Minimal surfaces. Recent stunning progress in topology, in particular a possible solution to one of the Clay Institute million dollar problems, using techniques from partial differential equations and minimal surfaces has made this area a hot topic. To attract researchers in this field to visit Australia and to train students in this area is a major part of this project.
Global Behaviour of Integrable Complex Systems. Complex systems as diverse as the weather and the solar system are modelled by non-linear equations that have elusive, unstable solutions. An infinitesimally small change in the state of the system at one place can lead to a vast change in its behaviour far away. Such extreme sensitivity is often take to be a sign of chaos, but it also occurs in completely ordered, integrable systems. Our main aim is to tackle the immense challenge of describing th ....Global Behaviour of Integrable Complex Systems. Complex systems as diverse as the weather and the solar system are modelled by non-linear equations that have elusive, unstable solutions. An infinitesimally small change in the state of the system at one place can lead to a vast change in its behaviour far away. Such extreme sensitivity is often take to be a sign of chaos, but it also occurs in completely ordered, integrable systems. Our main aim is to tackle the immense challenge of describing the global behaviour of such elusive solutions, particularly when the systems depend on many variables.Read moreRead less
Iwasawa N Groups. Semisimple Lie groups and related objects are important in mathematics, theoretical physics (e.g., quantum mechanics and string theory), theoretical computer science (e.g., construction of expanders), and many other areas. They may be studied from different points of view---algebraic, analytic, geometric and representation theoretic---and these different studies find different applications. The project aims to synthesize the different points of view, to understand their funda ....Iwasawa N Groups. Semisimple Lie groups and related objects are important in mathematics, theoretical physics (e.g., quantum mechanics and string theory), theoretical computer science (e.g., construction of expanders), and many other areas. They may be studied from different points of view---algebraic, analytic, geometric and representation theoretic---and these different studies find different applications. The project aims to synthesize the different points of view, to understand their fundamental unity, and to allow results of one type to be translated into another context.Read moreRead less
Equivalence Relations, Group Actions, and Descriptive Set Theory. This project is a contribution to basic and foundational research in the area of Pure Mathematics generally and Mathematical Logic specifically. Logic in particular appears in disciplines as diverse as Computer Science,Linguistics, and Philosophy, and the development of logic in these fields has been profoundly influenced by the foundational work of mathematical logicians. The innovative techniques introduced in this proposal will ....Equivalence Relations, Group Actions, and Descriptive Set Theory. This project is a contribution to basic and foundational research in the area of Pure Mathematics generally and Mathematical Logic specifically. Logic in particular appears in disciplines as diverse as Computer Science,Linguistics, and Philosophy, and the development of logic in these fields has been profoundly influenced by the foundational work of mathematical logicians. The innovative techniques introduced in this proposal will enable Australia to maintain a position at the forefront of Pure Mathematics, and by recruiting a recent winner of the highly prestigious Karp prize the country will be instantly established as one of the leading centers of Mathematical Logic.Read moreRead less
Knowledge for teaching primary mathematics: How teachers' pedagogical content knowledge develops and affects classroom practices and students' mathematics achievement. The study will investigate mathematics teaching in upper primary school, to identify the influence of teachers? mathematics-specific pedagogical knowledge, first on teaching practice and subsequently on students? learning outcomes. Case study evidence shows this influence is strong, but statistical evidence shows it is weak. This ....Knowledge for teaching primary mathematics: How teachers' pedagogical content knowledge develops and affects classroom practices and students' mathematics achievement. The study will investigate mathematics teaching in upper primary school, to identify the influence of teachers? mathematics-specific pedagogical knowledge, first on teaching practice and subsequently on students? learning outcomes. Case study evidence shows this influence is strong, but statistical evidence shows it is weak. This study aims to resolve this paradox by employing quality data that probes the heart of teaching and learning mathematics within a statistical study. The growth of knowledge and classroom practices of teachers graduating from two contrasting pre-service programs will also be tracked, to inform recommendations on the nature of discipline-specific pedagogical knowledge in teacher training.Read moreRead less
Conceptual Understanding and Problem-solving Approaches in the Presence of Graphics Calculators. The objectives of the project are to identify how students conceptualise mathematical relationships and formulate problem solutions, when graphics calculators are utilised. Graphics calculators are now common in schools and research is needed to provide sound bases for teaching and assessment. Investigation will centre on upper-secondary applied mathematics subjects because they are studied by a high ....Conceptual Understanding and Problem-solving Approaches in the Presence of Graphics Calculators. The objectives of the project are to identify how students conceptualise mathematical relationships and formulate problem solutions, when graphics calculators are utilised. Graphics calculators are now common in schools and research is needed to provide sound bases for teaching and assessment. Investigation will centre on upper-secondary applied mathematics subjects because they are studied by a high proportion of students for university entrance, are relevant to a wide range of careers and have received relatively little research attention in relation to calculator use. The project will yield, for school and research communities, new knowledge of mathematics learning with graphics calculators.Read moreRead less
