enhance Delayed Problem-Solving Performance Compared to Restudy

Four experiments investigated whether the testing effect also applies to the acquisition of problem-solving skills from worked examples. Experiment 1 (n=120) showed no beneficial effects of testing consisting of isomorphic problem solving or example recall on final test performance, which consisted of isomorphic problem solving, compared to continued study of isomorphic examples. Experiment 2 (n=124) showed no beneficial effects of testing consisting of identical problem solving compared to restudying an identical example. Interestingly, participants who took both an immediate and a delayed final test outperformed those taking only a delayed test. This finding suggested that testing might become beneficial for retention but only after a certain level of schema acquisition has taken place through restudying several examples. However, experiment 2 had no control condition restudying examples instead of taking the immediate test. Experiment 3 (n=129) included such a restudy condition, and there was no evidence that testing after studying four examples was more effective for final delayed test performance than restudying, regardless of whether restudied/tested problems were isomorphic or identical. Experiment 4 (n=75) used a similar design as experiment 3 (i.e., testing/restudy after four examples), but with examples on a different topic and with a different participant population. Again, no evidence of a testing effect was found. Thus, across four experiments, with different types of initial tests, different problem-solving domains, and different participant populations, we found no evidence that testing enhanced delayed test performance compared to restudy. These findings suggest that the testing effect might not apply to acquiring problem-solving skills from worked examples

Difference-based meta-analytic procedures for between-participant and/or within-participant designs : a tutorial review for sports and exercise scientists

The aim of this paper is to provide a contemporary summary of statistical and non-statistical meta-analytic procedures that have relevance to the type of experimental designs often used by sport scientists when examining differences/change in dependent measure(s) as a result of one or more independent manipulation(s). Using worked examples from studies on observational learning in the motor behaviour literature, we adopt a random effects model and give a detailed explanation of the statistical procedures for the three types of raw score difference-based analyses applicable to between-participant, within-participant, and mixed-participant designs. Major merits and concerns associated with these quantitative procedures are identified and agreed methods are reported for minimizing biased outcomes, such as those for dealing with multiple dependent measures from single studies, design variation across studies, different metrics (i.e. raw scores and difference scores), and variations in sample size. To complement the worked examples, we summarize the general considerations required when conducting and reporting a meta-analysis, including how to deal with publication bias, what information to present regarding the primary studies, and approaches for dealing with outliers. By bringing together these statistical and non-statistical meta-analytic procedures, we provide the tools required to clarify understanding of key concepts and principles.

Using Ownership to Reason About Inherent Parallelism in Object-Oriented Programs

With the emergence of multi-cores into the mainstream, there is a growing need for systems to allow programmers and automated systems to reason about data dependencies and inherent parallelismin imperative object-oriented languages. In this paper we exploit the structure of object-oriented programs to abstract computational side-effects. We capture and validate these effects using a static type system. We use these as the basis of sufficient conditions for several different data and task parallelism patterns. We compliment our static type system with a lightweight runtime system to allow for parallelization in the presence of complex data flows. We have a functioning compiler and worked examples to demonstrate the practicality of our solution.

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.

Whole System Design : An Integrated Approach to Sustainable Engineering

Whole System Design is increasingly being seen as one of the most cost effective ways to both increase the productivity and reduce the negative environmental impacts of an engineered system. A focus on design is critical, as the output from this stage of the project locks-in most of the economic and environmental performance of the designed system throughout its life, which can span from a few years to many decades. Indeed, it is now widely acknowledged that all designers – particularly engineers, architects and industrial designers – need to be able to understand and implement a whole system design approach. This book provides a clear design methodology, based on leading efforts in the field, and is supported by worked examples that demonstrate how advances in energy, materials and water productivity can be achieved through applying an integrated approach to sustainable engineering. Chapters 1–5 outline the approach and explain how it can be implemented to enhance the established Systems Engineering framework. Chapters 6–10 demonstrate, through detailed worked examples, the application of the approach to industrial pumping systems, passenger vehicles, electronics and computer systems, temperature control of buildings, and domestic water systems.

Computational Intelligence and Feature Selection : Rough and Fuzzy Approaches

Computational Intelligence and Feature Selection provides a high level audience with both the background and fundamental ideas behind feature selection with an emphasis on those techniques based on rough and fuzzy sets, including their hybridizations. It introduces set theory, fuzzy set theory, rough set theory, and fuzzy-rough set theory, and illustrates the power and efficacy of the feature selections described through the use of real-world applications and worked examples. Program files implementing major algorithms covered, together with the necessary instructions and datasets, are available on the Web.

The spatial turn: geographical approaches in the history of science

Over the past decade or so a number of historians of science and historical geographers, alert to the situated nature of scientific knowledge production and reception and to the migratory patterns of science on the move, have called for more explicit treatment of the geographies of past scientific knowledge. Closely linked to work in the sociology of scientific knowledge and science studies and connected with a heightened interest in spatiality evident across the humanities and social sciences this ‹spatial turn’ has informed a wide-ranging body of work on the history of science. This discussion essay revisits some of the theoretical props supporting this turn to space and provides a number of worked examples from the history of the life sciences that demonstrate the different ways in which the spaces of science have been comprehended.

Theory and Practice of Aircraft Performance

Textbook introducing the fundamentals of aircraft performance using industry standards and examples: bridging the gap between academia and industry
•Provides an extensive and detailed treatment of all segments of mission profile and overall aircraft performance
•Considers operating costs, safety, environmental and related systems issues
•Includes worked examples relating to current aircraft (Learjet 45, Tucano Turboprop Trainer, Advanced Jet Trainer and Airbus A320 types of aircraft)
•Suitable as a textbook for aircraft performance courses

Separation Science and Technology - Theory

I have completed 80% of a teaching text book (text and graphics) on Separation Science and Technology - Theory. The book's content is what I've learned over many years of practice and teaching with an emphasis on clarifying and explaining the nuances within the theories associated with various practical approaches to chemical and biochemical separations.

The book is divided into self-contained Chapters with many worked examples and practice questions. It very much aligns with my teaching on CHM3005D, CHM2010, CHM2007 and is ideal for PMY8105 and the new proposed MSci in Analytical Chemistry Programme. The book brings together diverse material in single space and will be a valuable pedagogical resource for the teaching of this key discipline within QUB and elsewhere.

Probability and statistics: selected problems

Probability and Statistics—Selected Problems is a unique book for senior undergraduate and graduate students to fast review basic materials in Probability and Statistics. Descriptive statistics are presented first, and probability is reviewed secondly. Discrete and continuous distributions are presented. Sample and estimation with hypothesis testing are presented in the last two chapters. The solutions for proposed excises are listed for readers to references.