Objectifying early-number : a visual nomenclature to express mathematical domain knowledge

To address issues of divisive ideologies in the Mathematics Education community and to subsequently advance educational practice, an alternative theoretical framework and operational model is proposed which represents a consilience of constructivist learning theories whilst acknowledging the objective but improvable nature of domain knowledge. Based upon Popper’s three-world model of knowledge, the proposed theory supports the differentiation and explicit modelling of both shared domain knowledge and idiosyncratic personal understanding using a visual nomenclature. The visual nomenclature embodies Piaget’s notion of reflective abstraction and so may support an individual’s experience-based transformation of personal understanding with regards to shared domain knowledge. Using the operational model and visual nomenclature, seminal literature regarding early-number counting and addition was analysed and described. Exemplars of the resultant visual artefacts demonstrate the proposed theory’s viability as a tool with which to characterise the reflective abstraction-based organisation of a domain’s shared knowledge. Utilising such a description of knowledge, future research needs to consider the refinement of the operational model and visual nomenclature to include the analysis, description and scaffolded transformation of personal understanding. A detailed model of knowledge and understanding may then underpin the future development of educational software tools such as computer-mediated teaching and learning environments.

A visual description of early-number counting, addition and subtraction knowledge

Early-number is a rich fabric of interconnected ideas that is often misunderstood and thus taught in ways that do not lead to rich understanding. In this presentation, a visual language is used to describe the organisation of this domain of knowledge. This visual language is based upon Piaget’s notion of reflective abstraction (Dubinsky, 1991; Piaget, 1977/2001), and thus captures the epistemological associations that link the problems, concepts and representations of the domain. The constructs of this visual language are introduced and then applied to the early-number domain. The introduction to this visual language may prompt reflection upon its suitability and significance to the description of other domains of knowledge. Through such a process of analysis and description, the visual language may serve as a scaffold for enhancing pedagogical content knowledge and thus ultimately improve learning outcomes.

A Popperian consilience : modelling mathematical knowledge and understanding

Goldin (2003) and McDonald, Yanchar, and Osguthorpe (2005) have called for mathematics learning theory that reconciles the chasm between ideologies, and which may advance mathematics teaching and learning practice. This paper discusses the theoretical underpinnings of a recently completed PhD study that draws upon Popper’s (1978) three-world model of knowledge as a lens through which to reconsider a variety of learning theories, including Piaget’s reflective abstraction. Based upon this consideration of theories, an alternative theoretical framework and complementary operational model was synthesised, the viability of which was demonstrated by its use to analyse the domain of early-number counting, addition and subtraction.

But does it work? Effectiveness of scientific visualisations in high school chemistry and physics instruction.

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 physics and chemistry classrooms. In general there was no statistically significant difference between teaching with and without visualisations, however there were intriguing differences around student sex and academic ability.

Young children's understandings about "square" in 3D virtual reality microworlds

This paper reports an investigation of primary school children’s understandings about "square". 12 students participated in a small group teaching experiment session, where they were interviewed and guided to construct a square in a 3D virtual reality learning environment (VRLE). Main findings include mixed levels of "quasi" geometrical understandings, misconceptions about length and angles, and ambiguous uses of geometrical language for location, direction, and movement. These have implications for future teaching and learning about 2D shapes with particular reference to VRLE.

Regenerateengageexperiment in 2011! - News from Spatial Science Discipline at QUT

Abstract: Goals and potential impacts of QUT corporate Blueprint3 framework, university has made significant investments in physical infrastructure, and investments to improve staff profiles, particularly in relation to science, technology, engineering, and mathematics (STEM) disciplines. The most significant physical change to the Faculty’s infrastructure has seen new workshop and teaching and research spaces located in Science and Technology precinct under construction. Also includes Alumni news, input and output numbers Spatial Science discussion, Work Integrated Learning (WIL) in 2011, some key teaching administrative dates in 2011.

Spatial Sciences Student Awards Recognition : News from School of Urban Development, QUT

Summary of Spatial Sciences (Surveying) Student Prize Ceremony were recently held at The Old Government House - QUT Cultural Precinct. This short industry article briefly outlines the 15 student award descriptions and some photos of 2011 recipients and thanks industry sponsors.

One approach to finding evidence for the effectiveness of scientific visualisations in high school physics and chemistry education

Enormous amounts of money and energy are being devoted to the development, use and organisation of computer-based scientific visualisations (e.g. animations and simulations) in science education. It seems plausible that visualisations that enable students to gain visual access to scientific phenomena that are too large, too small or occur too quickly or too slowly to be seen by the naked eye, or to scientific concepts and models, would yield enhanced conceptual learning. When the literature is searched, however, it quickly becomes apparent that there is a dearth of quantitative evidence for the effectiveness of scientific visualisations in enhancing students’ learning of science concepts. This paper outlines an Australian project that is using innovative research methodology to gather evidence on this question in physics and chemistry classrooms.

