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There is not just one mathematics taught at university level, nor is there one group of students. Mathematics is taught differently depending on the discipline and the perceived background of the student. There is engineering mathematics for the students heading towards engineering degrees, life science mathematics for those heading towards biology degrees and so on. This paper considers the phases of transitions that students experience as they embark on a course of study and then go on to professional life. We make inferences about the ways the curriculum should be designed to alleviate the difficulties of these phases as well as to take account of the capabilities that graduates will require in the workplace. It is not only where students are coming from that affects their learning but where they are heading to, in combination with their perceptions of that destination. (Contains 1 table and 1 figure.)

Teaching and learning of mathematics is challenging when lecturer and students are separated geographically. While student engagement and interaction with the course, with other students and with the lecturer is vital to mathematics learning, it is difficult to facilitate this electronically, because of the nature of mathematics. With tablet technology now becoming ubiquitous and many new and inexpensive models entering the market, it is timely to investigate how the distance student experience in mathematics can be impacted by the use of tablet technologies. This paper reports on a case study of a first year mathematics course at a regional Australian university, where distance students were provided with affordable tablet PCs. An investigation of the impact of this technology on engagement and interaction is at the centre of this study. Evidence from journals, students' assessment submissions, screen snippets, student communication and formal student evaluations is analysed. It was found that distance students acknowledged the value of tablets for communicating mathematics, particularly for assignment submission and feedback, but they also recognized the potential for easier interaction with content and the lecturer. This paper highlights the specific benefits and challenges tablet PCs present to the learning experiences in mathematics within the distance context. (Contains 10 figures.)

This paper focuses on very young students' ability to engage in repeating pattern tasks and identifying strategies that assist them to ascertain the structure of the pattern. It describes results of a study which is part of the Early Years Generalising Project (EYGP) and involves Australian students in Years 1 to 4 (ages 5-10). This paper reports on the results from the early years' cohort (Year 1 and 2 students). Clinical interviews were used to collect data concerning students' ability to determine elements in different positions when two units of a repeating pattern were shown. This meant that students were required to identify the multiplicative structure of the pattern. Results indicate there are particular strategies that assist students to predict these elements, and there appears to be a hierarchy of pattern activities that help students to understand the structure of repeating patterns. (Contains 9 tables.)

Closed captioning of instructional videos is a topic that has not seen much discussion despite its importance for hearing-impaired students and recent legal ramifications if videos are not appropriately captioned. In particular, it is unclear what best practice in captioning videos should be to benefit all learners in disciplines such as mathematics with a reliance on the development of visual explanation while providing audio narration. In this paper, we report on a study undertaken at an Australian university, to investigate the perceived level of usefulness of captions and their automatic translations in a mathematics course. We discovered that students broadly agreed that captions are a useful learning feature: to allow flexibility of where and when a video is watched, but also to help understand speaker accents, and clarify explanations that are difficult to hear in the recording. Due to the high levels of use and perceived educational benefits of closed captions in online video but limited literature, there is a significant need for new research in this area. An urgent discussion is needed to explore how students engage with closed captions, how they may support learning, and to investigate implications on instructional design of mathematical videos.

This paper is presented in two parts. Through an example the first part takes up the issue of applying mathematics to situations that form part of the life context of students--the priority expressed in three curriculum statements presented. Then, noting the particular point in time--development of a National Curriculum for Mathematics--the second part goes on to address broader curriculum issues that a purely illustrative exercise in real world problem solving might not normally engage. The chosen example relates to a real world question that is located within the domain of Australian Rules Football, and it is recognized that while this provides a familiar, and often an emotionally engaged context in the majority of states, it may not do so for all. The specific mathematical and modelling issues raised in this particular problem have no essential connection with the discussion in the final part of the paper (other than in providing illustrations), where issues regarding the place of modelling and applications in curricula are considered. For that purpose, the football example can be replaced by any authentic modelling problem. (Contains 1 figure and 2 tables.)

Trigonometry is a well known branch of Mathematics. The study of trigonometry is of great importance in surveying, astronomy, navigation, engineering, and in different branches of science. This paper reports on the discovery of flaws in the traditional definitions of trigonometric ratios of an angle, which (in most cases) make use of the most unrealistic concept of negative length (or distance). With a view to getting rid of the misleading concept of negative length (distance), the definitions of novel trigonometric ratios (falling within the purview of Year 9 to Year 10A in the "Australian Curriculum: Mathematics") have been offered first with the help of vector algebra and then subsequently employed to derive some important formulae of trigonometry. This paper first considers the traditional branch of trigonometry, examines it to see that it is very much unrealistic at its root level and finally it gives birth to the definitions of novel trigonometric ratios of an angle with the help of vector algebra so as to uproot the most unrealistic concept of negative length. It deals with a debatable issue regarding the misleading concept of negative length (distance) prevailing at the basic level of defining trigonometric ratios of an angle in the traditional literature and in fact reflects a discovery of real truth. (Contains 3 figures.)

