A case study of teachers' mathematics content knowledge and attitudes toward mathematics and teaching

This study intended to measure teacher mathematical content knowledge both before and after the first year of teaching and taking graduate teacher education courses in the Teach for America (TFA) program, as well as measure attitudes toward mathematics and teaching both before and after TFA teachers’ first year. There was a significant increase in both mathematical content knowledge and attitudes toward mathematics over the TFA teachers’ first year teaching. Additionally, several significant correlations were found between attitudes toward mathematics and content knowledge. Finally, after a year of teaching, TFA teachers had significantly better attitudes toward mathematics and teaching than neutral.

An investigation of the laws of thought, on which are founded the mathematical theories of logic and probabilities.

Mode of access: Internet.

An investigation of the laws of thought, on which are founded mathematical theories of logic and probabilities.

Mode of access: Internet.

It really is black and white when you look at it like this : reporting on a study into Australian professors' research and teaching priorities

Despite optimistic claims about the research-teaching nexus, Australian academics still face tension between research and teaching. The teaching and research priorities, beliefs and behaviours of 70 Professorial and Associate Professorial academics in Science, Information Technology and Engineering were examined in this study. The academics from 4 faculties in 3 Australian universities, were asked to rank 16 research activities and 16 matched learning and teaching (L&T) activities from each of three perspectives: job satisfaction, leadership behaviour, and perceptions of professional importance. The findings, which were remarkably consistent across the three universities, were unequivocally in favour of Research. The only L&T activity that was ranked consistently well was “Improving student satisfaction ratings for Teaching”. The data demonstrates that Australian government and university initiatives to raise the status of L&T activity are not impacting significantly on Australia’s future leaders of university learning.

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.

Research and/or learning and teaching : a study of Australian professors' priorities, beliefs and behaviours

This paper presents findings from an empirical study of key aspects of the teaching and research priorities, beliefs and behaviours of 72 professorial and associate professorial academics in Science, Information Technology and Engineering across four faculties in three Australian universities. The academics ranked 16 research activities and 16 matched learning and teaching (L&T) activities from three perspectives: job satisfaction, role model behaviour and perceptions of professional importance. The findings were unequivocally in favour of research in all three areas and remarkably consistent across the universities. The only L&T activity that was ranked consistently well was 'improving student satisfaction ratings for teaching', an area in which academics are increasingly held accountable. Respondents also indicated that their seniors encourage research efforts more than L&T efforts. Recommendations include that higher education rewards for quality L&T are maintained or improved and that recognition of L&T research domains is further strengthened.

The WIL (Work Integrated Learning) Report : A national scoping study [Australian Learning and Teaching Council (ALTC) Final report]

This report provides an account of the first large-scale scoping study of work integrated learning (WIL) in contemporary Australian higher education. The explicit aim of the project was to identify issues and map a broad and growing picture of WIL across Australia and to identify ways of improving the student learning experience in relation to WIL. The project was undertaken in response to high levels of interest in WIL, which is seen by universities both as a valid pedagogy and as a means to respond to demands by employers for work-ready graduates, and demands by students for employable knowledge and skills. Over a period of eight months of rapid data collection, 35 universities and almost 600 participants contributed to the project. Participants consistently reported the positive benefits of WIL and provided evidence of commitment and innovative practice in relation to enhancing student learning experiences. Participants provided evidence of strong partnerships between stakeholders and highlighted the importance of these relationships in facilitating effective learning outcomes for students. They also identified a range of issues and challenges that face the sector in growing WIL opportunities; these issues and challenges will shape the quality of WIL experiences. While the majority of comments focused on issues involved in ensuring quality placements, it was recognised that placements are just one way to ensure the integration of work with learning. Also, the WIL experience is highly contextualised and impacted by the expectations of students, employers, the professions, the university and government policy.

A case study of teaching English and multimodality with ICTs: Constraints and possibilities

Current Australian policies and curricular frameworks demand that teachers and students use technology creatively and meaningfully in classrooms to develop students into 21C technological citizens. English teachers and students also have to learn new metalanguage around visual grammar since multimodal tasks often combine creative with critical General Capabilities (GC) with that of the of ICTs and literacy in the Australian Curriculum: English (AC:E). Both teachers and learners come to these tasks with varying degrees of techno-literacy, skills and access to technologies. This paper reports on case-study research following a technology based collaborative professional development (PD) program between a university Lecturer facilitator and English Teachers in a secondary Catholic school. The study found that the possibilities for creative and critical engagement are rich, but there are real grounded constraints such as lack of time, impeding teachers’ ability to master and teach new technologies in classrooms. Furthermore, pedagogical approaches are affected by technical skill levels and school infrastructure concerns which can militate against effective use of ICTs in school settings. The research project was funded by the Brisbane Catholic Education Office and focused on how teachers can be supported in these endeavours in educational contexts as they prepare students of English to be creative global citizens who use technology creatively.

Mathematical study of complex networks : brain, internet, and power grid

The dissertation is concerned with the mathematical study of various network problems. First, three real-world networks are considered: (i) the human brain network (ii) communication networks, (iii) electric power networks. Although these networks perform very different tasks, they share similar mathematical foundations. The high-level goal is to analyze and/or synthesis each of these systems from a “control and optimization” point of view. After studying these three real-world networks, two abstract network problems are also explored, which are motivated by power systems. The first one is “flow optimization over a flow network” and the second one is “nonlinear optimization over a generalized weighted graph”. The results derived in this dissertation are summarized below.

