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Mathematics education is seen as a right for all children, and important to ensure a prosperous future. However, in Australia and other nations, rural students and students from low socioeconomic backgrounds both perform less well in mathematics and are less likely to pursue advanced mathematics. This paper presents a case study of a low socioeconomic status, rural government school that has high engagement and achievement in senior mathematics, despite its setting. The study uses a conceptual framework informed by Appreciative Inquiry and the theory of Practice Architectures to explore the activities and facilitatory elements that have likely contributed to the school's mathematics success. Rather than being attributed to one or two key programmes, the school's mathematics success seemed associated with a collection of whole-school factors. Setting high expectations while providing proactive learning support, differentiating instruction, emphasising the value of mathematics, linking mathematics to careers, and building mathematics teacher capacity were all associated with the school's higher than expected mathematics performance. Rather than hindering the school's mathematics programme, its small size and rural context were used to enable practices that contributed to mathematics success. [ABSTRACT FROM AUTHOR]

In this paper we explore how participation in a constructivist-oriented, classroom aligned mathematics intervention program advanced the learning and positive dispositions of Grade 1 students who were failing to thrive when learning mathematics. Intervention programs are an approach to differentiated instruction that some schools adopt, but there are questions about whether such interventions advance equity and inclusion for students. To provide insight about these issues, we draw on data from the Extending Mathematical Understanding for All study in NSW, Australia (2016-2020) to address two research aims. The first aim was to evaluate the effectiveness of the EMU intervention approach for progressing the mathematics learning of students who were failing to thrive mathematically, and for closing the performance gap with their peers. The second aim was to consider the impact of participating in EMU intervention on students' dispositions for learning mathematics. The findings confirm the potential of intensive constructivist-based intervention approaches for closing the performance gap for students who were not thriving in mathematics, and for improving the learning dispositions of these students. However, two years after the intervention, the performance gap was again apparent for many students. It is likely that a one-off intervention program is not sufficient for enabling all students to thrive mathematically, and that well-focused classroom-based differentiated instruction and further intervention support may be warranted for some students. [ABSTRACT FROM AUTHOR]

This paper identifies binary oppositions in the discourse of mathematics education and introduces a binary-epistemic model for (re)conceptualising these oppositions and the epistemic-pedagogic problems they represent. The model is attentive to the contextual relationships between pedagogically relevant binaries (e.g., traditional/progressive, student-centred/teacher-centred, discovery/transmission, constructivist/behaviourist) and epistemically relevant binaries (e.g., concrete/abstract, pure/applied, interpretivist/positivist, subjective/objective) that operate in mathematics classrooms. The premise of this paper is that ways of knowing mathematics (i.e., epistemologies) are actualised in ways of teaching mathematics (i.e., pedagogies), and vice-versa. The binary-epistemic model describes oppositional, equipositional and parapositional ways of knowing and teaching in relation to these binaries. We argue for a more a relational-contextual or parapositional approach to binary polarities that have otherwise proven divisive in mathematical discourse. In the context of the new Australian Curriculum, we illustrate epistemically differentiated ways of teaching measurement in a Year 5 mathematics classroom. [ABSTRACT FROM AUTHOR]

This paper identifies binary oppositions in the discourse of mathematics education and introduces a binary-epistemic model for (re)conceptualising these oppositions and the epistemic-pedagogic problems they represent. The model is attentive to the contextual relationships between pedagogically relevant binaries (e.g., traditional/progressive, student-centred/teacher-centred, discovery/transmission, constructivist/behaviourist) and epistemically relevant binaries (e.g., concrete/abstract, pure/applied, interpretivist/positivist, subjective/objective) that operate in mathematics classrooms. The premise of this paper is that ways of knowing mathematics (i.e., epistemologies) are actualised in ways of teaching mathematics (i.e., pedagogies), and vice-versa. The binary-epistemic model describes oppositional, equipositional and parapositional ways of knowing and teaching in relation to these binaries. We argue for a more relational-contextual or parapositional approach to binary polarities that have otherwise proven divisive in mathematical discourse. In the context of the new Australian Curriculum, we illustrate epistemically differentiated ways of teaching measurement in a Year 5 mathematics classroom. [ABSTRACT FROM AUTHOR]

