Main streams and fine rivers : thinking the aporetics of edge

This paper takes up the question (reframed by Deleuze and Guattari) of where expansion takes place: at the ends or from the centre. Despite the connotations of mediocrity that can be attributed to the term ‘mainstream’, it is possible to rethink what happens at close range as the space of radical openings. Writers can often believe that what is most abnormal or fringe will produce the highest probability of creative ‘event’. The question, however, can be posed – framed by the lineage of deconstruction – whether the key to unlocking any system of totality or closed possibility may lie in a very central (although physically peripheral) location. If, instead of the classical image, expansion may occur from re-imagined ‘middles’ rather than conventional ‘margins’, this reading of where potential can arise may offer a more resilient model than that of fragile peripheries, forever exposed to being amputated from staid centres of status and restricted participation. Drawing on the writings of Deleuze and Guattari, Derrida and Badiou, this paper seeks to unsettle any simplistic approach to the notion of edge, reinscribing it within the repetitiveness of our situations, to argue that right in the middle of the so-called mainstream, there might be the fine rivers of aporia that when encountered in thought can constitutes gates to that which is most radical in writing and other creative practices.

An investigation of middle secondary students' mathematical conceptions of rate

This study identified four educationally critical aspects of ‘rate’ through analysis of phenomenographic, video-recorded interviews with Year 10 students. Further analysis indicated understandings in one representation or context were not necessarily transferable.

Development of a mathematical model for solar module in photovoltaic systems

A mathematical model of a solar module is presented. This model takes into account solar model temperature and solar radiation. The experimental data of a solar module under natural environment condition (NEC) have been obtained to determine the model parameters. The experimental results are compared with those calculated by using a mathematical model. It shows that the mathematical model accurately simulates the current-voltage characteristics of the solar module under the NEC and therefore is suitable for photovoltaic system design and performance analysis.

The mathematical and science skills of students who are deaf or hard of hearing educated in inclusive settings

This study examined the science and mathematics achievements of 16 Year 9 students with hearing loss in an inclusive high-school setting in Western Australia. Results from the Monitoring Standards in Education (MSE) compulsory state tests were compared with state and class averages for students with normal hearing. Data were collected from three cohorts of Year 9 students across a 3-year period (2005‐2007). Results from mathematics MSE9 and the MSE9 science assessments showed that the majority of students with hearing loss performed below the state average (88%). Findings in this study suggest that students with hearing loss demonstrated more mathematical strength in the areas of space and measurement, which use visuo-spatial skills. Results for students with hearing loss in the five sections of the science assessment suggest more consistency across the different areas tested in the MSE. Comparisons with the MSE9 English paper for the 2005 cohort of students with hearing loss suggest a strong relationship between reading and writing skills and performance on mathematics and science assessment. In particular, questions with high language content created difficulty. On the science assessment, questions requiring a written explanation appeared to be particularly challenging. These findings have implications for teaching and learning in these crucial areas for students with hearing loss in inclusive secondary school settings. Greater attention to the interpretation of the language of mathematics and to writing about science concepts may help to improve outcomes for students with hearing loss on statewide assessments

Deepening the mathematical knowledge of secondary mathematics teachers who lack tertiary mathematics qualifications

A professional learning program for unqualified practising secondary mathematics teachers regarding senior secondary mathematics teaching is described in this paper. The VCE (Victorian Certificate of Education) mathematics professional learning program for senior secondary mathematics was designed for practising secondary teachers of mathematics who had no experience of teaching advanced senior secondary mathematics and who had not completed the recommended qualifications. Professional learning episodes, artefacts and reflections of three teachers who participated in the program are analysed to identify the development of these teachers' mathematical and pedagogical content knowledge (PCK). The PCK framework developed by Chick et al. was used to analyse teachers' knowledge, and the cases of teachers' knowledge presented in the paper illustrate the entwining of knowledge of mathematics and knowledge of teaching and learning The findings indicate that a program designed for senior secondary mathematics can enable practising teachers to deepen and broaden their understanding of junior secondary mathematical pedagogy.

Dean's great discovery : multiplication, division and fractions

Multiplication, division and fractions are 'hotspots' for students in the middle years with many students experiencing difficulty with these concepts (Siemon, Virgona & Cornielle, 2001). Arrays effectively model multiplication and help children develop multiplicative thinking and learn multiplication facts (Young-Loveridge, 2005). In this article we show how an open-ended array problem enabled a Grade 5/6 student to think about the relationship between multiplication, division and fractions. In the article we describe the project and 'hot spot' mathematical tasks that we used and provide some background on multiplicative thinking before presenting the case and a commentary (Western Melbourne Roundtable, 1997) of one student's exploration. This case was documented whilst we were working on a collaborative project with a team of upper primary teachers and a group of pre-service teachers at a local primary school.

Connecting with the horizon : developing teachers' appreciation of mathematical structure

A professional learning program for teachers of junior secondary mathematics regarding the content and pedagogy of senior secondary mathematics is the context for this study of teachers’ mathematical and pedagogical knowledge. The analysis of teachers’ reflections on their learning explored teachers’ understanding of mathematical connections and their appreciation of mathematical structure. The findings indicate that a professional learning program about senior secondary mathematics can enable practicing teachers to deepen and broaden their knowledge for teaching junior secondary mathematics and develop their practice to support their students’ present and future learning of mathematics. Further research is needed about professional learning approaches and tasks that may enable teachers to imbed and develop awareness of structure in their practice.

Teaching secondary school mathematics : research and practice for the 21st century

For the last decade or so, educational policy makers and researchers in many countries have been calling for significant changes to the way mathematics is taught in secondary schools. Australian mathematics curriculum documents now promote learning goals that go beyond mastery of a pre-determined body of knowledge and procedures - the traditional emphasis on facts, skills, formulae - to include mathematical reasoning and problem solving, communication, and real world applications. There is also pressure to move away from over-reliance on teacher-centred practices such as exposition and individual seatwork, towards activities that promote learners' involvement in constructing, applying, and evaluating mathematical ideas. Further impetus for reform comes from research recommending that if learners are to develop mathematically powerful forms of thinking and habits of mind, then classrooms should immerse them in the authentic practices of the discipline by supporting a culture of collaboration and sense-making. Teaching Secondary School Mathematics - incorporates recent developments in research and practice and applications to teaching mathematics in Australian secondary schools. Covering such areas as curriculum, pedagogy and assessment; teaching mathematical content; equity and diversity in the classroom; and professional and community engagement, it is an invaluable resource for all practising and pre-service mathematics teachers.