Theory and its role in mathematics education

The increased recognition of the theory in mathematics education is evident in numerous handbooks, journal articles, and other publications. For example, Silver and Herbst (2007) examined ―Theory in Mathematics Education Scholarship‖ in the Second Handbook of Research on Mathematics Teaching and Learning (Lester, 2007) while Cobb (2007) addressed ―Putting Philosophy to Work: Coping with Multiple Theoretical Perspectives‖ in the same handbook. And a central component of both the first and second editions of the Handbook of International Research in Mathematics Education (English, 2002; 2008) was ―advances in theory development.‖ Needless to say, the comprehensive second edition of the Handbook of Educational Psychology (Alexander & Winne, 2006) abounds with analyses of theoretical developments across a variety of disciplines and contexts. Numerous definitions of ―theory‖ appear in the literature (e.g., see Silver & Herbst, in Lester, 2007). It is not our intention to provide a ―one-size-fits-all‖ definition of theory per se as applied to our discipline; rather we consider multiple perspectives on theory and its many roles in improving the teaching and learning of mathematics in varied contexts.

Hydrogen-bonding in the structures of the hydrated proton-transfer compounds of isonipecotamide with the isomeric indole-2 and indole-3-carboxylic acids

The structures of two hydrated proton-transfer compounds of 4-piperidinecarboxamide (isonipecotamide) with the isomeric heteroaromatic carboxylic acids indole-2-carboxylic acid and indole-3-carboxylic acid, namely 4-carbamoylpiperidinium indole-2-carboxylate dihydrate (1) and 4-carbamoylpiperidinium indole-3-carboxylate hemihydrate (2) have been determined at 200 K. Crystals of both 1 and 2 are monoclinic, space groups P21/c and P2/c respectively with Z = 4 in cells having dimensions a = 10.6811(4), b = 12.2017(4), c = 12.5456(5) Å, β = 96.000(4)o (1) and a = 15.5140(4), b = 10.2908(3), c = 9.7047(3) Å, β = 97.060(3)o (2). Hydrogen-bonding in 1 involves a primary cyclic interaction involving complementary cation amide N-H…O(carboxyl) anion and anion hetero N-H…O(amide) cation hydrogen bonds [graph set R22(9)]. Secondary associations involving also the water molecules of solvation give a two-dimensional network structure which includes weak water O-H…π interactions. In the three-dimensional hydrogen-bonded structure of 2, there are classic centrosymmetric cyclic head-to-head hydrogen-bonded amide-amide interactions [graph set R22(8)] as well as lateral cyclic amide-O linked amide-amide extensions [graph set R24(8)]. The anions and the water molecule, which lies on a twofold rotation axis, are involved in secondary extensions.

Thomas Young’s investigations in gradient-index optics

Purpose: James Clerk Maxwell is usually recognized as being the first, in 1854, to consider using inhomogeneous media in optical systems. However, some fifty years earlier Thomas Young, stimulated by his interest in the optics of the eye and accommodation, had already modeled some applications of gradient-index optics. These applications included using an axial gradient to provide spherical aberration-free optics and a spherical gradient to describe the optics of the atmosphere and the eye lens. We evaluated Young’s contributions. Method: We attempted to derive Young’s equations for axial and spherical refractive index gradients. Raytracing was used to confirm accuracy of formula. Results: We did not confirm Young’s equation for the axial gradient to provide aberration-free optics, but derived a slightly different equation. We confirmed the correctness of his equations for deviation of rays in a spherical gradient index and for the focal length of a lens with a nucleus of fixed index surrounded by a cortex of reducing index towards the edge. Young claimed that the equation for focal length applied to a lens with part of the constant index nucleus of the sphere removed, such that the loss of focal length was a quarter of the thickness removed, but this is not strictly correct. Conclusion: Young’s theoretical work in gradient-index optics received no acknowledgement from either his contemporaries or later authors. While his model of the eye lens is not an accurate physiological description of the human lens, with the index reducing least quickly at the edge, it represented a bold attempt to approximate the characteristics of the lens. Thomas Young’s work deserves wider recognition.

Direct evaluation of IEC 61850-9-2 process bus network performance

This letter presents a technique to assess the overall network performance of sampled value process buses based on IEC 61850-9-2 using measurements from a single location in the network. The method is based upon the use of Ethernet cards with externally synchronized time stamping, and characteristics of the process bus protocol. The application and utility of the method is demonstrated by measuring latency introduced by Ethernet switches. Network latency can be measured from a single set of captures, rather than comparing source and destination captures. Absolute latency measures will greatly assist the design testing, commissioning and maintenance of these critical data networks.

The effect of Tai Chi on health related quality of life in people with elevated blood glucose or diabetes : a randomized controlled trial

Purpose The aim was to assess the effects of a Tai Chi based program on health related quality of life (HR-QOL) in people with elevated blood glucose or diabetes who were not on medication for glucose control. Method 41 participants were randomly allocated to either a Tai Chi intervention group (N = 20) or a usual medical care control group (N = 21). The Tai Chi group involved 3 x 1.5 hour supervised and group-based training sessions per week for 12 weeks. Indicators of HR-QOL were assessed by self-report survey immediately prior to and after the intervention. Results There were significant improvements in favour of the Tai Chi group for the SF36 subscales of physical functioning (mean difference = 5.46, 95% CI = 1.35-9.57, P < 0.05), role physical (mean difference = 18.60, 95% CI = 2.16-35.05, P < 0.05), bodily pain (mean difference = 9.88, 95%CI = 2.06-17.69, P < 0.05) and vitality (mean difference = 9.96, 95% CI = 0.77-19.15, P < 0.05). Conclusions The findings show that this Tai Chi program improved indicators of HR-QOL including physical functioning, role physical, bodily pain and vitality in people with elevated blood glucose or diabetes who were not on diabetes medication.

