958 research outputs found
Understanding technology integration in secondary mathematics: Theorising the role of the teacher
Previous research on computers and graphics calculators in mathematics education has examined effects on curriculum content and students’ mathematical achievement and attitudes while less attention has been given to the relationship between technology use and issues of pedagogy, in particular the impact on teachers’ professional learning in specific classroom and school environments. This observation is critical in the current context of educational policy making, where it is assumed – often incorrectly – that supplying schools with hardware and software will increase teachers’ use of technology and encourage more innovative teaching approaches. This paper reports on a research program that aimed to develop better understanding of how and under what conditions Australian secondary school mathematics teachers learn to effectively integrate technology into their practice. The research adapted Valsiner’s concepts of the Zone of Proximal Development, Zone of Free Movement and Zone of Promoted Action to devise a theoretical framework for analysing relationships between factors influencing teachers’ use of technology in mathematics classrooms. This paper illustrates how the framework may be used by analysing case studies of a novice teacher and an experienced teacher in different school settings
Grain boundary melting in ice
We describe an optical scattering study of grain boundary premelting in water
ice. Ubiquitous long ranged attractive polarization forces act to suppress
grain boundary melting whereas repulsive forces originating in screened Coulomb
interactions and classical colligative effects enhance it. The liquid enhancing
effects can be manipulated by adding dopant ions to the system. For all
measured grain boundaries this leads to increasing premelted film thickness
with increasing electrolyte concentration. Although we understand that the
interfacial surface charge densities and solute concentrations can
potentially dominate the film thickness, we can not directly measure them
within a given grain boundary. Therefore, as a framework for interpreting the
data we consider two appropriate dependent limits; one is dominated by
the colligative effect and one is dominated by electrostatic interactions.Comment: 6 pages, 5 figure
Phase behaviour of binary mixtures of diamagnetic colloidal platelets in an external magnetic field
Using fundamental measure density functional theory we investigate
paranematic-nematic and nematic-nematic phase coexistence in binary mixtures of
circular platelets with vanishing thicknesses. An external magnetic field
induces uniaxial alignment and acts on the platelets with a strength that is
taken to scale with the platelet area. At particle diameter ratio lambda=1.5
the system displays paranematic-nematic coexistence. For lambda=2, demixing
into two nematic states with different compositions also occurs, between an
upper critical point and a paranematic-nematic-nematic triple point. Increasing
the field strength leads to shrinking of the coexistence regions. At high
enough field strength a closed loop of immiscibility is induced and phase
coexistence vanishes at a double critical point above which the system is
homogeneously nematic. For lambda=2.5, besides paranematic-nematic coexistence,
there is nematic-nematic coexistence which persists and hence does not end in a
critical point. The partial orientational order parameters along the binodals
vary strongly with composition and connect smoothly for each species when
closed loops of immiscibility are present in the corresponding phase diagram.Comment: 9 pages, to appear in J.Phys:Condensed Matte
A sociocultural analysis of the development of pre-service and beginning teachers’ pedagogical identities as users of technology
This paper reports on a study that investigated the pedagogical practices and beliefs of pre-service and beginning teachers in integrating technology into the teaching of secondary school mathematics. A case study documents how one teachers modes of working with technology changed over time and across different school contexts, and identifies relationships between a range of personal and contextual factors that influenced the development of his identity as a teacher. This analysis views teachers learning as increasing participation in sociocultural practices, and uses Valsiners concepts of the Zone of Proximal Development, Zone of Free Movement, and Zone of Promoted Action to offer a dynamic way of theorising teacher learning as identity formation
Do science students graduate knowing what they know and don’t know: The case of quantitative skills
In the sciences, the undergraduate curriculum has often come under scrutiny by scientists like Carl Wieman and Jo Handelsman for being content-focused with rote learning assessment that does not prepare graduates for the scientific workforce. There has been an international push to reform undergraduate science education to better align curricula with the capabilities required of modern scientists. In Australia, there has been a focus on degree program curriculum with the Science Threshold Learning Outcomes, which are intended to guide holistic curriculum development to enable students to graduate with the appropriate level of skills, knowledge and attributes needed of modern day scientists. Agreeing on science graduate outcomes was an essential first step for the Australian science higher education sector. As Beverly Oliver’s Assuring Graduate Outcomes Office for Learning and Teaching Guide indicates, the challenge now is to assess these outcomes. Assessing such outcomes is a challenge because graduate level learning outcomes are complex, inexplicably linked with disciplinary contexts and instruments do not exist for most outcomes. For students to be motivated, engaged and ready for the workforce, be it a science-related career or not, we need to start understanding what students can do and what they know they can do. In the context of a particular graduate learning outcome, we pose the question: do students actually know what they know?
