Developing mathematical proficiency

It has long been recognised that successful mathematical learning comprises much more than just knowledge of skills and procedures. For example, Skemp (1976) identified the advantages of teaching mathematics for what he referred to as “relational” rather than “Instrumental” understanding. More recently, Kilpatrick, Swafford and Findell (2001) proposed five “intertwining strands” of mathematical proficiency, namely Conceptual Understanding, Procedural Fluency, Strategic Competence, Adaptive Reasoning, and Productive Disposition. In Australia, the new Australian Curriculum: Mathematics (F–10), which will be implemented from 2013, has adapted and adopted the first four of these proficiency strands to emphasise the breadth of mathematical capabilities that students need to acquire through their study of the various content strands. This paper addresses the question of what types of classroom practice can provide opportunities for the development of these capabilities in elementary schools. It draws on data from a number of projects, as well as the literature, to provide illustrative examples. Finally, the paper argues that developing the full set of capabilities requires complex changes in teachers’ pedagogy.

Establishing quality online: supporting productive academic teams

Quality online education requires successful management of resources and services. This paper examines the increasing need to support productive academic teams and foster collaboration in developing a high quality online environment. The paper is based on a study into academic support services and collaboration at Deakin University. The provision of quality support was found to be increasingly challenging given the complexity of the online university environment. A number of recommendations arise out of the study including some practical changes to service, the need to commit to innovation, the importance of frameworks and standards as well as a range of broader cultural, organisational and political changes.

Turbulence and stratification in priest pot, a productive pond in a sheltered environment

Priest Pot is an example of the abundant ponds that, collectively, contribute crucially to species diversity. Despite extensive biological study, little has been reported about the physical framework that supports its ecological richness. This article elucidates the physical character of Priest Pot’s water column and thus that of similar water bodies. Vertical thermal microstructure profiles were recorded during summer 2003 and analyzed alongside concurrent meteorological data. During summer stratification, the thermal structure appeared to be dominated by surface heat fluxes. Surface wind stress, limited by sheltering vegetation, caused turbulent overturns once a surface mixed layer was present but appeared to contribute little to setting up the thermal structure. Variations in full-depth mean stratification occurred predominantly over seasonal and ∼5-day time scales, the passage of atmospheric pressure systems being posited as the cause of the latter. In the uppermost ∼0.5 m, where the stratification varied at subdaily time scales, turbulence was active (sensu Ivey and Imberger 1991) when this layer was mixed, with dissipation values ε ∼ 10⁻⁸ m² s⁻³ and vertical diffusivity K_Z = 10^₋₄ — 10_⁻⁶ m^₂ s⁻¹. Where the water column was stratified, turbulence was strongly damped by both buoyancy and viscosity, and K_Z was an order of magnitude smaller. Vertical transport in the mixed layer occurred via many small overturns (Thorpe scale r.m.s. and maximum values were typically 0.02 m and 0.10 m, respectively), and seston were fully mixed through the water column.

Productive on-line student support : developing a system for primary mathematics trainee teachers

This paper outlines the development project for the 'Productive on-line student support system', a student "self-help" system, at Deakin University. The aim of this project was to provide Deakin primary teacher education students with a web-based learning tool that allowed them to assess and diagnose their strengths and weaknesses in mathematics, and supports students in their mathematics learning, and in so doing produce mathematically competent graduates. This project was, like similar programs, a development of peer or cross-age tutoring common in primary and secondary schools. A grant under the Deakin University Strategic Teaching and Learning Grant Scheme enabled a staff team from the mathematics education group, to develop a sophisticated and well-designed system that catered for a wide range of student needs, provided useful feedback, and was engaging and easy to use. The under-pinning software for the system was WebCT, available to staff through the Deakin Studies On-line system, to which students are connected also. The 'Productive on-line student support system' enabled students to determine their own mathematical needs, and have these addressed whenever they wished, as often as they wished, and allowed self-monitoring of progress. An outline of the system and examples of the assessment materials will be presented.

