Mathematics funds of knowledge : sotmaute and sermaute fish in a Torres Strait Islander community

The purpose of this article is to describe a project with one Torres Strait Islander Community. It provides some insights into parents’ funds of knowledge that are mathematical in nature, such as sorting shells and giving fish. The idea of funds of knowledge is based on the premise that people are competent and have knowledge that has been historically and culturally accumulated into a body of knowledge and skills essential for their functioning and well-being. This knowledge is then practised throughout their lives and passed onto the next generation of children. Through adopting a community research approach, funds of knowledge that can be used to validate the community’s identities as knowledgeable people, can also be used as foundations for future learnings for teachers, parents and children in the early years of school. They can be the bridge that joins a community’s funds of knowledge with schools validating that knowledge.

A novel quadratic Edge-based Smoothed Conforming Point Interpolation Method (ES-CPIM) for elasticity problems

his paper formulates an edge-based smoothed conforming point interpolation method (ES-CPIM) for solid mechanics using the triangular background cells. In the ES-CPIM, a technique for obtaining conforming PIM shape functions (CPIM) is used to create a continuous and piecewise quadratic displacement field over the whole problem domain. The smoothed strain field is then obtained through smoothing operation over each smoothing domain associated with edges of the triangular background cells. The generalized smoothed Galerkin weak form is then used to create the discretized system equations. Numerical studies have demonstrated that the ES-CPIM possesses the following good properties: (1) ES-CPIM creates conforming quadratic PIM shape functions, and can always pass the standard patch test; (2) ES-CPIM produces a quadratic displacement field without introducing any additional degrees of freedom; (3) The results of ES-CPIM are generally of very high accuracy.

Learning communities learning series

In 2008 the introduction of the National Assessment Program – Literacy and Numeracy (NAPLAN), combined with the publication of the international comparative analyses of student achievement data (such as the Programme of International Student Assessment (PISA) developed by the Organisation for Economic Co-operation and Development (OECD) and the Trends in International Mathematics and Science Study (TIMSS) of the International Association for the Evaluation of Educational Achievement (IEA)) highlighted a significant priority for Australian education by identifying low levels of equity.

Learning to think spatially : what do students 'see' in numeracy test items?

Learning to think spatially in mathematics involves developing proficiency with graphics. This paper reports on 2 investigations of spatial thinking and graphics. The first investigation explored the importance of graphics as 1 of 3 communication systems (i.e. text, symbols, graphics) used to provide information in numeracy test items. The results showed that graphics were embedded in at least 50 % of test items across 3 year levels. The second investigation examined 11 – 12-year-olds’ performance on 2 mathematical tasks which required substantial interpretation of graphics and spatial thinking. The outcomes revealed that many students lacked proficiency in the basic spatial skills of visual memory and spatial perception and the more advanced skills of spatial orientation and spatial visualisation. This paper concludes with a reaffirmation of the importance of spatial thinking in mathematics and proposes ways to capitalize on graphics in learning to think spatially.

Students’ approaches to learning a new mathematical model

In this article, we report on the findings of an exploratory study into the experience of undergraduate students as they learn new mathematical models. Qualitative and quanti- tative data based around the students’ approaches to learning new mathematical models were collected. The data revealed that students actively adopt three approaches to under- standing a new mathematical model: gathering information for the task of understanding the model, practising with and using the model, and finding interrelationships between elements of the model. We found that the students appreciate mathematical models that have a real world application and that this can be used to engage students in higher level learning approaches.

Does 'habitus' count in Chinese Australians' mathematics achievement?

Large-scale international comparative studies and cross-ethnic studies have revealed that Chinese students, whether living in China or overseas, consistently outperform their counterparts in mathematics achievement. These studies tended to explain this result from psychological, educational, or cultural perspectives. However, there is scant sociological investigation addressing Chinese students’ better mathematics achievement. Drawing on Bourdieu’s sociological theory, this study conceptualises Chinese Australians’ “Chineseness” by the notion of ‘habitus’ and considers this “Chineseness” generating but not determinating mechanism that underpins Chinese Australians’ mathematics learning. Two hundred and thirty complete responses from Chinese Australian participants were collected by an online questionnaire. Simple regression model statistically significantly well predicted mathematics achievement by “Chineseness” (F = 141.90, R = .62, t = 11.91, p < .001). Taking account of “Chineseness” as a sociological mechanism for Chinese Australians’ mathematics learning, this study complements psychological and educational impacts on better mathematics achievement of Chinese students revealed by previous studies. This study also challenges the cultural superiority discourse that attributes better mathematics achievement of Chinese students to cultural factors.

