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.

An improved modal strain energy method for damage assessment

The modal strain energy method, which depends on the vibration characteristics of the structure, has been reasonably successful in identifying and localising damage in the structure. However, existing strain energy methods require the first few modes to be measured to provide meaningful damage detection. Use of individual modes with existing strain energy methods may indicate false alarms or may not detect the damage at or near the nodal points. This paper proposes a new modal strain energy based damage index which can detect and localize the damage using any one of the modes measured and illustrates its application for beam structures. It becomes evident that the proposed strain energy based damage index also has potential for damage quantification.

Does the acid hydrolysis-incubation method measure meaningful soil organic carbon pools?

The literature was reviewed and analyzed to determine the feasibility of using a combination of acid hydrolysis and CO2-C release during long-term incubation to determine soil organic carbon (SOC) pool sizes and mean residence times (MRTs). Analysis of 1100 data points showed the SOC remaining after hydrolysis with 6 M HCI ranged from 30 to 80% of the total SOC depending on soil type, depth, texture, and management. Nonhydrolyzable carbon (NHC) in conventional till soils represented 48% of SOC; no-till averaged 56%, forest 55%, and grassland 56%. Carbon dates showed an average of 1200 yr greater MRT for the NHC fraction than total SOC. Longterm incubation, involving measurement of CO2 evolution and curve fitting, measured active and slow pools. Active-pool C comprised 2 to 8% of the SOC with MRTs of days to months; the slow pool comprised 45 to 65% of the SOC and had MRTs of 10 to 80 yr. Comparison of field C-14 and (13) C data with hydrolysis-incubation data showed a high correlation between independent techniques across soil types and experiments. There were large differences in MRTs depending on the length of the experiment. Insertion of hydrolysis-incubation derived estimates of active (C-a), slow (C-s), and resistant Pools (C-r) into the DAYCENT model provided estimates of daily field CO2 evolution rates. These were well correlated with field CO2 measurements. Although not without some interpretation problems, acid hydrolysis-laboratory incubation is useful for determining SOC pools and fluxes especially when used in combination with associated measurements.

Deriving grassland management factors for a carbon accounting method developed by the intergovernmental panel on climate change

Grassland management affects soil organic carbon (SOC) storage and can be used to mitigate greenhouse gas emissions. However, for a country to assess emission reductions due to grassland management, there must be an inventory method for estimating the change in SOC storage. The Intergovernmental Panel on Climate Change (IPCC) has developed a simple carbon accounting approach for this purpose, and here we derive new grassland management factors that represent the effect of changing management on carbon storage for this method. Our literature search identified 49 studies dealing with effects of management practices that either degraded or improved conditions relative to nominally managed grasslands. On average, degradation reduced SOC storage to 95% +/- 0.06 and 97% +/- 0.05 of carbon stored under nominal conditions in temperate and tropical regions, respectively. In contrast, improving grasslands with a single management activity enhanced SOC storage by 14% 0.06 and 17% +/- 0.05 in temperate and tropical regions, respectively, and with an additional improvement(s), storage increased by another 11% +/- 0.04. We applied the newly derived factor coefficients to analyze C sequestration potential for managed grasslands in the U.S., and found that over a 20-year period changing management could sequester from 5 to 142 Tg C yr(-1) or 0.1 to 0.9 Mg C ha(-1) yr(-1), depending on the level of change. This analysis provides revised factor coefficients for the IPCC method that can be used to estimate impacts of management; it also provides a methodological framework for countries to derive factor coefficients specific to conditions in their region.

Stability and convergence of an effective numerical method for the time-space fractional Fokker-Planck equation with a nonlinear source term

Fractional Fokker-Planck equations (FFPEs) have gained much interest recently for describing transport dynamics in complex systems that are governed by anomalous diffusion and nonexponential relaxation patterns. However, effective numerical methods and analytic techniques for the FFPE are still in their embryonic state. In this paper, we consider a class of time-space fractional Fokker-Planck equations with a nonlinear source term (TSFFPE-NST), which involve the Caputo time fractional derivative (CTFD) of order α ∈ (0, 1) and the symmetric Riesz space fractional derivative (RSFD) of order μ ∈ (1, 2). Approximating the CTFD and RSFD using the L1-algorithm and shifted Grunwald method, respectively, a computationally effective numerical method is presented to solve the TSFFPE-NST. The stability and convergence of the proposed numerical method are investigated. Finally, numerical experiments are carried out to support the theoretical claims.

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.

Towards a method of constructing self-efficacy narratives.

This paper outlines a method of constructing narratives about an individual’s self-efficacy. Self-efficacy is defined as “people’s judgments of their capabilities to organise and execute courses of action required to attain designated types of performances” (Bandura, 1986, p. 391), and as such represents a useful construct for thinking about personal agency. Social cognitive theory provides the theoretical framework for understanding the sources of self-efficacy, that is, the elements that contribute to a sense of self-efficacy. The narrative approach adopted offers an alternative to traditional, positivist psychology, characterised by a preoccupation with measuring psychological constructs (like self-efficacy) by means of questionnaires and scales. It is argued that these instruments yield scores which are somewhat removed from the lived experience of the person—respondent or subject—associated with the score. The method involves a cyclical and iterative process using qualitative interviews to collect data from participants – four mature aged university students. The method builds on a three-interview procedure designed for life history research (Dolbeare & Schuman, cited in Seidman, 1998). This is achieved by introducing reflective homework tasks, as well as written data generated by research participants, as they are guided in reflecting on those experiences (including behaviours, cognitions and emotions) that constitute a sense of self-efficacy, in narrative and by narrative. The method illustrates how narrative analysis is used “to produce stories as the outcome of the research” (Polkinghorne, 1995, p.15), with detail and depth contributing to an appreciation of the ‘lived experience’ of the participants. The method is highly collaborative, with narratives co-constructed by researcher and research participants. The research outcomes suggest an enhanced understanding of self-efficacy contributes to motivation, application of effort and persistence in overcoming difficulties. The paper concludes with an evaluation of the research process by the students who participated in the author’s doctoral study.

A new method to quantify the application thickness of sunscreen on skin

Proper application of sunscreen is essential as an effective public health strategy for skin cancer prevention. Insufficient application is common among sunbathers, results in decreased sun protection and may therefore lead to increased UV damage of the skin. However, no objective measure of sunscreen application thickness (SAT) is currently available for field-based use. We present a method to detect SAT on human skin for determining the amount of sunscreen applied and thus enabling comparisons to manufacturer recommendations. Using a skin swabbing method and subsequent spectrophotometric analysis, we were able to determine SAT on human skin. A swabbing method was used to derive SAT on skin (in mg sunscreen per cm2 of skin area) through the concentration–absorption relationship of sunscreen determined in laboratory experiments. Analysis differentiated SATs between 0.25 and 4 mg cm−2 and showed a small but significant decrease in concentration over time postapplication. A field study was performed, in which the heterogeneity of sunscreen application could be investigated. The proposed method is a low cost, noninvasive method for the determination of SAT on skin and it can be used as a valid tool in field- and population-based studies.