Exploring optimistic and pessimistic attributions in depression-specific mood

Cognitive theories of depression include maladaptive thinking styles as depressive vulnerabilities. The hopelessness theory of depression (Abramson, Metalsky, & Alloy, 1989) particularly implicates stable and global attributions for negative events as influences upon depression. Positive event attributions are considered less influential, yet they have shown equal predictiveness to negative event attributions for depression-specific mood. Previous research has provided equivocal results largely because of cross-sectional design and modest psychometric properties of the measures. The present research aimed to: create a new instrument to measure optimistic and pessimistic attributions; test the relatedness of attributions for positive and negative events; and, clarify relationships of the scales with optimism and mood. Three studies were undertaken, all of which used structural equation modeling. Two cross-sectional studies, using 342 and 332 community participants respectively, developed and validated the Questionnaire of Explanatory Style (QES). A final longitudinal study with 250 community participants tested the predictive validity of the QES. Overall, six scales were developed, three of which were optimistic and three of which were negative. The scales were acceptable to community samples and had adequate psychometric properties. The optimistic scales were attributions for positive events and the negative scales were attributions for negative events rather than pessimistic scales. Cross-sectional results indicated that only one of the negative scales weakly directly predicted depression-specific mood, but all predicted general psychological distress. By contrast, the optimistic scales were more directly predictive of depression-specific mood, particularly the Positive Disposition scale. Longitudinal results indicated that two of the optimistic scales were the most important QES predictors of depression-specific mood two months later. The optimistic scale Positive Disposition appears most central to the prediction of both concurrent and subsequent depression-specific mood. The scale content represents explanations for positive events that are internal and stable characteristics. These may be construed as personal competencies to bring about positive outcomes. This scale is closely allied to measures of optimism. Findings affirm the importance of optimistic attributions to the understanding of depression-specific mood and provide a productive focus for therapeutic intervention and future research.

Are workers with a disability less productive or less understood? An empirical investigation from an entrepreneurial business planning perspective

This study investigated selected work-performance data of a large call centre using the entrepreneurial business planning paradigm as a theoretical framework and tested the hypothesis that levels of productivity would be different for each group between workers with a disability and workers without a disability. On five measures of productivity, no significant differences were discernible but on a sixth measure, length of employment, it was found that disability workers remained in employment significantly longer. These results strongly refute the ‘intuitive wisdom’ that workers with a disability are less productive. The results support a growing body of corporate experience and descriptive research indicating that workers with a disability perform as well as or better than their non-disability colleagues. Yet workers with a disability remain disproportionately under-employed. The key to translating the growing evidence of this research into higher levels of employment of workers with disabilities will depend upon employers adopting an entrepreneurial approach to the planning of human resource management.

Disposition pathways and pharmacokinetics of herbal medicines in humans

Pharmacokinetic studies have become an integral part of modern drug development, but these studies are not regulatory needs for herbal remedies. This paper updates our current knowledge on the disposition pathways and pharmacokinetic properties of commonly used herbal medicines in humans. To retrieve relevant data, the authors have searched through computer-based literatures by full text search in Medline (via Pubmed), ScienceDirect, Current Contents Connect (ISI), Cochrance Library, CINAHL (EBSCO), CrossRef Search and Embase (all from inception to May 2010). Many herbal compounds undergo Phase I and/or Phase II metabolism in vivo, with cytochrome P450s (CYPs) and uridine diphosphate glucuronosyltransferases (UGTs) playing a major role. Some herbal ingredients are substrates of P-glycoprotein (P-gp) which is highly expressed in the intestine, liver, brain and kidney. As such, the activities of these drug metabolizing enzymes and drug transporters are determining factors for the in vivo bioavailability, disposition and distribution of herbal remedies. There are increasing pharmacokinetic studies of herbal remedies, but these studies are mainly focused on a small number of herbal remedies including St John's wort, milk thistle, sculcap, curcumin, echinacea, ginseng, ginkgo, and ginger. The pharmacokinetic data of a small number of purified herbal ingredients, including anthocyanins, berberine, catechins, curcumin, lutein and quercetin, are available. For the majority of herbal remedies used in folk medicines, data on their disposition and biological fate in humans are lacking or in paucity. For a herbal medicine, the pharmacological effect is achieved when the bioactive agents or the metabolites reach and sustain proper levels at their sites of action. Both the dose levels and fates of active components in the body govern their target-site concentrations after administration of an herbal remedy. In this regard, a safe and optimal use of herbal medicines requires a full understanding of their pharmacokinetic profiles. To optimize the use of herbal remedies, further clinical studies to explore their biological fate including the disposition pathways and kinetics in the human body are certainly needed.

