Investigating the effectiveness of an ecological approach to learning design in a first year mathematics for engineering unit

This is presentation of the refereed paper accepted for the Conferences' proceedings. The presentation was given on Tuesday, 1 December 2015.

A note on acyclic edge coloring of complete bipartite graphs

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic (2-colored) cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a'(G). Let Delta = Delta(G) denote the maximum degree of a vertex in a graph G. A complete bipartite graph with n vertices on each side is denoted by K-n,K-n. Alon, McDiarmid and Reed observed that a'(K-p-1,K-p-1) = p for every prime p. In this paper we prove that a'(K-p,K-p) <= p + 2 = Delta + 2 when p is prime. Basavaraju, Chandran and Kummini proved that a'(K-n,K-n) >= n + 2 = Delta + 2 when n is odd, which combined with our result implies that a'(K-p,K-p) = p + 2 = Delta + 2 when p is an odd prime. Moreover we show that if we remove any edge from K-p,K-p, the resulting graph is acyclically Delta + 1 = p + 1-edge-colorable. (C) 2009 Elsevier B.V. All rights reserved.

Unsteady compressible second-order boundary layers at the stagnation point of two-dimensional and axisymmetric bodies

The unsteady laminar compressible boundary-layer flow over two-dimensional and axisymmetric bodies at the stagnation point with mass transfer has been studied for all second-order boundary layer effects when the basic potential flow admits selfsimilarity. The solutions for the governing equations are obtained by using an implicit finite-difference scheme. Computations have been carried out for different values of the parameters characterizing the unsteadiness in the free stream velocity, wall temperature, mass transfer rate and variable gas properties. The results are found to be strongly affected by the unsteadiness in the free stream velocity. For large injection rates the second-orderboundary layer effects may prevail over the first-order boundary layer, but reverse is true for suction. The wall temperature and the variation of the density-viscosity product across the boundary layer appreciably change the skin-friction and heat-transfer rates due to second-order boundary-layer effects.

All of Us

All of Us is a ground-breaking Australian government approved anti-bullying educational resource comprised of seven online videos that feature gender diverse, sexual diverse and intersex youths. The videos, along with unit guides and student handouts, have been designed to address a gap in high school curriculum as they teach not just about sexual diversity and gender diversity but also the values of empathy and respect, which has been demonstrated to improve students’ wellbeing and educational engagement. The resource captures the real life experiences of lesbian, gay, bisexual, transgender and intersex young people through a collection of short videos and teaching activities that are aligned to the Year 7/8 Health and Physical Education learning area of the Australian Curriculum. All Of Us has been developed to have a real impact on student attitudes towards lesbian, gay, bisexual, transgender and intersex people and to encourage whole school change that affirms and supports the right of all students, staff and families to feel safe at school. This free video resource is widely available and allows all schools, regardless of experience, location or funding, the chance to create an environment where every student can learn, every teacher can teach and every family can belong from the beginning of 2016. The resource was launched on Thursday, 26 November 2015 at Treasury Theatre, 1 Macarthur St, Melbourne. The launch was attended by almost 200 people including former Safe Schools Coalition Ambassador Jason Ball, Victorian Commissioner for Gender and Sexuality Ro Allen, Chris Bush, Executive Producer of All Of Us, Micah Scott, CEO of Minus18, All Of Us Margot Fink; Safe Schools Coalition Victoria's Manager Roz Ward and; Sally Richardson, National Program Director of Safe Schools Coalition Australia.

Mathematics, programming, and STEM

Learning mathematics is a complex and dynamic process. In this paper, the authors adopt a semiotic framework (Yeh & Nason, 2004) and highlight programming as one of the main aspects of the semiosis or meaning-making for the learning of mathematics. During a 10-week teaching experiment, mathematical meaning-making was enriched when primary students wrote Logo programs to create 3D virtual worlds. The analysis of results found deep learning in mathematics, as well as in technology and engineering areas. This prompted a rethinking about the nature of learning mathematics and a need to employ and examine a more holistic learning approach for the learning in science, technology, engineering, and mathematics (STEM) areas.