Australian learning and teaching council projects in the mathematical sciences : a retrospective

Since 2004, the Australian Learning and Teaching Council (ALTC) and its predecessor, the Carrick Institute for Learning and Teaching in Higher Education, have funded numerous teaching and educational research-based projects in the Mathematical Sciences. In light of the Commonwealth Government’s decision to close the ALTC in 2011, it is appropriate to take account of the ALTCs input into the Mathe- matical Sciences in higher education. Here we present an overview of ALTC projects in the Mathematical Sciences, as well as report on the contributions they have made to the Discipline.

Modeling as a bridge between real world problems and school mathematics

This article argues for an interdisciplinary approach to mathematical problem solving at the elementary school, one that draws upon the engineering domain. A modeling approach, using engineering model eliciting activities, might provide a rich source of meaningful situations that capitalize on and extend students’ existing mathematical learning. The study reports on the developments of 48 twelve-year old students who worked on the Bridge Design activity. Results revealed that young students, even before formal instruction, have the capacity to deal with complex interdisciplinary problems. A number of students created quite appropriate models by developing the necessary mathematical constructs to solve the problem. Students’ difficulties in mathematizing the problem, and in revising and documenting their models are presented and analysed, followed by a discussion on the appropriateness of a modeling approach as a means for introducing complex problems to elementary school students.

A Summative Evaluation of the Stronger Smarter Learning Communities Project : Vol 1 and Vol 2

This is a summative evaluation of the Stronger Smarter Learning Communities (SSLC) project that examines whether and how the SSLC project had an impact on Australian state schools which adopted its models and approaches. Drawing from qualitative and quantitative data sets, it also presents the largest scale and most comprehensive analysis of Indigenous education practices and outcomes to date. It includes empirical findings on: success in changing school ethos and community engagement; challenges in progress at closure of the 'gap' in conventionally measured achievement and performance; schools' and principals' choices in curriculum and instruction; profiles of teachers' and principals' training and views on teacher education; and a strong emphasis on community and school Indigenoous voices and views on Indigenous education.

Learning with FIRST LEGO League

Robotics is a valuable tool for engaging students in the hands-on application of science, technology, engineering, and mathematics (STEM) concepts. Robotics competitions such as FIRST LEGO League (FLL) can increase students’ interest in the STEM subjects and can foster their problem solving and teamwork skills. This paper reports on a study investigating students’ perceptions on the influence of participating in a FLL competition on their learning. The students completed questionnaires regarding their perceptions of their learning during the FLL challenge and were also interviewed to gain a deeper understanding of their questionnaire responses. The results show that the students were engaged with the FLL challenge and held positive views regarding their experience. The results also suggest that students involved with the FLL challenge improved their learning about real-world applications, problem solving, engagement, communication, and the application of the technology/engineering cycle.