This article is intended to assist people who have never written for a journal, or who perhaps have never even thought about doing so. In this article, the authors provide some advice for budding Australian Primary Mathematics Classroom (APMC) authors. Information on where to start, what's already been done, what will be in the paper, who will read the paper, what happens after the paper is submitted, and the technical aspects of submitting your work is included.

In this paper, the authors describe the initial stage of developing a framework designed to support out-of-field, less experiences or isolated mathematics and science teachers to make decisions about the use of resources in their teaching. The process highlighted the complexity and extent of the knowledge on which expert teachers draw in making such decisions and thus underscored the enormity of the task of teaching out-of-field. The eventual product, the Science, Technology, Engineering and Mathematics: Critical Appraisal for Teachers (STEMCrAfT) framework has proven useful not only for the target audience, but also as a tool for colleagues who take on a mentoring role. The authors begin with a brief description of teacher knowledge before describing the project and then presenting what they unearthed about expert teachers' thinking and knowledge.

Two decades ago, in an award-winning paper, Dan Kennedy (1995) likened learning mathematics to climbing a tree, for which there was only one way to climb: up a large and solid trunk. In the limited time that is available, many students give up the climb, impede others, fall off the trunk, or fail to climb the tree sufficiently well. In the case of integration, the solid trunk seems to be heavily laden with algebraic manipulation. Kennedy suggested that technology might provide help in the form of ladders to climb the tree in other ways. Just as the use of technology allowed us to bypass the numerical requirements to calculate square roots (and other aspects of basic mathematics), it now seems time to look carefully at the use of computer algebra to reconsider how much of the algebraic trunk is really needed to help students climb the tree, look around and start to explore the branches of the tree that look interesting to them.

Although refuted many times, the commonly accepted story about Indigenous communities in Australia is that they had few counting words and thus were lacking in ways to quantify amounts. In this paper, we use the case of quantifying to discuss how Indigenous mathematics can be used, not just to help Indigenous students transition into the classroom but also back into their home communities. We argue that mathematics education must take seriously its responsibility to support Indigenous students to gain school mathematics and also to help maintain the use of traditional mathematical ideas. If this does not occur, mathematics educators will contribute, intentionally or unintentionally to the loss of Indigenous knowledge that present and future generations of Indigenous people will hold them responsible for.

This paper explores how a secondary school in western Sydney used educational research as an impetus to change its mathematical education culture over a three year period. Key changes occurred in four areas: leadership; pedagogy; structures for teaching and learning; and mathematical environments. These included increased professional conversations, adoption of a numeracy lesson structure, regular use of manipulatives and open ended tasks and a structured intervention program for mathematically vulnerable students. Critical to the development of these changes were partnerships with a university academic and the CEDP system leadership team as well as school leadership participation in professional learning.

Pedagogical reform in Australia over the last few decades has resulted in a reduced emphasis on the teaching of computational algorithms and a diversity of alternative mechanisms to teach students whole number computations. The effect of these changes upon student recording of whole number computations has had little empirical investigation. As reported in this paper, Years 4 to 7 students across three schools were tested for their ability to carry out written computations. A range of recording methods were documented, many of which seemed to be adaptations of mental methods of computation. Students who used alternative methods tended to be less successful than students who used traditional algorithms. The results suggest there is merit in conducting further research into the effects of using alternative written computational methods upon students' learning of mathematics. (Contains 24 figures and 3 tables.)

The need for appraising the effective integration of technologies into teaching and learning within a disciplinary context is crucial for upholding quality teaching standards in schools and formulating professional development programs. This paper describes the development and validation of an instrument aimed at characterising the integration of technological knowledge in secondary school mathematics teachers. The Technological Pedagogical Content Knowledge (TPACK) framework is used to underpin the development and validation of the questionnaire. The questionnaire consisting of three 10-item scales was administered to a sample of 280 teachers across the state of New South Wales, Australia. The factor analysis undertaken confirms the structurally soundness of the instrument in terms of validity and reliability. (Contains 3 figures and 7 tables.)

At the start of the first formal year of schooling in New South Wales, teachers gather information on a number of aspects of children's numeracy to guide their teaching program. This information is essential to planning teaching activities to meet the needs of all students. This paper reports on some key aspects of number knowledge held by 65,000 children with an average age of 5.3 years when they started in NSW public schools in 2011. The data highlights the diverse yet interconnected number knowledge children possess when they start school, and suggests directions for further enquiry. (Contains 4 tables.)

