Surveying theories and philosophies of mathematics education

Any theory of thinking or teaching or learning rests on an underlying philosophy of knowledge. Mathematics education is situated at the nexus of two fields of inquiry, namely mathematics and education. However, numerous other disciplines interact with these two fields which compound the complexity of developing theories that define mathematics education. We first address the issue of clarifying a philosophy of mathematics education before attempting to answer whether theories of mathematics education are constructible? In doing so we draw on the foundational writings of Lincoln and Guba (1994), in which they clearly posit that any discipline within education, in our case mathematics education, needs to clarify for itself the following questions: (1) What is reality? Or what is the nature of the world around us? (2) How do we go about knowing the world around us? [the methodological question, which presents possibilities to various disciplines to develop methodological paradigms] and, (3) How can we be certain in the “truth” of what we know? [the epistemological question]

The effect of monocular and binocular cataract blur on postural stability among older adults

Purpose: First-eye cataract surgery can reduce the rate of falls among older adults, yet the effect of second-eye surgery on the rate of falling remains unclear. The present study investigated the effect of monocular and binocular simulated cataract blur on postural stability among older adults. Methods: Postural stability was assessed on 34 healthy older adults (mean 68.2 years, SD 3.5) with normal vision, using a portable force platform (BT4, HUR Labs, Finland) which collected data on centre of pressure (COP) displacement. Stability was assessed on firm and foam surfaces under four binocular viewing conditions using Vistech filters to simulate cataract blur: [1] best-corrected vision both eyes; [2] blur over non-dominant eye, [3] blur over dominant eye and [4] blur over both eyes. Binocular logMAR visual acuity, Pelli-Robson contrast sensitivity and stereoacuity were also measured under these viewing conditions and ocular dominance measured using the hole-in-card test. Generalized estimating equations with an exchangeable correlation structure examined the effect of the surface and vision conditions on postural stability. Results: Visual acuity and contrast sensitivity were significantly reduced under monocular and binocular cataract blur compared to normal viewing. All blur conditions resulted in loss of stereoacuity. Binocular cataract blur significantly reduced postural stability compared to normal vision on the firm (COP path length; p=0.013) and foam surface (anterior-posterior COP RMS, COP path length and COP area; p<0.01). However, no significant differences in postural stability were found between the monocular blur conditions compared to normal vision, or between the dominant and non-dominant monocular blur conditions on either the firm or foam surfaces. Conclusions: Findings indicate that binocular blur significantly impairs postural stability, and suggests that improvements in postural stability may justify first-eye cataract surgery, particularly during somatosensory disruption. Postural stability was not significantly impaired in the monocular cataract blur conditions compared to the normal vision condition, nor was there any effect of ocular dominance on postural stability in the presence of monocular cataract blur.

Modeling corneal surfaces with three-dimensional basis functions

Purpose: To ascertain the effectiveness of object-centered three-dimensional representations for the modeling of corneal surfaces. Methods: Three-dimensional (3D) surface decomposition into series of basis functions including: (i) spherical harmonics, (ii) hemispherical harmonics, and (iii) 3D Zernike polynomials were considered and compared to the traditional viewer-centered representation of two-dimensional (2D) Zernike polynomial expansion for a range of retrospective videokeratoscopic height data from three clinical groups. The data were collected using the Medmont E300 videokeratoscope. The groups included 10 normal corneas with corneal astigmatism less than −0.75 D, 10 astigmatic corneas with corneal astigmatism between −1.07 D and 3.34 D (Mean = −1.83 D, SD = ±0.75 D), and 10 keratoconic corneas. Only data from the right eyes of the subjects were considered. Results: All object-centered decompositions led to significantly better fits to corneal surfaces (in terms of the RMS error values) than the corresponding 2D Zernike polynomial expansions with the same number of coefficients, for all considered corneal surfaces, corneal diameters (2, 4, 6, and 8 mm), and model orders (4th to 10th radial orders) The best results (smallest RMS fit error) were obtained with spherical harmonics decomposition which lead to about 22% reduction in the RMS fit error, as compared to the traditional 2D Zernike polynomials. Hemispherical harmonics and the 3D Zernike polynomials reduced the RMS fit error by about 15% and 12%, respectively. Larger reduction in RMS fit error was achieved for smaller corneral diameters and lower order fits. Conclusions: Object-centered 3D decompositions provide viable alternatives to traditional viewer-centered 2D Zernike polynomial expansion of a corneal surface. They achieve better fits to videokeratoscopic height data and could be particularly suited to the analysis of multiple corneal measurements, where there can be slight variations in the position of the cornea from one map acquisition to the next.