Productive pedagogies : is it an intelligible language for preservice teachers?

Australian teacher educators and teachers have become increasingly familiar with the notion of ‘Productive Pedagogies’, itself the product of longitudinal research on school reform recently undertaken in Queensland, Australia (Lingard et al., 2001a, , 2001b) . One of its strengths has been its efficacy for in-service teachers to use as a language to talk about their pedagogical work and hence a way of reclaiming some of the ground on what constitutes good teaching. In part, this can be attributed to the numerous observations of teachers’ classroom practice that informed the construction of Productive Pedagogies (PPs). That is, many teachers understand these as naming what ‘good’ teachers have always done. In this paper the value of PPs as a metalanguage for developing pre-service teachers’ knowledge and understanding of teaching is examined; whether PPs is a language that is intelligible for pre-service teachers without access to this prior teacher knowledge or whether its elements and dimensions merely constitute an isolated vocabulary. A case study of four pre-service teachers provides the context for this exploration and its empirical data. Drawing on their fieldwork observations of teaching practice, voiced in the language of PPs, the paper argues that PPs language is indeed useful in the development of pre-service teachers’ understanding of teaching, particularly in assisting them to name evidence of teachers’ recognition of and engagement with difference.

Identification and genetic determination of an early life risk disposition for depressive disorder : atypical stress-related behaviour in early childhood

Progress in psychiatric genetics has been slow despite evidence of high heritability for most mental disorders. We argue that greater use of early detectable intermediate traits (endophenotypes) with the highest likely aetiological significance to depression, rather than complex clinical phenotypes, would be advantageous. Longitudinal data from the Western Australian Pregnancy Cohort (Raine) Study were used to identify an early life behavioural endophenotype for atypical hypothalamic-pituitaryadrenocortical function in adolescence, a neurobiological indicator of anxiety and depression. A set of descriptors representing rigid and reactive behaviour at age 1 year discriminated those in the top 20% of the free salivary cortisol exposure at age 17 years. Genetic association analysis revealed a male-sensitive effect to variation in three specific single nucleotide polymorphisms within selected genes underpinning the overall stress response. Furthermore, support for a polygenic effect on stress-related behaviour in childhood is presented.

Clinical audit, guidelines and standards : a productive relation for managing clinical practices

This paper contributes to the knowledge about the process of standardisation within the domain of medicine. Standardisation has become an important form of governance and co-ordination, and there is limited empirical knowledge about its nature and consequences (Brunsson et al., 2000). This paper aims to explore the development, circulation and standardisation process of a specific clinical audit programme: the Scottish Hip Fracture Audit. This audit started as a local initiative and now has developed into a sophisticated arena (Sahlin-Andersson, 2000) which provides Scottish hospitals with monthly ‘real-time reports’ outlining their performance against Scottish government targets. The paper argues that the interrelation between clinical audit and evidence-based medicine (EBM) can become a ‘productive relation’ (Mykhalovskiy, 2003), that opens up spaces of intervention, in which the clinical communities engage with processes of change of clinical procedures, and in these spaces, clinicians and managers are in a position to refine clinical practice and service organisation, to reflect upon their own actions and to allow insight into the rationalities of their work (Berg, 1997).