Assessing university students' prior knowledge

The aim of this dissertation was to explore how different types of prior knowledge influence student achievement and how different assessment methods influence the observed effect of prior knowledge. The project started by creating a model of prior knowledge which was tested in various science disciplines. Study I explored the contribution of different components of prior knowledge on student achievement in two different mathematics courses. The results showed that the procedural knowledge components which require higher-order cognitive skills predicted the final grades best and were also highly related to previous study success. The same pattern regarding the influence of prior knowledge was also seen in Study III which was a longitudinal study of the accumulation of prior knowledge in the context of pharmacy. The study analysed how prior knowledge from previous courses was related to student achievement in the target course. The results implied that students who possessed higher-level prior knowledge, that is, procedural knowledge, from previous courses also obtained higher grades in the more advanced target course. Study IV explored the impact of different types of prior knowledge on students’ readiness to drop out from the course, on the pace of completing the course and on the final grade. The study was conducted in the context of chemistry. The results revealed again that students who performed well in the procedural prior-knowledge tasks were also likely to complete the course in pre-scheduled time and get higher final grades. On the other hand, students whose performance was weak in the procedural prior-knowledge tasks were more likely to drop out or take a longer time to complete the course. Study II explored the issue of prior knowledge from another perspective. Study II aimed to analyse the interrelations between academic self-beliefs, prior knowledge and student achievement in the context of mathematics. The results revealed that prior knowledge was more predictive of student achievement than were other variables included in the study. Self-beliefs were also strongly related to student achievement, but the predictive power of prior knowledge overruled the influence of self-beliefs when they were included in the same model. There was also a strong correlation between academic self-beliefs and prior-knowledge performance. The results of all the four studies were consistent with each other indicating that the model of prior knowledge may be used as a potential tool for prior knowledge assessment. It is useful to make a distinction between different types of prior knowledge in assessment since the type of prior knowledge students possess appears to make a difference. The results implied that there indeed is variation between students’ prior knowledge and academic self-beliefs which influences student achievement. This should be taken into account in instruction.

An Exact Analysis of Unsteady Convective Diffusion in an Annular Pipe

An exact solution to the unsteady convective diffusion equation for the dispersion of a solute in a fully developed laminar flow in an annular pipe is obtained. Generalized dispersion model which is valid for all time after the injection of solute in the flow is used to evaluate the dispersion coefficients as functions of time. It is observed that the axial dispersion decreases with an increase in the radius of the inner cylinder.

Managing for rainfall variability: effect of grazing strategy on cattle production in a dry tropical savanna

Rainfall variability is a challenge to sustainable and pro. table cattle production in northern Australia. Strategies recommended to manage for rainfall variability, like light or variable stocking, are not widely adopted. This is due partly to the perception that sustainability and profitability are incompatible. A large, long-term grazing trial was initiated in 1997 in north Queensland, Australia, to test the effect of different grazing strategies on cattle production. These strategies are: (i) constant light stocking (LSR) at long-term carrying capacity (LTCC); (ii) constant heavy stocking (HSR) at twice LTCC; (iii) rotational wet-season spelling (R/Spell) at 1.5 LTCC; (iv) variable stocking (VAR), with stocking rates adjusted in May based on available pasture; and (v) a Southern Oscillation Index (SOI) variable strategy, with stocking rates adjusted in November, based on available pasture and SOI seasonal forecasts. Animal performance varied markedly over the 10 years for which data is presented, due to pronounced differences in rainfall and pasture availability. Nonetheless, lighter stocking at or about LTCC consistently gave the best individual liveweight gain (LWG), condition score and skeletal growth; mean LWG per annum was thus highest in the LSR (113 kg), intermediate in the R/Spell (104 kg) and lowest in the HSR(86 kg). MeanLWGwas 106 kg in the VAR and 103 kg in the SOI but, in all years, the relative performance of these strategies was dependent upon the stocking rate applied. After 2 years on the trial, steers from lightly stocked strategies were 60-100 kg heavier and received appreciable carcass price premiums at the meatworks compared to those under heavy stocking. In contrast, LWG per unit area was greatest at stocking rates of about twice LTCC; mean LWG/ha was thus greatest in the HSR (21 kg/ha), but this strategy required drought feeding in four of the 10 years and was unsustainable. Although LWG/ha was lower in the LSR (mean 14 kg/ha), or in strategies that reduced stocking rates in dry years like the VAR(mean 18 kg/ha) and SOI (mean 17 kg/ha), these strategies did not require drought feeding and appeared sustainable. The R/Spell strategy (mean 16 kg/ha) was compromised by an ill-timed fire, but also performed satisfactorily. The present results provide important evidence challenging the assumption that sustainable management in a variable environment is unprofitable. Further research is required to fully quantify the long-term effects of these strategies on land condition and profitability and to extrapolate the results to breeder performance at the property level.