Shape-formed ceramic superconductors by slip-casting

In order to rigorously test emerging applications using prototypes and pilot designs, high temperature superconductor (HTS) materials must be fabricated into a variety of shapes in an economical manner. We have developed a simple, economical, ceramic slip-casting approach to form complex shaped monolithic HTS articles for which high bulk density has been achieved. The sintered articles exhibit good Meissner signal and consist of phase-pure HTSC phase. A low transport critical current density is observed and is explained on the basis of densification and grain growth. © 1995 The Metallurgical of Society of AIME.

First steps towards modeling a multi-scale Earth system

Recent advances in computational geodynamics are applied to explore the link between Earth’s heat, its chemistry and its mechanical behavior. Computational thermal-mechanical solutions are now allowing us to understand Earth patterns by solving the basic physics of heat transfer. This approach is currently used to solve basic convection patterns of terrestrial planets. Applying the same methodology to smaller scales delivers promising similarities between observed and predicted structures which are often the site of mineral deposits. The new approach involves a fully coupled solution to the energy, momentum and continuity equations of the system at all scales, allowing the prediction of fractures, shear zones and other typical geological patterns out of a randomly perturbed initial state. The results of this approach are linking a global geodynamic mechanical framework over regional-scale mineral deposits down to the underlying micro-scale processes. Ongoing work includes the challenge of incorporating chemistry into the formulation.

Ab initio studies of hydrogen desorption from low index magnesium hydride surface

The low index Magnesium hydride surfaces, MgH2(0 0 1) and MgH2(1 1 0), have been studied by ab intio Density Functional Theory (DFT) calculations. It was found that the MgH2(1 1 0) surface is more stable than MgH2(0 0 1) surface, which is in good agreement with the experimental observation. The H2 desorption barriers vary depending on the crystalline surfaces that are exposed and also the specific H atom sites involved – they are found to be generally high, due to the thermodynamic stability of the MgH2 system, and are larger for the MgH2(0 0 1) surface. The pathway for recombinative desorption of one in-plane and one bridging H atom from the MgH2(1 1 0) surface was found to be the lowest energy barrier amongst those computed (172 KJ/mol) and is in good agreement with the experimental estimates.

Complex Modelling in the Primary and Middle School Years : An Interdisciplinary Approach

The world’s increasing complexity, competitiveness, interconnectivity, and dependence on technology generate new challenges for nations and individuals that cannot be met by continuing education as usual. With the proliferation of complex systems have come new technologies for communication, collaboration, and conceptualisation. These technologies have led to signifi cant changes in the forms of mathematical and scientifi c thinking required beyond the classroom. Modelling, in its various forms, can develop and broaden students’ mathematical and scientific thinking beyond the standard curriculum. This chapter first considers future competencies in the mathematical sciences within an increasingly complex world. Consideration is then given to interdisciplinary problem solving and models and modelling, as one means of addressing these competencies. Illustrative case studies involving complex, interdisciplinary modelling activities in Years 1 and 7 are presented.

Metacognition in substance misuse

Metacognitive theory provides a novel conceptual framework to understand the development and maintenance of psychopathology. It emphasizes the importance of stored knowledge guiding the individual’s plan for coping with heightened cognitive-affective arousal. According to the metacognitive model individuals experience strong affective responses and engage in a process of metacognitive appraisal and initiation of coping responses in the pursuit of cognitive-affective self-regulation. This chapter outlines the details of this theoretical approach as applied to substance misuse and the metacognitive treatment components aimed at interrupting the selection of maladaptive coping responses.

Intra-arterial waveform analysis: a study of senior nurse knowledge in a general intensive care unit

The aim of this small-scale study was to assess what knowledge senior nurses within a general intensive care unit (GICU) had in relation to intra-arterial blood pressure (IABP) waveform analysis. Its core objective was: To assess what knowledge was held by the senior nursing team with regard to arterial waveform interpretation, arterial waveform morphology and the technical aspects associated with arterial waveform monitoring.

High-level expression of Rhodotorula gracilis d-amino acid oxidase in Pichia pastoris

By combining gene design and heterologous over-expression of Rhodotorula gracilis D-amino acid oxidase (RgDAO) in Pichia pastoris, enzyme production was enhanced by one order of magnitude compared to literature benchmarks, giving 350 kUnits/l of fed-batch bioreactor culture with a productivity of 3.1 kUnits/l h. P. pastoris cells permeabilized by freeze-drying and incubation in 2-propanol (10% v/v) produce a highly active (1.6 kUnits/g dry matter) and stable oxidase preparation. Critical bottlenecks in the development of an RgDAO catalyst for industrial applications have been eliminated.