Brain Networks: Neuroimaging data reveals the coordinated activity of spatially distinct brain regions, which may be represented mathematically as a network of nodes (brain regions) and links (interdependencies). To obtain the brain connectivity network, the graphs associated with the correlation matrix and the inverse covariance matrix—describing marginal and conditional dependencies between brain regions—have been proposed in the literature. A question arises as to whether any of these graphs provides useful information about the brain connectivity. Due to the electrical properties of the brain, this problem will be investigated in the context of electrical circuits. First, we consider an electric circuit model and show that the inverse covariance matrix of the node voltages reveals the topology of the circuit. Second, we study the problem of finding the topology of the circuit based on only measurement. In this case, by assuming that the circuit is hidden inside a black box and only the nodal signals are available for measurement, the aim is to find the topology of the circuit when a limited number of samples are available. For this purpose, we deploy the graphical lasso technique to estimate a sparse inverse covariance matrix. It is shown that the graphical lasso may find most of the circuit topology if the exact covariance matrix is well-conditioned. However, it may fail to work well when this matrix is ill-conditioned. To deal with ill-conditioned matrices, we propose a small modification to the graphical lasso algorithm and demonstrate its performance. Finally, the technique developed in this work will be applied to the resting-state fMRI data of a number of healthy subjects.

Communication Networks: Congestion control techniques aim to adjust the transmission rates of competing users in the Internet in such a way that the network resources are shared efficiently. Despite the progress in the analysis and synthesis of the Internet congestion control, almost all existing fluid models of congestion control assume that every link in the path of a flow observes the original source rate. To address this issue, a more accurate model is derived in this work for the behavior of the network under an arbitrary congestion controller, which takes into account of the effect of buffering (queueing) on data flows. Using this model, it is proved that the well-known Internet congestion control algorithms may no longer be stable for the common pricing schemes, unless a sufficient condition is satisfied. It is also shown that these algorithms are guaranteed to be stable if a new pricing mechanism is used.

Electrical Power Networks: Optimal power flow (OPF) has been one of the most studied problems for power systems since its introduction by Carpentier in 1962. This problem is concerned with finding an optimal operating point of a power network minimizing the total power generation cost subject to network and physical constraints. It is well known that OPF is computationally hard to solve due to the nonlinear interrelation among the optimization variables. The objective is to identify a large class of networks over which every OPF problem can be solved in polynomial time. To this end, a convex relaxation is proposed, which solves the OPF problem exactly for every radial network and every meshed network with a sufficient number of phase shifters, provided power over-delivery is allowed. The concept of “power over-delivery” is equivalent to relaxing the power balance equations to inequality constraints.

Flow Networks: In this part of the dissertation, the minimum-cost flow problem over an arbitrary flow network is considered. In this problem, each node is associated with some possibly unknown injection, each line has two unknown flows at its ends related to each other via a nonlinear function, and all injections and flows need to satisfy certain box constraints. This problem, named generalized network flow (GNF), is highly non-convex due to its nonlinear equality constraints. Under the assumption of monotonicity and convexity of the flow and cost functions, a convex relaxation is proposed, which always finds the optimal injections. A primary application of this work is in the OPF problem. The results of this work on GNF prove that the relaxation on power balance equations (i.e., load over-delivery) is not needed in practice under a very mild angle assumption.

Generalized Weighted Graphs: Motivated by power optimizations, this part aims to find a global optimization technique for a nonlinear optimization defined over a generalized weighted graph. Every edge of this type of graph is associated with a weight set corresponding to the known parameters of the optimization (e.g., the coefficients). The motivation behind this problem is to investigate how the (hidden) structure of a given real/complex valued optimization makes the problem easy to solve, and indeed the generalized weighted graph is introduced to capture the structure of an optimization. Various sufficient conditions are derived, which relate the polynomial-time solvability of different classes of optimization problems to weak properties of the generalized weighted graph such as its topology and the sign definiteness of its weight sets. As an application, it is proved that a broad class of real and complex optimizations over power networks are polynomial-time solvable due to the passivity of transmission lines and transformers.

The link between logic, mathematics and imagination: evidence from children with developmental dyscalculia and mathematically gifted children

This study examined performance on transitive inference problems in children with developmental dyscalculia (DD), typically developing controls matched on IQ, working memory and reading skills, and in children with outstanding mathematical abilities. Whereas mainstream approaches currently consider DD as a domain-specific deficit, we hypothesized that the development of mathematical skills is closely related to the development of logical abilities, a domain-general skill. In particular, we expected a close link between mathematical skills and the ability to reason independently of one's beliefs. Our results showed that this was indeed the case, with children with DD performing more poorly than controls, and high maths ability children showing outstanding skills in logical reasoning about belief-laden problems. Nevertheless, all groups performed poorly on structurally equivalent problems with belief-neutral content. This is in line with suggestions that abstract reasoning skills (i.e. the ability to reason about content without real-life referents) develops later than the ability to reason about belief-inconsistent fantasy content.A video abstract of this article can be viewed at http://www.youtube.com/watch?v=90DWY3O4xx8.

Linking Research and Teaching: an Applied Soft Systems Methodology Case Study

This paper links research and teaching through an applied Soft Systems Methodology case study. The case study focuses on the redevelopment of a Research and Professional Skills module to provide support for international postgraduate students through the use of formative feedback with the aim of increasing academic research skills and confidence. The stages of the Soft Systems Methodology were used as a structure for the redevelopment of module content and assessment. It proved to be a valuable tool for identifying complex issues, a basis for discussion and debate from which an enhanced understanding was gained and a successful solution implemented together with a case study that could be utilised for teaching Soft Systems Methodology concepts. Changes to the module were very successful and resulted in significantly higher grades and a higher pass rate.