Synthesis and modifications of metal oxide nanostructures and their applications

Transition metal oxides are functional materials that have advanced applications in many areas, because of their diverse properties (optical, electrical, magnetic, etc.), hardness, thermal stability and chemical resistance. Novel applications of the nanostructures of these oxides are attracting significant interest as new synthesis methods are developed and new structures are reported. Hydrothermal synthesis is an effective process to prepare various delicate structures of metal oxides on the scales from a few to tens of nanometres, specifically, the highly dispersed intermediate structures which are hardly obtained through pyro-synthesis. In this thesis, a range of new metal oxide (stable and metastable titanate, niobate) nanostructures, namely nanotubes and nanofibres, were synthesised via a hydrothermal process. Further structure modifications were conducted and potential applications in catalysis, photocatalysis, adsorption and construction of ceramic membrane were studied. The morphology evolution during the hydrothermal reaction between Nb2O5 particles and concentrated NaOH was monitored. The study demonstrates that by optimising the reaction parameters (temperature, amount of reactants), one can obtain a variety of nanostructured solids, from intermediate phases niobate bars and fibres to the stable phase cubes. Trititanate (Na2Ti3O7) nanofibres and nanotubes were obtained by the hydrothermal reaction between TiO2 powders or a titanium compound (e.g. TiOSO4·xH2O) and concentrated NaOH solution by controlling the reaction temperature and NaOH concentration. The trititanate possesses a layered structure, and the Na ions that exist between the negative charged titanate layers are exchangeable with other metal ions or H+ ions. The ion-exchange has crucial influence on the phase transition of the exchanged products. The exchange of the sodium ions in the titanate with H+ ions yields protonated titanate (H-titanate) and subsequent phase transformation of the H-titanate enable various TiO2 structures with retained morphology. H-titanate, either nanofibres or tubes, can be converted to pure TiO2(B), pure anatase, mixed TiO2(B) and anatase phases by controlled calcination and by a two-step process of acid-treatment and subsequent calcination. While the controlled calcination of the sodium titanate yield new titanate structures (metastable titanate with formula Na1.5H0.5Ti3O7, with retained fibril morphology) that can be used for removal of radioactive ions and heavy metal ions from water. The structures and morphologies of the metal oxides were characterised by advanced techniques. Titania nanofibres of mixed anatase and TiO2(B) phases, pure anatase and pure TiO2(B) were obtained by calcining H-titanate nanofibres at different temperatures between 300 and 700 °C. The fibril morphology was retained after calcination, which is suitable for transmission electron microscopy (TEM) analysis. It has been found by TEM analysis that in mixed-phase structure the interfaces between anatase and TiO2(B) phases are not random contacts between the engaged crystals of the two phases, but form from the well matched lattice planes of the two phases. For instance, (101) planes in anatase and (101) planes of TiO2(B) are similar in d spaces (~0.18 nm), and they join together to form a stable interface. The interfaces between the two phases act as an one-way valve that permit the transfer of photogenerated charge from anatase to TiO2(B). This reduces the recombination of photogenerated electrons and holes in anatase, enhancing the activity for photocatalytic oxidation. Therefore, the mixed-phase nanofibres exhibited higher photocatalytic activity for degradation of sulforhodamine B (SRB) dye under ultraviolet (UV) light than the nanofibres of either pure phase alone, or the mechanical mixtures (which have no interfaces) of the two pure phase nanofibres with a similar phase composition. This verifies the theory that the difference between the conduction band edges of the two phases may result in charge transfer from one phase to the other, which results in effectively the photogenerated charge separation and thus facilitates the redox reaction involving these charges. Such an interface structure facilitates charge transfer crossing the interfaces. The knowledge acquired in this study is important not only for design of efficient TiO2 photocatalysts but also for understanding the photocatalysis process. Moreover, the fibril titania photocatalysts are of great advantage when they are separated from a liquid for reuse by filtration, sedimentation, or centrifugation, compared to nanoparticles of the same scale. The surface