This paper focuses on the role of language and some issues associated with identifying appropriate language of instruction for three foundational Maths ideas in the Early Years of schooling. These are considered in relation to the project: Strong Literacy and Numeracy in Communities -- Numeracy Component. This had two broad goals, firstly to work with paraprofessional Indigenous teachers to determine an effective language of instruction for specific foundational numeracy concepts and secondly, to create a resource to enable this to be shared. Only two of the project sites are considered here. Both are in Yolŋui communities in northeast Arnhem Land, where English is not widely used for interaction. We focus on the use of first language, Djambarrpuyŋu, for the children's concept development. The English language that can be used is determined by what is possible for early second language learners. We will share some samples of the Djambarrpuyŋu identified for teaching early number ideas. We will describe the process by which suitable expressions for the key ideas in Djambarrpuyŋu were identified and some issues that arose regarding the use of language for comparing numbers. The project showed how 'Maths' lessons are a time both for concept development and for language development. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In early years' (primary grade) classrooms in Australia repeated patterns are commonly explored as an early introductory activity to mathematics. Most young students have an extensive knowledge of and exhibit success in copying, continuing, creating and transferring patterns into other media. By contrast, research indicates one of the most difficult concepts with which students grapple in their later years of elementary school is the notion of ratio. This paper reports on a design (teaching) experiment conducted over a fourlesson period in two classrooms comprising 51 students whose average age was 9 years and 6 months. The focus of these lessons was using students' knowledge of repeating patterns, an understanding that traditionally remains in the precinct of early years, to scaffold the introduction of ratio. The theoretical frameworks that underpinned the classroom interactions and learning were the socio-constructivist theory of learning, inquiry-based discourse and the simultaneous use of multi-representations to build new knowledge. The results show that after a short intervention period, repeating patterns can act as effective bridges for introducing the ratio concept. They also show that particular representations and teacher actions assisted students to identify ratio, recognize equivalence between particular ratios, and begin to represent these ideas in abstract notation systems. [ABSTRACT FROM AUTHOR]

John Anthony Hartigan was born on July 2, 1937 in Sydney, Australia. He attended the University of Sydney, earning a B.Sc. degree in mathematics in 1959 and an M.Sc. degree in mathematics the following year. In 1960 John moved to Princeton where he studied for his Ph.D. in statistics under the guidance of John Tukey and Frank Anscombe. He completed his Ph.D. in 1962, and worked as an Instructor at Princeton in 1962-1963, and as a visiting lecturer at the Cambridge Statistical Laboratory in 1963-1964. In 1964 he joined the faculty at Princeton. He moved to Yale as Associate Professor with tenure in 1969, became a Professor in 1972 and, in 1983, became Eugene Higgins Professor of Statistics at Yale--a position previously held by Jimmie Savage. He served as Chairman of the Statistics Department at Yale from 1973 to 1975 and again from 1988 to 1994. John was instrumental in the establishment of the Social Sciences Statistical Laboratory at Yale and served as its Director from 1985 to 1989 and again from 1991 to 1993. He served as Chairman of the National Research Council Committee on the General Aptitude Test Battery from 1987 to 1990. John's research interests cover the foundations of probability and statistics, classification, clustering, Bayes methods and statistical computing. He has published over 80 journal papers and two books: Clustering Algorithms in 1975 and Bayes Theory in 1983. He is a Fellow of the American Statistical Association and of the Institute of Mathematical Statistics. He served as President of the Classification Society from 1978 to 1980 and as Editor of Statistical Science from 1984 to 1987. John married Pamela Harvey in 1960. They have three daughters and three grandchildren. [ABSTRACT FROM AUTHOR]