Linkage Infrastructure, Equipment And Facilities - Grant ID: LE0211588
Funder
Australian Research Council
Funding Amount
$120,000.00
Summary
The Classroom Learning Laboratory. A facility is proposed to support the collection, configuration, storage and analysis of data (particularly video data) related to learning and teaching in classrooms. The Co-Applicants currently direct major projects at all levels of institutionalised education from early-years to tertiary, particularly in mathematics and technology education. The facility will provide the infrastructure for several large-scale projects involving many researchers and in the l ....The Classroom Learning Laboratory. A facility is proposed to support the collection, configuration, storage and analysis of data (particularly video data) related to learning and teaching in classrooms. The Co-Applicants currently direct major projects at all levels of institutionalised education from early-years to tertiary, particularly in mathematics and technology education. The facility will provide the infrastructure for several large-scale projects involving many researchers and in the long-term has the potential to catalyse new activity by educational researchers throughout Australia and significant overseas collaborative involvement. The proposed facility addresses a growing need locally, nationally, and internationally, offering both data storage and efficient access for analysis.Read moreRead less
The role of technology-enriched, technology-mediated learning communities in reforming mathematics teacher education. This project examines the impact of a technology-enriched teacher education program on beginning teachers' integration of educational technologies into secondary school mathematics classrooms. It seeks to increase theoretical understanding of how beginning teachers are initiated into a collaborative professional community featuring both web-based and face to face interaction, and ....The role of technology-enriched, technology-mediated learning communities in reforming mathematics teacher education. This project examines the impact of a technology-enriched teacher education program on beginning teachers' integration of educational technologies into secondary school mathematics classrooms. It seeks to increase theoretical understanding of how beginning teachers are initiated into a collaborative professional community featuring both web-based and face to face interaction, and how participation in such a community shapes their pedagogical beliefs and actions. Of central interest is the role of technologically knowledgeable pre-service and beginning teachers as agents ofinnovation and reform in secondary school mathematics. Outcomes will inform the design and implementation of models of pre-service teacher education and professional development.Read moreRead less
International Research Network on Learning Environments of the Future. This project represents a unique opportunity to participate in a productive, multidisciplinary international network that is developing powerful learning environments of the future- where distributed, electronically mediated, collaborative communities will become the norm. Special opportunities will be provided for doctoral students and postdocs to work with renowned researchers at the Knowledge Media Research Centre (Germany ....International Research Network on Learning Environments of the Future. This project represents a unique opportunity to participate in a productive, multidisciplinary international network that is developing powerful learning environments of the future- where distributed, electronically mediated, collaborative communities will become the norm. Special opportunities will be provided for doctoral students and postdocs to work with renowned researchers at the Knowledge Media Research Centre (Germany) and the Learning Sciences Laboratory (Singapore). The development of an undergraduate virtual international learning community will also lay groundwork for future collaborations among the participating countries. The project will chart research directions that will influence future educational settings worldwide.
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Researching Collective Argumentation in Mathematics and Science Classrooms. The project will provide evidence-based pedagogical strategies for the reform of classroom teaching and learning in the crucial areas of mathematics and science. We will develop a form of pedagogy (Collective Argumentation) that enables students to be confident in deploying mathematical and scientific knowledge and skills in relation to the economic and social choices that they make in everyday contexts. Collective Argum ....Researching Collective Argumentation in Mathematics and Science Classrooms. The project will provide evidence-based pedagogical strategies for the reform of classroom teaching and learning in the crucial areas of mathematics and science. We will develop a form of pedagogy (Collective Argumentation) that enables students to be confident in deploying mathematical and scientific knowledge and skills in relation to the economic and social choices that they make in everyday contexts. Collective Argumentation can induct students into 'habits of mind and social practices' necessary for building an innovative learning community. This project will enable us to extend this innovative approach and to further develop its effectiveness.Read moreRead less