structure of TiO2 also plays a significant role in catalysis and photocatalysis. Four types of large surface area TiO2 nanotubes with different phase compositions (labelled as NTA, NTBA, NTMA and NTM) were synthesised from calcination and acid treatment of the H-titanate nanotubes. Using the in situ FTIR emission spectrescopy (IES), desorption and re-adsorption process of surface OH-groups on oxide surface can be trailed. In this work, the surface OH-group regeneration ability of the TiO2 nanotubes was investigated. The ability of the four samples distinctively different, having the order: NTA > NTBA > NTMA > NTM. The same order was observed for the catalytic when the samples served as photocatalysts for the decomposition of synthetic dye SRB under UV light, as the supports of gold (Au) catalysts (where gold particles were loaded by a colloid-based method) for photodecomposition of formaldehyde under visible light and for catalytic oxidation of CO at low temperatures. Therefore, the ability of TiO2 nanotubes to generate surface OH-groups is an indicator of the catalytic activity. The reason behind the correlation is that the oxygen vacancies at bridging O2- sites of TiO2 surface can generate surface OH-groups and these groups facilitate adsorption and activation of O2 molecules, which is the key step of the oxidation reactions. The structure of the oxygen vacancies at bridging O2- sites is proposed. Also a new mechanism for the photocatalytic formaldehyde decomposition with the Au-TiO2 catalysts is proposed: The visible light absorbed by the gold nanoparticles, due to surface plasmon resonance effect, induces transition of the 6sp electrons of gold to high energy levels. These energetic electrons can migrate to the conduction band of TiO2 and are seized by oxygen molecules. Meanwhile, the gold nanoparticles capture electrons from the formaldehyde molecules adsorbed on them because of gold’s high electronegativity. O2 adsorbed on the TiO2 supports surface are the major electron acceptor. The more O2 adsorbed, the higher the oxidation activity of the photocatalyst will exhibit. The last part of this thesis demonstrates two innovative applications of the titanate nanostructures. Firstly, trititanate and metastable titanate (Na1.5H0.5Ti3O7) nanofibres are used as intelligent absorbents for removal of radioactive cations and heavy metal ions, utilizing the properties of the ion exchange ability, deformable layered structure, and fibril morphology. Environmental contamination with radioactive ions and heavy metal ions can cause a serious threat to the health of a large part of the population. Treatment of the wastes is needed to produce a waste product suitable for long-term storage and disposal. The ion-exchange ability of layered titanate structure permitted adsorption of bivalence toxic cations (Sr2+, Ra2+, Pb2+) from aqueous solution. More importantly, the adsorption is irreversible, due to the deformation of the structure induced by the strong interaction between the adsorbed bivalent cations and negatively charged TiO6 octahedra, and results in permanent entrapment of the toxic bivalent cations in the fibres so that the toxic ions can be safely deposited. Compared to conventional clay and zeolite sorbents, the fibril absorbents are of great advantage as they can be readily dispersed into and separated from a liquid. Secondly, new generation membranes were constructed by using large titanate and small ã-alumina nanofibres as intermediate and top layers, respectively, on a porous alumina substrate via a spin-coating process. Compared to conventional ceramic membranes constructed by spherical particles, the ceramic membrane constructed by the fibres permits high flux because of the large porosity of their separation layers. The voids in the separation layer determine the selectivity and flux of a separation membrane. When the sizes of the voids are similar (which means a similar selectivity of the separation layer), the flux passing through the membrane increases with the volume of the voids which are filtration passages. For the ideal and simplest texture, a mesh constructed with the nanofibres 10 nm thick and having a uniform pore size of 60 nm, the porosity is greater than 73.5 %. In contrast, the porosity of the separation layer that possesses the same pore size but is constructed with metal oxide spherical particles, as in conventional ceramic membranes, is 36% or less. The membrane constructed by titanate nanofibres and a layer of randomly oriented alumina nanofibres was able to filter out 96.8% of latex spheres of 60 nm size, while maintaining a high flux rate between 600 and 900 Lm–2 h–1, more than 15 times higher than the conventional membrane reported in the most recent study.