When questioned, secondary mathematics teachers in rural and regional schools in Australia refer to their limited opportunities to engage and share experiences with peers in other schools as an under-utilised and cost-effective mechanism to support their professional learning and enhance their students' learning. The paper reports on the creation and evaluation of a network of learning communities of rural secondary mathematics teachers around a common purpose--enhancement and increased engagement of student learning in mathematics. To achieve this goal, teams of teachers from six rural schools identified an issue hindering improved student learning of mathematics in their school. Working collaboratively with support from university personnel with expertise in curriculum, assessment and quality pedagogy, teachers developed and implemented strategies to address an identified issue in ways that were relevant to their teaching contexts. The research study identifies issues in mathematics of major concern to rural teachers of mathematics, the successes and challenges the teachers faced in working in learning communities on the issue they identified, and the efficacy of the professional learning model.

This paper examines what students can tell us about their strategic decision to engage or disengage from learning. A means of accessing student knowledge and experience about teaching and learning is explicated, along with a discussion of student reasoning for making an investment in learning. It is argued that disengagement is a reasoned decision based on questions of relevance, usefulness and student capacity to be successful. (Contains 2 tables.)

This paper examines the relationships between interests and subject choice in senior secondary schooling, and between interests and occupational choices. Career interest results (N = 7477) were obtained from the "Career Interest Test" ("Version 3.1") administered on the Federal Government's "My Future" website (http://www.myfuture.edu.au) and were then compared with the nature of high school course enrolments and structure of employment. Work-related interests were fairly evenly spread across Outdoor, Practical, Scientific, Creative, Business, Office and People Contact activities. In contrast, employment in Australia was skewed towards Business and Practical activities (48.6%). On the other hand, Mathematics courses (20.1%) and Science (17.1%) dominated senior secondary school enrolments. It is possible that the interests and preferences of Australians are not satisfied either by the curriculum offered to them or by the work opportunities available. (Contains 4 tables and 5 figures.)

In writing this paper we draw considerably on the work of Jo Boaler and Leone Burton. Boaler's studies of classrooms have been particularly poignant in alerting the mathematics education community to a number of key features of successful classrooms, and how such features can turn around the successes for students who traditionally perform poorly in school mathematics. This is supplemented by the recent work of Leone Burton who worked extensively with research mathematicians in order to understand their communities and ways of working. Collectively these two seminal works provide valuable insights into potential ways to move the field of school mathematics forward. In times when there is international recognition of the plight of school mathematics, there is a need for new teaching practices that overcome the hiatus of contemporary school mathematics. (Contains 4 figures.)

The concept of a function is fundamental to virtually every aspect of mathematics and every branch of quantitative science. Presently this type of thinking is carolled at the secondary level, and yet it has many benefits for deepening the understanding of early arithmetic. This is particularly so in the way that operations can be considered as "changing" and how it explicitly illustrates the way in which addition and subtraction are inverse operations, with each "undoing" the other. With the move to introduce algebraic thinking into the elementary classrooms, this paper explores activities that exemplify this thinking with 6 year-old children. The authors collaboratively planned and implemented a series of hands-on activities over an eight-lesson program. The aim of these learning activities was to assist young children in understanding the key ideas in this area of mathematics. The activities not only encouraged active learning but also reflected the principles of socio-constructivist learning. (Contains 3 figures.)

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]

This paper is intended to provide a source of critical and theoretical reflection on the current mathematics educational objectives for Indigenous students in Australia, which are premised on acceptance of underlying concepts of 'equity'. It is not the intention of this paper to identify 'how' Indigenous knowledge can be positioned within mathematics curricula, as this would entail a philosophical inquiry much deeper than has been afforded thus far. The intent here is a consideration, facilitated through the lens of key concepts of Foucault, of some of the boundaries currently shaping the ways in which this positioning is being influenced in the mathematics, albeit neoliberal education context. Acknowledging the interplay between the social, and unconsciously shaped adoptions of what can be considered truth; knowledge; and therefore power, is a first step toward developing the openness of heart and mind needed to make real and transformative changes to education for future societies. [ABSTRACT FROM AUTHOR]

This paper argues for Teaching for Mathematising as a pedagogy that supports teaching mathematics for understanding in primary school. Mathematics education in Australia currently emphasises teaching for mathematical understanding, a shift that redirects children's learning from merely memorising computation procedures to helping children construct knowledge of the mathematics that informs mathematical concept and processes. The shift to teaching for understanding however is not reflected in students' item responses in international and national achievement studies. This paper provides one example that illustrates a learning trajectory for supporting mathematical understanding of both conceptual and procedural knowledge through teaching that builds on the framework of Teaching for Mathematising. A corresponding field-test will then be used to illustrated how students learn pragmatically. [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]