Parameter estimation and sensitivity analysis of fat deposition models in beef steers using acslXtreme.

The Davis Growth Model (a dynamic steer growth model encompassing 4 fat deposition models) is currently being used by the phenotypic prediction program of the Cooperative Research Centre (CRC) for Beef Genetic Technologies to predict P8 fat (mm) in beef cattle to assist beef producers meet market specifications. The concepts of cellular hyperplasia and hypertrophy are integral components of the Davis Growth Model. The net synthesis of total body fat (kg) is calculated from the net energy available after accounting tor energy needs for maintenance and protein synthesis. Total body fat (kg) is then partitioned into 4 fat depots (intermuscular, intramuscular, subcutaneous, and visceral). This paper reports on the parameter estimation and sensitivity analysis of the DNA (deoxyribonucleic acid) logistic growth equations and the fat deposition first-order differential equations in the Davis Growth Model using acslXtreme (Hunstville, AL, USA, Xcellon). The DNA and fat deposition parameter coefficients were found to be important determinants of model function; the DNA parameter coefficients with days on feed >100 days and the fat deposition parameter coefficients for all days on feed. The generalized NL2SOL optimization algorithm had the fastest processing time and the minimum number of objective function evaluations when estimating the 4 fat deposition parameter coefficients with 2 observed values (initial and final fat). The subcutaneous fat parameter coefficient did indicate a metabolic difference for frame sizes. The results look promising and the prototype Davis Growth Model has the potential to assist the beef industry meet market specifications.

Survival probability for a diffusive process on a growing domain

We consider the motion of a diffusive population on a growing domain, 0 < x < L(t ), which is motivated by various applications in developmental biology. Individuals in the diffusing population, which could represent molecules or cells in a developmental scenario, undergo two different kinds of motion: (i) undirected movement, characterized by a diffusion coefficient, D, and (ii) directed movement, associated with the underlying domain growth. For a general class of problems with a reflecting boundary at x = 0, and an absorbing boundary at x = L(t ), we provide an exact solution to the partial differential equation describing the evolution of the population density function, C(x,t ). Using this solution, we derive an exact expression for the survival probability, S(t ), and an accurate approximation for the long-time limit, S = limt→∞ S(t ). Unlike traditional analyses on a nongrowing domain, where S ≡ 0, we show that domain growth leads to a very different situation where S can be positive. The theoretical tools developed and validated in this study allow us to distinguish between situations where the diffusive population reaches the moving boundary at x = L(t ) from other situations where the diffusive population never reaches the moving boundary at x = L(t ). Making this distinction is relevant to certain applications in developmental biology, such as the development of the enteric nervous system (ENS). All theoretical predictions are verified by implementing a discrete stochastic model.

The Alpha-Method Direct Transcription In Path Constrained Dynamic Optimization

Numerically discretized dynamic optimization problems having active inequality and equality path constraints that along with the dynamics induce locally high index differential algebraic equations often cause the optimizer to fail in convergence or to produce degraded control solutions. In many applications, regularization of the numerically discretized problem in direct transcription schemes by perturbing the high index path constraints helps the optimizer to converge to usefulm control solutions. For complex engineering problems with many constraints it is often difficult to find effective nondegenerat perturbations that produce useful solutions in some neighborhood of the correct solution. In this paper we describe a numerical discretization that regularizes the numerically consistent discretized dynamics and does not perturb the path constraints. For all values of the regularization parameter the discretization remains numerically consistent with the dynamics and the path constraints specified in the, original problem. The regularization is quanti. able in terms of time step size in the mesh and the regularization parameter. For full regularized systems the scheme converges linearly in time step size.The method is illustrated with examples.

Applying pure mathematics: mathematics in the natural sciences

The book of nature is written in the language of mathematics. This quotation, attributed to Galileo, seemed to hold to an unreasonable1 extent in the era of quantum mechanics.

Future switching technology: bacterial protein-based programmable all-optical switch for integrated optics applications?

We report on the bacterial protein-based all-optical switches which operate at low laser power, high speed and fulfil most of the requirements to be an ideal all-optical switch without any moving parts involved. This consists of conventional optical waveguides coated with bacteriorhodopsin films at switching locations. The principle of operation of the switch is based on the light-induced refractive index change of bacteriorhodopsin. This approach opens the possibility of realizing proteinbased all-optical switches for communication network, integrated optics and optical computers.