We initiated a pilot study with 211 final year biomedical science students to investigate students’ ability to self-assess effectively their acquisition of quantitative skills. The Quantitative Skills Assessment of Science Students was developed to gather this data, which comprised questions from existing performance assessment tasks developed as part of National Science Foundation funded projects (ARTIST, CAOS and Mathbench projects). In total, the instrument included 35 questions across mathematical (10 questions) and statistical (25 questions) topics. The questions were further organised into sub-topics that examined students’ understanding of typical quantitative skills in the biosciences (e.g. serial dilutions, probability, metric conversions, correlation and causation). Following completion of the questions for each sub-topic, students were asked to indicate their level of task-specific confidence using a four point, alpha Likert scale. Bandura’s task specific self-efficacy theory was adopted to measure students’ self-assessment via the confidence scale. We explored the alignment between students’ performance and confidence, drawing on Sadler’s notion of evaluative expertise to interpret the results. Performance scores and confidence indicators were categorised and students allocated to one of four categories: high performance-high confidence, high performance-low confidence, low performance-low confidence and low performance-high confidence. Overall results revealed that approximately half of the students fell into one of the two aligned categories, high performance-high confidence or low performance-low confidence, suggesting they were reasonable evaluator experts (effectively self-assessed). Analysis by sub-topics displayed wider ranges of distributions across categories. Findings will be presented along with broad implications for how the science higher education might begin to tackle the challenge of assessing outcomes and assuring our graduates are aware of the learning outcomes gained during their undergraduate degree programs
Real-Gas Effects and Phase Separation in Underexpanded Jets at Engine-Relevant Conditions
A numerical framework implemented in the open-source tool OpenFOAM is
presented in this work combining a hybrid, pressure-based solver with a
vapor-liquid equilibrium model based on the cubic equation of state. This
framework is used in the present work to investigate underexpanded jets at
engine-relevant conditions where real-gas effects and mixture induced phase
separation are probable to occur. A thorough validation and discussion of the
applied vapor-liquid equilibrium model is conducted by means of general
thermodynamic relations and measurement data available in the literature.
Engine-relevant simulation cases for two different fuels were defined. Analyses
of the flow field show that the used fuel has a first order effect on the
occurrence of phase separation. In the case of phase separation two different
effects could be revealed causing the single-phase instability, namely the
strong expansion and the mixing of the fuel with the chamber gas. A comparison
of single-phase and two-phase jets disclosed that the phase separation leads to
a completely different penetration depth in contrast to single-phase injection
and therefore commonly used analytical approaches fail to predict the
penetration depth.Comment: Preprint submitted to AIAA Scitech 2018, Kissimmee, Florid
Fresnel filtering in lasing emission from scarred modes of wave-chaotic optical resonators
We study lasing emission from asymmetric resonant cavity (ARC) GaN
micro-lasers. By comparing far-field intensity patterns with images of the
micro-laser we find that the lasing modes are concentrated on three-bounce
unstable periodic ray orbits, i.e. the modes are scarred. The high-intensity
emission directions of these scarred modes are completely different from those
predicted by applying Snell's law to the ray orbit. This effect is due to the
process of ``Fresnel filtering'' which occurs when a beam of finite angular
spread is incident at the critical angle for total internal reflection.Comment: 4 pages, 3 figures (eps), RevTeX 3.1, submitted to Phys. Rev. Lett;
corrected a minor (transcription) erro
Biaxial nematic phases in fluids of hard board-like particles
We use density-functional theory, of the fundamental-measure type, to study
the relative stability of the biaxial nematic phase, with respect to
non-uniform phases such as smectic and columnar, in fluids made of hard
board-like particles with sizes . A
restricted-orientation (Zwanzig) approximation is adopted. Varying the ratio
while keeping , we
predict phase diagrams for various values of which include all the
uniform phases: isotropic, uniaxial rod- and plate-like nematics, and biaxial
nematic. In addition, spinodal instabilities of the uniform phases with respect
to fluctuations of the smectic, columnar and plastic-solid type, are obtained.
In agreement with recent experiments, we find that the biaxial nematic phase
begins to be stable for . Also, as predicted by previous
theories and simulations on biaxial hard particles, we obtain a region of
biaxility centred on which widens as
increases. For \kappa_2\agt 5 the region of the
packing-fraction vs. phase diagrams exhibits interesting topologies
which change qualitatively with . We have found that an increasing
biaxial shape anisotropy favours the formation of the biaxial nematic phase.
Our study is the first to apply FMT theory to biaxial particles and, therefore,
it goes beyond the second-order virial approximation. Our prediction that the
phase diagram must be asymmetric is a genuine result of the present approach,
which is not accounted for by previous studies based on second-order theories.Comment: Preprint format. 18 pages, 5 figure
Gyrotropic impact upon negatively refracting surfaces
Surface wave propagation at the interface between different types of gyrotropic materials and an isotropic negatively refracting medium, in which the relative permittivity and relative permeability are, simultaneously, negative is investigated. A general approach is taken that embraces both gyroelectric and gyromagnetic materials, permitting the possibility of operating in either the low GHz, THz or the optical frequency regimes. The classical transverse Voigt configuration is adopted and a complete analysis of non-reciprocal surface wave dispersion is presented. The impact of the surface polariton modes upon the reflection of both plane waves and beams is discussed in terms of resonances and an example of the influence upon the Goos–Hänchen shift is given
Local Anisotropy of Fluids using Minkowski Tensors
Statistics of the free volume available to individual particles have
previously been studied for simple and complex fluids, granular matter,
amorphous solids, and structural glasses. Minkowski tensors provide a set of
shape measures that are based on strong mathematical theorems and easily
computed for polygonal and polyhedral bodies such as free volume cells (Voronoi
cells). They characterize the local structure beyond the two-point correlation
function and are suitable to define indices of
local anisotropy. Here, we analyze the statistics of Minkowski tensors for
configurations of simple liquid models, including the ideal gas (Poisson point
process), the hard disks and hard spheres ensemble, and the Lennard-Jones
fluid. We show that Minkowski tensors provide a robust characterization of
local anisotropy, which ranges from for vapor
phases to for ordered solids. We find that for fluids,
local anisotropy decreases monotonously with increasing free volume and
randomness of particle positions. Furthermore, the local anisotropy indices
are sensitive to structural transitions in these simple
fluids, as has been previously shown in granular systems for the transition
from loose to jammed bead packs
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