The strategic mindset of Australian manufacturing managers : some missing links

Manufacturing managers have a measurable mindset (or frame) that structures their response to the manufacturing environment. Most importantly, this frame represents a set of assumptions about the relative prominence of concepts in the manufacturing domains, about the nature of people, and about the sensemaking processes required to understand the nature of the manufacturing environment as seen through the eyes of manufacturing managers. This paper uses work in the area of text analysis and extends the scope of a methodology that has been approached from two different directions by Carley ( Journal of Organizational Behavior , 18 (51), 533-558, 1997) and Gephart ( Journal of Organizational Behavior , 18 (51), 583-622, 1997). This methodology is termed collocate analysis. Based on the analysis of transcripts of interviews of Australian manufacturing managers mind maps of the concepts used by these managers have been constructed. From an analysis of these mind maps it is argued that strategy plays a minor role in their thinking second only to the improvement domain, whereas design and related concepts play a dominant role in their day-to-day thinking.

Yet to be known

TBA: Triptych: Digital Print, PVC Text, Acrylic Sheet Total Size: 252cm x 119cm---------- The work employs text based representations of indigenous plants (3500 species names) and quotations from an eminent botanist. This information is spatialised to represent the geographic area within which the plants where recorded (by others-Gov’t database).---------- The work was exhibited at Eyes wide open (curators K Bradby and A Brandenberg) which was held at Gorepani Gallery, Albany WA to coincide with the first national screening on SBS Television of the Western Australian documentary A Million Acres a Year (Rijavec, F, Harrison, N & Bradby K (directors), Snakewood Films & Film Australia, c2003).

Many Mount Barrens

Cibachrome photographic prints, Digital print, Acrylic Sheet , wire & card.--------- Total size: 170cm x 119cm x 15cm---------- The work employs a terrestrial photography and cartographic technique to represent a diversity of landscape types surrounding West Mt Barren in Western Australia. Sixteen views of West Mt Barren were captured over a two week period from map grid coordinates in the surround landscape. These images are configured in Many Mount Barrens in a manner which corresponds to the position from which they were recorded.---------- The work was exhibited at Eyes wide open (curators K Bradby and A Brandenberg) which was held at Gorepani Gallery, Albany WA to coincide with the first national screening on SBS Television of the Western Australian documentary A Million Acres a Year (Rijavec, F, Harrison, N & Bradby K (directors), Snakewood Films & Film Australia, c2003).

Sandplain

Triptych: Digital print, Acrylic Sheet--------- Total size: 252 cm x 119cm---------- The work employs text based representations of agricultural plants (26 species names). This information is spatialised to represent the geographic area within which the plant species are harvested.---------- The work was exhibited at Eyes wide open (curators K Bradby and A Brandenberg) which was held at Gorepani Gallery, Albany WA to coincide with the first national screening on SBS Television of the Western Australian documentary A Million Acres a Year (Rijavec, F, Harrison, N & Bradby K (directors), Snakewood Films & Film Australia, c2003).