Robust image hash functions using higher order spectra

Robust hashing is an emerging field that can be used to hash certain data types in applications unsuitable for traditional cryptographic hashing methods. Traditional hashing functions have been used extensively for data/message integrity, data/message authentication, efficient file identification and password verification. These applications are possible because the hashing process is compressive, allowing for efficient comparisons in the hash domain but non-invertible meaning hashes can be used without revealing the original data. These techniques were developed with deterministic (non-changing) inputs such as files and passwords. For such data types a 1-bit or one character change can be significant, as a result the hashing process is sensitive to any change in the input. Unfortunately, there are certain applications where input data are not perfectly deterministic and minor changes cannot be avoided. Digital images and biometric features are two types of data where such changes exist but do not alter the meaning or appearance of the input. For such data types cryptographic hash functions cannot be usefully applied. In light of this, robust hashing has been developed as an alternative to cryptographic hashing and is designed to be robust to minor changes in the input. Although similar in name, robust hashing is fundamentally different from cryptographic hashing. Current robust hashing techniques are not based on cryptographic methods, but instead on pattern recognition techniques. Modern robust hashing algorithms consist of feature extraction followed by a randomization stage that introduces non-invertibility and compression, followed by quantization and binary encoding to produce a binary hash output. In order to preserve robustness of the extracted features, most randomization methods are linear and this is detrimental to the security aspects required of hash functions. Furthermore, the quantization and encoding stages used to binarize real-valued features requires the learning of appropriate quantization thresholds. How these thresholds are learnt has an important effect on hashing accuracy and the mere presence of such thresholds are a source of information leakage that can reduce hashing security. This dissertation outlines a systematic investigation of the quantization and encoding stages of robust hash functions. While existing literature has focused on the importance of quantization scheme, this research is the first to emphasise the importance of the quantizer training on both hashing accuracy and hashing security. The quantizer training process is presented in a statistical framework which allows a theoretical analysis of the effects of quantizer training on hashing performance. This is experimentally verified using a number of baseline robust image hashing algorithms over a large database of real world images. This dissertation also proposes a new randomization method for robust image hashing based on Higher Order Spectra (HOS) and Radon projections. The method is non-linear and this is an essential requirement for non-invertibility. The method is also designed to produce features more suited for quantization and encoding. The system can operate without the need for quantizer training, is more easily encoded and displays improved hashing performance when compared to existing robust image hashing algorithms. The dissertation also shows how the HOS method can be adapted to work with biometric features obtained from 2D and 3D face images.

Integration-segregation decisions under general value functions: "create your own bundle - choose 1, 2, or all 3!",

Whether to keep products segregated (e.g., unbundled) or integrate some or all of them (e.g., bundle) has been a problem of profound interest in areas such as portfolio theory in finance, risk capital allocations in insurance and marketing of consumer products. Such decisions are inherently complex and depend on factors such as the underlying product values and consumer preferences, the latter being frequently described using value functions, also known as utility functions in economics. In this paper, we develop decision rules for multiple products, which we generally call ‘exposure units’ to naturally cover manifold scenarios spanning well beyond ‘products’. Our findings show, e.g. that the celebrated Thaler's principles of mental accounting hold as originally postulated when the values of all exposure units are positive (i.e. all are gains) or all negative (i.e. all are losses). In the case of exposure units with mixed-sign values, decision rules are much more complex and rely on cataloging the Bell number of cases that grow very fast depending on the number of exposure units. Consequently, in the present paper, we provide detailed rules for the integration and segregation decisions in the case up to three exposure units, and partial rules for the arbitrary number of units.

Quantifying spatial structure in experimental observations and agent-based simulations using pair-correlation functions

We define a pair-correlation function that can be used to characterize spatiotemporal patterning in experimental images and snapshots from discrete simulations. Unlike previous pair-correlation functions, the pair-correlation functions developed here depend on the location and size of objects. The pair-correlation function can be used to indicate complete spatial randomness, aggregation or segregation over a range of length scales, and quantifies spatial structures such as the shape, size and distribution of clusters. Comparing pair-correlation data for various experimental and simulation images illustrates their potential use as a summary statistic for calibrating discrete models of various physical processes.

Outcomes of the Chemistry Discipline Network Mapping Exercises: Are the Threshold Learning Outcomes met?

The Chemistry Discipline Network has recently completed two distinct mapping exercises. The first is a snapshot of chemistry taught at 12 institutions around Australia in 2011. There were many similarities but also important differences in the content taught and assessed at different institutions. There were also significant differences in delivery, particularly laboratory contact hours, as well as forms and weightings of assessment. The second mapping exercise mapped the chemistry degrees at three institutions to the Threshold Learning Outcomes for chemistry. Importantly, some of the TLOs were addressed by multiple units at all institutions, while others were not met, or were met at an introductory level only. The exercise also exposed some challenges in using the TLOs as currently written.