Perspectives on Reconceptualizing Early Mathematics Learning

This introductory section provides an overview of the different perspectives on reconceptualizing early mathematics learning. The chapters provide a broad scope in their topics and approaches to advancing young children’s mathematical learning. They incorporate studies that highlight the importance of pattern and structure across the curriculum, studies that target particular content such as statistics, early algebra, and beginning number, and studies that consider how technology and other tools can facilitate early mathematical development. Reconceptualizing the professional learning of teachers in promoting young children’s mathematics, including a consideration of the role of play, is also addressed. Although these themes are diffused throughout the chapters, we restrict our introduction to the core focus of each of the chapters.

Reconceptualizing Early Mathematics Learning : The Fundamental Role of Pattern and Structure

The Pattern and Structure Mathematics Awareness Program (PASMAP) was developed concurrently with the studies of AMPS and the development of the Pattern and Structure Assessment (PASA) interview. We summarize some early classroom-based teaching studies and describe the PASMAP that resulted. A large-scale two-year longitudinal study, Reconceptualizing Early Mathematics Learning (REML) resulted. We provide an overview of the REML study and discuss the consequences for our view of early mathematics learning. A purposive sample of four large primary schools, two in Sydney and two in Brisbane, representing 316 students from diverse socio-economic and cultural contexts, participated in an evaluation of the PASMAP intervention throughout the 2009 school year and a follow-up assessment in 2010. Two different mathematics programs were implemented: in each school, two Kindergarten teachers implemented the PASMAP and another two implemented their regular program. The study shows that both groups of students made substantial gains on the ‘I Can Do Maths’ standardized assessment and the PASA interview, but highly significant differences were found on the latter with PASMAP students outperforming the regular group on PASA scores. Qualitative analysis of students’ responses for structural development showed increased levels for the PASMAP students. Implications for pedagogy and curriculum are discussed.

Accelerating the Mathematics Learning of Low Socio-Economic Status Junior Secondary Students : an early report

The Accelerating the Mathematics Learning of Low Socio-Economic Status Junior Secondary Students project aims to address the issues faced by very underperforming mathematics students as they enter high school. Its aim is to accelerate learning of mathematics through a vertical curriculum to enable students to access Year 10 mathematics subjects, thus improving life chances. This paper reports upon the theory underpinning this project and illustrates it with examples of the curriculum that has been designed to achieve acceleration.

Reflections on chemistry sessions at the 2012 Healthy Buildings Conference

Scores of well-researched individual papers and posters specifically or indirectly addressing the occurrence, measurement or exposure impacts of chemicals in buildings were presented at 2012 Healthy Buildings Conference. Many of these presentations offered advances in sampling and characterisation of chemical pollutants while others extended the frontiers of knowledge on the emission, adsorption, risk, fate and compositional levels of chemicals in indoor and outdoor microenvironments. Several modelled or monitored indoor chemistry, including processes that generated secondary pollutants. This article provides an overview of the state of knowledge on healthy buildings based on papers presented in chemistry sessions at Healthy Buildings 2012 (HB2012) Conference. It also suggests future directions in healthy buildings research.

A RBF meshless approach for modeling a fractal mobile/immobile transport model

A fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBFs) to discretize the space variable. In contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example which is presented to describe a fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating fractional differential equations, and it has good potential in the development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.

Computational fluid dynamic analysis of intracranial aneurysmal bleb formation

Background The management of unruptured aneurysms is controversial with the decision to treat influenced by aneurysm characteristics including size and morphology. Aneurysmal bleb formation is thought to be associated with an increased risk of rupture. Objective To correlate computational fluid dynamic (CFD) indices with bleb formation. Methods Anatomical models were constructed from three-dimensional rotational angiogram (3DRA) data in 27 patients with cerebral aneurysms harbouring single blebs. Additional models representing the aneurysm before bleb formation were constructed by digitally removing the bleb. We characterised haemodynamic features of models both with and without the bleb using CFDs. Flow structure, wall shear stress (WSS), pressure and oscillatory shear index (OSI) were analysed. Results There was a statistically significant association between bleb location at or adjacent to the point of maximal WSS (74.1%, p=0.019), irrespective of rupture status. Aneurysmal blebs were related to the inflow or outflow jet in 88.9% of cases (p<0.001) whilst 11.1% were unrelated. Maximal wall pressure and OSI were not significantly related to bleb location. The bleb region attained a lower WSS following its formation in 96.3% of cases (p<0.001) and was also lower than the average aneurysm WSS in 86% of cases (p<0.001). Conclusion Cerebral aneurysm blebs generally form at or adjacent to the point of maximal WSS and are aligned with major flow structures. Wall pressure and OSI do not contribute to determining bleb location. The measurement of WSS using CFD models may potentially predict bleb formation and thus improve the assessment of rupture risk in unruptured aneurysms.