4-(4-Nitrobenzyl)pyridinium 5-nitrosalicylate

In the title salt, C12H11N2O2+·C7H4NO5-, the cations and anions interact through asymmetric cyclic pyridinium-carboxylate N-HO,O' hydrogen-bonding associations [graph set R12(4)], giving discrete heterodimers having weak cation-anion - aromatic ring interactions [minimum ring centroid separation = 3.7116 (9) Å]

Bis[2-(2,4-dinitrobenzyl)pyridinium] biphenyl-4,4'-disulfonate

In the structure of the title compound, the salt 2(C12H10N3O4+) (C12H8O6S2)2- . 3H2O, determined at 173 K, the biphenyl-4,4'-disulfonate dianions lie across crystallographic inversion centres with the sulfonate groups interacting head-to-head through centrosymmetric cyclic bis(water)-bridged hydrogen-bonding associations [graph set R4/4(11)], forming chain structures. The 2-(2,4-dinitrobenzyl)pyridinium cations are linked to these chains through N+-H...O(water) hydrogen bonds and a two-dimensional network structure is formed through water bridges between sulfonate and 2-nitro O atoms, while the structure also has weak cation--anion pi-pi aromatic ring interactions [minimum ring centroid separation 3.8441(13)A].

Infrared spectroscopic investigation of the effects of titania photocatalyst on the degradation of linear low density polyethylene film for commercial applications

There is a need in industry for a commodity polyethylene film with controllable degradation properties that will degrade in an environmentally neutral way, for applications such as shopping bags and packaging film. Additives such as starch have been shown to accelerate the degradation of plastic films, however control of degradation is required so that the film will retain its mechanical properties during storage and use, and then degrade when no longer required. By the addition of a photocatalyst it is hoped that polymer film will breakdown with exposure to sunlight. Furthermore, it is desired that the polymer film will degrade in the dark, after a short initial exposure to sunlight. Research has been undertaken into the photo- and thermo-oxidative degradation processes of 25 ìm thick LLDPE (linear low density polyethylene) film containing titania from different manufacturers. Films were aged in a suntest or in an oven at 50 °C, and the oxidation product formation was followed using IR spectroscopy. Degussa P25, Kronos 1002, and various organic-modified and doped titanias of the types Satchleben Hombitan and Hunstsman Tioxide incorporated into LLDPE films were assessed for photoactivity. Degussa P25 was found to be the most photoactive with UVA and UVC exposure. Surface modification of titania was found to reduce photoactivity. Crystal phase is thought to be among the most important factors when assessing the photoactivity of titania as a photocatalyst for degradation. Pre-irradiation with UVA or UVC for 24 hours of the film containing 3% Degussa P25 titania prior to aging in an oven resulted in embrittlement in ca. 200 days. The multivariate data analysis technique PCA (principal component analysis) was used as an exploratory tool to investigate the IR spectral data. Oxidation products formed in similar relative concentrations across all samples, confirming that titania was catalysing the oxidation of the LLDPE film without changing the oxidation pathway. PCA was also employed to compare rates of degradation in different films. PCA enabled the discovery of water vapour trapped inside cavities formed by oxidation by titania particles. Imaging ATR/FTIR spectroscopy with high lateral resolution was used in a novel experiment to examine the heterogeneous nature of oxidation of a model polymer compound caused by the presence of titania particles. A model polymer containing Degussa P25 titania was solvent cast onto the internal reflection element of the imaging ATR/FTIR and the oxidation under UVC was examined over time. Sensitisation of 5 ìm domains by titania resulted in areas of relatively high oxidation product concentration. The suitability of transmission IR with a synchrotron light source to the study of polymer film oxidation was assessed as the Australian Synchrotron in Melbourne, Australia. Challenges such as interference fringes and poor signal-to-noise ratio need to be addressed before this can become a routine technique.

The phenomenon of resilience as described by adults who have experienced mental illness

Aim: This paper is a report of a study to explore the phenomenon of resilience in the lives of adult patients of mental health services who have experienced mental illness. ---------- Background: Mental illness is a major health concern worldwide, and the majority experiencing it will continue to battle with relapses throughout their lives. However, in many instances people go on to overcome their illness to lead productive and socially engaged lives. Contemporary mental health nursing practice primarily focuses on symptom reduction, and working with resilience has not generally been a consideration. ---------- Method: A descriptive phenomenological study was carried out in 2006. One participant was recruited through advertisements in community newspapers and newsletters and the others using the snowballing method. Information was gathered through in-depth individual interviews which were tape-recorded and subsequently transcribed. Colaizzi's original seven-step approach was used for data analysis, with the inclusion of two additional steps. ---------- Findings: The following themes were identified: Universality, Acceptance, Naming and knowing, Faith, Hope, Being the fool and Striking a balance, Having meaning and meaningful relationships, and 'Just doing it'. The conceptualization identified as encapsulating the themes was 'Viewing life from the ridge with eyes wide open', which involved knowing the risks and dangers ahead and making a decision for life amid ever-present hardships. ---------- Conclusion: Knowledge about resilience should be included in the theoretical and practical education of nursing students and experienced nurses. Early intervention, based on resilience factors identified through screening processes, is needed for people with mental illness.

