Towards a model for the analysis and description of mathematical knowledge and understanding

Mathematics education literature has called for an abandonment of ontological and epistemological ideologies that have often divided theory-based practice. Instead, a consilience of theories has been sought which would leverage the strengths of each learning theory and so positively impact upon contemporary educational practice. This research activity is based upon Popper’s notion of three knowledge worlds which differentiates the knowledge shared in a community from the personal knowledge of the individual, and Bereiter’s characterisation of understanding as the individual’s relationship to tool-like knowledge. Using these notions, a re-conceptualisation of knowledge and understanding and a subsequent re-consideration of learning theories are proposed as a way to address the challenge set by literature. Referred to as the alternative theoretical framework, the proposed theory accounts for the scaffolded transformation of each individual’s unique understanding, whilst acknowledging the existence of a body of domain knowledge shared amongst participants in a scientific community of practice. The alternative theoretical framework is embodied within an operational model that is accompanied by a visual nomenclature with which to describe consensually developed shared knowledge and personal understanding. This research activity has sought to iteratively evaluate this proposed theory through the practical application of the operational model and visual nomenclature to the domain of early-number counting, addition and subtraction. This domain of mathematical knowledge has been comprehensively analysed and described. Through this process, the viability of the proposed theory as a tool with which to discuss and thus improve the knowledge and understanding with the domain of mathematics has been validated. Putting of the proposed theory into practice has lead to the theory’s refinement and the subsequent achievement of a solid theoretical base for the future development of educational tools to support teaching and learning practice, including computer-mediated learning environments. Such future activity, using the proposed theory, will advance contemporary mathematics educational practice by bringing together the strengths of cognitivist, constructivist and post-constructivist learning theories.

Minimising wave drag for free surface flow past a two-dimensional stern

Free surface flow past a two-dimensional semi-infinite curved plate is considered, with emphasis given to solving for the shape of the resulting wave train that appears downstream on the surface of the fluid. This flow configuration can be interpreted as applying near the stern of a wide blunt ship. For steady flow in a fluid of finite depth, we apply the Wiener-Hopf technique to solve a linearised problem, valid for small perturbations of the uniform stream. Weakly nonlinear results found using a forced KdV equation are also presented, as are numerical solutions to the fully nonlinear problem, computed using a conformal mapping and a boundary integral technique. By considering different families of shapes for the semi-infinite plate, it is shown how the amplitude of the waves can be minimised. For plates that increase in height as a function of the direction of flow, reach a local maximum, and then point slightly downwards at the point at which the free surface detaches, it appears the downstream wavetrain can be eliminated entirely.

Association between indoor air pollution measurements and respiratory health in women and children in Lao PDR

This article presents the results of a study on the association between measured air pollutants and the respiratory health of resident women and children in Lao PDR, one of the least developed countries in Southeast Asia. The study, commissioned by the World Health Organisation, included PM10, CO and NO2 measurements made inside 181 dwellings in nine districts within two provinces in Lao PDR over a 5- month period (12/05–04/06), and respiratory health information (via questionnaires and peak expiratory flow rate (PEFR) measurements) for all residents in the same dwellings. Adjusted odds ratios were calculated separately for each health outcome using binary logistic regression. There was a strong and consistent positive association between NO2 and CO for almost all questionnaire-based health outcomes for both women and children. Women in dwellings with higher measured NO2 had more than triple of the odds of almost all of the health outcomes, and higher concentrations of NO2 and CO were significantly associated with lower PEFR. This study supports a growing literature confirming the role of indoor air pollution in the burden of respiratory disease in developing countries. The results will directly support changes in health and housing policy in Lao PDR.

Correlations between designability and various structural characteristics of protein lattice models

Using six kinds of lattice types (4×4 ,5×5 , and6×6 square lattices;3×3×3 cubic lattice; and2+3+4+3+2 and4+5+6+5+4 triangular lattices), three different size alphabets (HP ,HNUP , and 20 letters), and two energy functions, the designability of proteinstructures is calculated based on random samplings of structures and common biased sampling (CBS) of proteinsequence space. Then three quantities stability (average energy gap),foldability, and partnum of the structure, which are defined to elucidate the designability, are calculated. The authors find that whatever the type of lattice, alphabet size, and energy function used, there will be an emergence of highly designable (preferred) structure. For all cases considered, the local interactions reduce degeneracy and make the designability higher. The designability is sensitive to the lattice type, alphabet size, energy function, and sampling method of the sequence space. Compared with the random sampling method, both the CBS and the Metropolis Monte Carlo sampling methods make the designability higher. The correlation coefficients between the designability, stability, and foldability are mostly larger than 0.5, which demonstrate that they have strong correlation relationship. But the correlation relationship between the designability and the partnum is not so strong because the partnum is independent of the energy. The results are useful in practical use of the designability principle, such as to predict the proteintertiary structure.

Near infrared optical materials from polymeric amorphous carbon synthesized by collisional plasma process

The synthesis of polymerlike amorphous carbon(a-C:H) thin-films by microwave excited collisional hydrocarbon plasma process is reported. Stable and highly aromatic a-C:H were obtained containing significant inclusions of poly(p-phenylene vinylene) (PPV). PPV confers universal optoelectronic properties to the synthesized material. That is a-C:H with tailor-made refractive index are capable of becoming absorption-free in visible (red)-near infrared wavelength range. Production of large aromatic hydrocarbon including phenyl clusters and/or particles is attributed to enhanced coagulation of elemental plasma species under collisional plasma conditions. Detailed structural and morphological changes that occur in a-C:H during the plasma synthesis are also described.

Reverse biased Pt/nanostructured MoO3/SiC Schottky diode based hydrogen gas sensors

Pt/nanostructured molybdenum oxide (MoO3) /SiC Schottky diode based gas sensors were fabricated for hydrogen (H2) gas sensing. Due to the enhanced performance, which is ascribed to the application of MoO3 nanostructures, these devices were used in reversed bias. MoO3 characterization by scanning electron microscopy showed morphology of randomly orientated nanoplatelets with thicknesses between 50 and 500 nm. An α-Β mixed phase crystallographic structure of MoO3 was characterized by x-ray diffraction. At 180 °C, 1.343 V voltage shift in the reverse I-V curve and a Pt/ MoO3 barrier height change of 20 meV were obtained after exposure to 1% H2 gas in synthetic air. © 2009 American Institute of Physics.