Year 7 students’ approaches to understanding and solving NAPLAN numeracy problems

This study investigated how the interpretation of mathematical problems by Year 7 students impacted on their ability to demonstrate what they can do in NAPLAN numeracy testing. In the study, mathematics is viewed as a culturally and socially determined system of signs and signifiers that establish the meaning, origins and importance of mathematics. The study hypothesises that students are unable to succeed in NAPLAN numeracy tests because they cannot interpret the questions, even though they may be able to perform the necessary calculations. To investigate this, the study applied contemporary theories of literacy to the context of mathematical problem solving. A case study design with multiple methods was used. The study used a correlation design to explore the connections between NAPLAN literacy and numeracy outcomes of 198 Year 7 students in a Queensland school. Additionally, qualitative methods provided a rich description of the effect of the various forms of NAPLAN numeracy questions on the success of ten Year 7 students in the same school. The study argues that there is a quantitative link between reading and numeracy. It illustrates that interpretation (literacy) errors are the most common error type in the selected NAPLAN questions, made by students of all abilities. In contrast, conceptual (mathematical) errors are less frequent amongst more capable students. This has important implications in preparing students for NAPLAN numeracy tests. The study concluded by recommending that increased focus on the literacies of mathematics would be effective in improving NAPLAN results.

School education as social and economic governance : responsibilising communities through industry-school engagement

This article examines shifts in educational and social governance taking place in Queensland, Australia, through Industry School Engagement Strategy of Education Queensland and its Gateway Schools program. This significant educational initiative is set within the context of the social investment agenda first articulated in the education policy framework, Queensland State Education-2010. The article traces the historic extension of this governmental strategy through establishment of the Gateway Schools concept that brokers industry-school partnerships with global players in the Queensland economy. Industry sectors forming the partnerships include Minerals and Energy, Aerospace, Wine Tourism, Agribusiness, Manufacturing and Engineering, Building and Construction and ICT. We argue that this ‘post-bureaucratic’ model of schooling represents a new social settlement of neoliberal governance, in which educational outcomes align with economic objectives, and frame the conditions for community self-governance.

Providing a law degree for the 'real world' : perspective of an Australian law school

This paper focuses on the ‘real world’ approach to the degree achieved through the first year program, embedding and scaffolding law graduate capabilities through authentic and valid assessment and work integrated learning to assist graduates with transition into the workplace.

An advanced meshless method for time fractional diffusion equation

Recently, because of the new developments in sustainable engineering and renewable energy, which are usually governed by a series of fractional partial differential equations (FPDEs), the numerical modelling and simulation for fractional calculus are attracting more and more attention from researchers. The current dominant numerical method for modeling FPDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings including difficulty in simulation of problems with the complex problem domain and in using irregularly distributed nodes. Because of its distinguished advantages, the meshless method has good potential in simulation of FPDEs. This paper aims to develop an implicit meshless collocation technique for FPDE. The discrete system of FPDEs is obtained by using the meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of fractional partial differential equations.

A node-based smoothed conforming point interpolation method (NS-CPIM) for elasticity problems

This paper formulates a node-based smoothed conforming point interpolation method (NS-CPIM) for solid mechanics. In the proposed NS-CPIM, the higher order conforming PIM shape functions (CPIM) have been constructed to produce a continuous and piecewise quadratic displacement field over the whole problem domain, whereby the smoothed strain field was obtained through smoothing operation over each smoothing domain associated with domain nodes. The smoothed Galerkin weak form was then developed to create the discretized system equations. Numerical studies have demonstrated the following good properties: NS-CPIM (1) can pass both standard and quadratic patch test; (2) provides an upper bound of strain energy; (3) avoid the volumetric locking; (4) provides the higher accuracy than those in the node-based smoothed schemes of the original PIMs.

“Have you talked with a teacher yet?": how helpline counsellors support young callers being bullied at school

When seeking help and support about being bullied, children and young people weigh up the benefits and risks of talking to their friends, parents, teachers and counsellors about their experiences. The focus of this paper are calls to an Australian helpline for children and young people where the strategy of “talking to the teacher” is discussed by callers and counsellors as a possible way of dealing with the caller’s bullying situation at school. Transcribed and analysed data extracts of calls show how the young callers’ bullying experiences are being heard by the counsellor, and also reveals the skill of the counsellors in managing these calls within the philosophy and guidelines of the service.

Your voice counts : Listening to the voice of high school students with autism spectrum disorder

Supporting students with Autism Spectrum Disorders (ASD) in inclusive settings presents both opportunities and significant challenges to school communities. This study, which explored the lived-experience of nine students with ASD in an inclusive high school in Australia, is based on the belief that by listening to the voices of students, school communities will be in a better position to collaboratively create supportive learning and social environments. The findings of this small-scale study deepen our knowledge from the student perspective of the inclusive educational practices that facilitate and constrain the learning and participation of students with ASD. The students’ perspectives were examined in relation to the characteristics of successful inclusive schools identified by Kluth. Implications for inclusive educational practice that meets the needs of students with ASD are presented.