Effects of age on peripheral ocular aberrations

On-axis monochromatic higher-order aberrations increase with age. Few studies have been made of peripheral refraction along the horizontal meridian of older eyes, and none of their off-axis higher-order aberrations. We measured wave aberrations over the central 42°x32° visual field for a 5mm pupil in 10 young and 7 older emmetropes. Patterns of peripheral refraction were similar in the two groups. Coma increased linearly with field angle at a significantly higher rate in older than in young emmetropes (−0.018±0.007 versus −0.006±0.002 µm/deg). Spherical aberration was almost constant over the measured field in both age groups and mean values across the field were significantly higher in older than in young emmetropes (+0.08±0.05 versus +0.02±0.04 µm). Total root-mean-square and higher-order aberrations increased more rapidly with field angle in the older emmetropes. However, the limits to monochromatic peripheral retinal image quality are largely determined by the second-order aberrations, which do not change markedly with age, and under normal conditions the relative importance of the increased higher-order aberrations in older eyes is lessened by the reduction in pupil diameter with age. Therefore it is unlikely that peripheral visual performance deficits observed in normal older individuals are primarily attributable to the increased impact of higher-order aberration.

4-Methylpyridinium 2-carboxy-4,5-dichlorobenzoate

In the structure of the 1:1 proton-transfer compound of 4-methylpyridine (\g-picoline) with 4,5-dichlorophthalic acid, C6H8N+ C8H3Cl2O4- . H2O, determined at 200 K, the 4,5-dichlorophthalate anions are bridged by the water molecule through O--H...O~carboxyl~ hydrogen bonds, giving zig-zag chains which extend along the c axial direction of the unit cell. The 4-methylpyridine cations are linked to the chains through single N--H...O~water~ hydrogen bonds and occupy the voids within the chains in the one-dimensional structure. The anions have the common 'planar' conformation with the short intramolecular O--H...O(carboxyl) hydrogen bond.

Phenyl-ring disorder in the two-dimensional hydrogen-bonded structure of the 1:1 proton-transfer salt of the diazo-dye precursor 4-(phenyldiazenyl)aniline (aniline yellow) with L-tartaric acid

The structure of the 1:1 proton-transfer compound from the reaction of L-tartaric acid with the azo-dye precursor aniline yellow [4-(phenylazo)aniline], 4-(phenyldiazenyl)anilinium hydrogen 2R,3R-tartrate C12H12N3+ . C4H6O6- has been determined at 200 K. The asymmetric unit of the compound contains two independent phenylazoanilinium cations and two hydrogen L-tartrate anions. The structure is unusual in that all four phenyl rings of both cations have identical 50% rotational disorder. The two hydrogen L-tartrate anions form independent but similar chains through head-to-tail carboxylic O--H...O~carboxyl~ hydrogen bonds [graph set C7] which are then extended into a two-dimensional hydrogen-bonded sheet structure through hydroxyl O--H...O hydrogen-bonding links. The anilinium groups of the phenyldiazenyl cations are incorporated into the sheets and also provide internal hydrogen-bonding extensions while their aromatic tails layer in the structure without significant interaction except for weak \p--\p interactions [minimum ring centroid separation, 3.844(3) \%A]. The hydrogen L-tartrate residues of both anions have the common short intramolecular hydroxyl O--H...O~carboxyl~ hydogen bonds. This work has provided a solution to the unusual disorder problem inherent in the structure of this salt as well as giving another example of the utility of the hydrogen tartrate in the generation of sheet substructures in molecular assembly processes.