A conceptual framework for the cultural integration of cooperative learning : a Thai primary mathematics education perspective

The Thailand education reform adopted cooperative learning to improve the quality of education. However, it has been reported that the introduction and maintenance of cooperative learning has been difficult and uncertain because of the cultural differences. The study proposed a conceptual framework developed based on making a connection between Thai cultures and cooperative learning elements, and implemented a small-scale research project in a Thai primary mathematics class with a teacher and thirty-two Grade 4 students. The results uncovered that the three components including preparation of teachers, instructional strategies and preparation of students can be vehicles for the culture integration in cooperative learning.

The combination of empirical mode decomposition and minimum entropy deconvolution for roller bearing diagnostics in non-stationary operation

Diagnostics is based on the characterization of mechanical system condition and allows early detection of a possible fault. Signal processing is an approach widely used in diagnostics, since it allows directly characterizing the state of the system. Several types of advanced signal processing techniques have been proposed in the last decades and added to more conventional ones. Seldom, these techniques are able to consider non-stationary operations. Diagnostics of roller bearings is not an exception of this framework. In this paper, a new vibration signal processing tool, able to perform roller bearing diagnostics in whatever working condition and noise level, is developed on the basis of two data-adaptive techniques as Empirical Mode Decomposition (EMD), Minimum Entropy Deconvolution (MED), coupled by means of the mathematics related to the Hilbert transform. The effectiveness of the new signal processing tool is proven by means of experimental data measured in a test-rig that employs high power industrial size components.

'In the Room' and 'School Chemistry Class'

Two poems in journal Axon. 2013 Issue 4.

Modelling as a vehicle for philosophical inquiry in the mathematics curriculum

Philosophical inquiry in the teaching and learning of mathematics has received continued, albeit limited, attention over many years (e.g., Daniel, 2000; English, 1994; Lafortune, Daniel, Fallascio, & Schleider, 2000; Kennedy, 2012a). The rich contributions these communities can offer school mathematics, however, have not received the deserved recognition, especially from the mathematics education community. This is a perplexing situation given the close relationship between the two disciplines and their shared values for empowering students to solve a range of challenging problems, often unanticipated, and often requiring broadened reasoning. In this article, I first present my understanding of philosophical inquiry as it pertains to the mathematics classroom, taking into consideration the significant work that has been undertaken on socio-political contexts in mathematics education (e.g., Skovsmose & Greer, 2012). I then consider one approach to advancing philosophical inquiry in the mathematics classroom, namely, through modelling activities that require interpretation, questioning, and multiple approaches to solution. The design of these problem activities, set within life-based contexts, provides an ideal vehicle for stimulating philosophical inquiry.

An evaluation of the Australian ‘reconceptualising early mathematics learning’ project : key findings and implications

The Pattern and Structure Mathematics Awareness Project (PASMAP) has investigated the development of patterning and early algebraic reasoning among 4 to 8 year olds over a series of related studies. We assert that an awareness of mathematical pattern and structure (AMPS) enables mathematical thinking and simple forms of generalization from an early age. This paper provides an overview of key findings of the Reconceptualizing Early Mathematics Learning empirical evaluation study involving 316 Kindergarten students from 4 schools. The study found highly significant differences on PASA scores for PASMAP students. Analysis of structural development showed increased levels for the PASMAP students; those categorised as low ability developed improved structural responses over a short period of time.

Numerical study of lid-driven square cavity with heat generation using LBM

In this study, the mixed convection heat transfer and fluid flow behaviors in a lid-driven square cavity filled with high Prandtl number fluid (Pr = 5400, ν = 1.2×10-4 m2/s) at low Reynolds number is studied using thermal Lattice Boltzmann method (TLBM) where ν is the viscosity of the fluid. The LBM has built up on the D2Q9 model and the single relaxation time method called the Lattice-BGK (Bhatnagar-Gross-Krook) model. The effects of the variations of non dimensional mixed convection parameter called Richardson number(Ri) with and without heat generating source on the thermal and flow behavior of the fluid inside the cavity are investigated. The results are presented as velocity and temperature profiles as well as stream function and temperature contours for Ri ranging from 0.1 to 5.0 with other controlling parameters that present in this study. It is found that LBM has good potential to simulate mixed convection heat transfer and fluid flow problem. Finally the simulation results have been compared with the previous numerical and experimental results and it is found to be in good agreement.

Scientific visualisations for developing students’ understanding of concepts in chemistry : some findings and some lessons learned

Scientific visualisations such as computer-based animations and simulations are increasingly a feature of high school science instruction. Visualisations are adopted enthusiastically by teachers and embraced by students, and there is good evidence that they are popular and well received. There is limited evidence, however, of how effective they are in enabling students to learn key scientific concepts. This paper reports the results of a quantitative study conducted in Australian chemistry classrooms. The visualisations chosen were from free online sources, intended to model the ways in which classroom teachers use visualisations, but were found to have serious flaws for conceptual learning. There were also challenges in the degree of interactivity available to students using the visualisations. Within these limitations, no significant difference was found for teaching with and without these visualisations. Further study using better designed visualisations and with explicit attention to the pedagogy surrounding the visualisations will be required to gather high quality evidence of the effectiveness of visualisations for conceptual development.

Starting out in STEM : a study of young men and women in first year science, technology, engineering and mathematics courses

In late 2011, first year university students in science, technology, engineering and mathematics (STEM) courses across Australia were invited to participate in the international Interests and Recruitment in Science (IRIS) study. IRIS investigates the influences on young people's decisions to choose university STEM courses and their subsequent experiences of these courses. The study also has a particular focus on the motivations and experiences of young women in courses such as physics, IT and engineering given the low rates of female participation in these fields. Around 3500 students from 30 Australian universities contributed their views on the relative importance of various school and non-school influences on their decisions, as well as insights into their experiences of university STEM courses so far. It is hoped that their contributions will help improve recruitment, retention and gender equity in STEM higher education and careers.

Gas-Phase Transformation of Phosphatidylcholine Cations to Structurally Informative Anions via Ion/Ion Chemistry

Gas-phase transformation of synthetic phosphatidylcholine (PC) monocations to structurally informative anions is demonstrated via ion/ion reactions with doubly deprotonated 1,4-phenylenedipropionic acid (PDPA). Two synthetic PC isomers, 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (PC16:0/18:1) and 1-oleoyl-2-palmitoyl-sn-glycero-3-phosphocholine (PC18:1/16:0), were subjected to this ion/ion chemistry. The product of the ion/ion reaction is a negatively charged complex, \[PC + PDPA - H](-). Collisional activation of the long-lived complex causes transfer of a proton and methyl cation to PDPA, generating \[PC - CH3](-). Subsequent collisional activation of the demethylated PC anions produces abundant fatty acid carboxylate anions and low-abundance acyl neutral losses as free acids and ketenes. Product ion spectra of \[PC - CH3](-) suggest favorable cleavage at the sn-2 position over the sn-1 due to distinct differences in the relative abundances. In contrast, collisional activation of PC cations is absent of abundant fatty acid chain-related product ions and typically indicates only the lipid class via formation of the phosphocholine cation. A solution phase method to produce the gas-phase adducted PC anion is also demonstrated. Product ion spectra derived from the solution phase method are similar to the results generated via ion/ion chemistry. This work demonstrates a gas-phase means to increase structural characterization of phosphatidylcholines via ion/ion chemistry. Grant Number ARC/CE0561607, ARC/DP120102922