Many students are unsuccessful in the study of school mathematics, not because of some innate ability, but because of pedagogical practices. Bernstein (1996) has argued that pedagogy serves as a mechanism for cultural reproduction, so that for those students whose cultures are different from that represented in and through pedagogy, the task of constructing school mathematics is made more difficult. The paper explores the ways in which a teacher changes the pedagogic relay in order to be more inclusive of her students. Her practice is informed by understanding the ways in which pedagogy is a subtle tool for marginalization in mathematics. [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 extended the analyses of Ng (2005) and explored the differences between students with polarized schematic views in learning mathematics. Two groups of high school students from Hong Kong and Australia completed a questionnaire tapping their views on their cognitions of the self or academic self-schemas, achievement goals, learning approaches and anticipated performance. Ng (2005) located two groups of schematic students across both cultures demonstrating consistent characteristics in motivational and learning processes. The current investigation explored the differences between corresponding schematic groups found in this previous study. It was found that positive schematic students in Hong Kong are less schematicised than Australian students. In contrast, negative schematic students in Hong Kong were more schematicized than their Australian counterparts. These differences in the development of schematicised selves among students in two different cultures could be attributed to the difference in evaluation practice in two different educational systems. The results draw our attention to teaching and learning processes in schools and call for more reformative effort in Mathematics learning in order to prevent premature dropping of the subject due to the development of a negative self. [ABSTRACT FROM AUTHOR]

While mathematics education research has become increasingly concerned with issues of equity, including girls' participation in the subject, the field remains troubled with conceptualising and operationalising gender. To date, few studies of gender and school mathematics participation have moved beyond conflating gender with sex or categorising masculinities and femininities through the body. This failure to engage with gender conceptualisation has persisted despite the apparent intractability of girls' underrepresentation in senior secondary mathematics in many contexts, including Australia. In this article, I provide fresh insights into girls' mathematics participation by employing a conceptualisation of gender as heteroglossic to explore the post-compulsory mathematics participation choices of two school students, one girl and one boy. Using these theoretical tools to decentre the students' bodies, I demonstrate that the reasons why these students chose to participate in Mathematics Advanced do not distinguish them by their sex/gender, as would be expected in the monoglossic gender system. While femininity was performed, both students' subject choices were primarily characterised as masculine performances, including establishing themselves as having mathematics brains and seeking to use their mathematics participation to attain prestige. I argue that recognising and normalising girls' masculinity and boys' femininity, rather than simply categorising gender differences, will be essential to increasing girls' belonging and participation in mathematics. This will require greater attention to the differences within, and similarities between, the categories of boy and girl. [ABSTRACT FROM AUTHOR]

In Australia, many students, especially girls, choose not to study advanced mathematics in Year 12 even though their schools offer relevant subjects. Previous studies have rarely examined, using nationally representative samples of Australian students, the extent to which teenage educational experiences and occupational expectations influence gender differences in later pursuits of advanced mathematics subjects. To fill this gap, I use multilevel logistic regression models to analyse the data from the 2003 cohort of the Longitudinal Survey of Australian Youth. My results show that students’ mathematics achievement, occupational expectations and self-assessed mathematical competence are crucial in explaining why boys are considerably more likely than girls to enrol in advanced mathematics subjects. The gender gap would decrease greatly if girls were as likely as boys to perform well in mathematics, to aspire to mathematically intensive careers and to have more confidence in their mathematical abilities when they were 15 years old. [ABSTRACT FROM AUTHOR]

The practices of effective primary school teachers including students with Down syndrome in their mathematics classes are largely unexplored and many teachers feel unprepared to teach students with an intellectual disability. The authors sought to find out what these specific professional learning (PL) needs were and if they changed over time. A mixed methods study was undertaken to investigate the practices of primary mathematics teachers including students with Down syndrome in regular class lessons in two Australia educational jurisdictions. A variety of approaches was used to gain an understanding of their practices. Findings are based on responses to a questionnaire administered to teaching teams at the beginning and end of the school year. There was a strong endorsement of inclusion as an appropriate practice in primary mathematics. The PL needs of teaching teams changed across the teaching year. Early requirements concerned understanding Down syndrome and its impact on learning and behavior. As the school year progressed, PL needs changed toward a greater focus on the need for specific resources and strategies for teaching mathematics. The PL requirements of teachers included the need for 'in-time' support. The authors conclude that even if it may be infrequent when a teacher has a student with Down syndrome in a mathematics class, teachers still need access to PL that evolves across the school year, from less focus on syndrome-specific information to greater emphasis on teaching mathematics through adjusting learning outcomes and teaching approaches. [ABSTRACT FROM AUTHOR]

Transforming teachers and their approach to teaching Indigenous students requires partnerships with the Indigenous community, planning, small steps, and funds. This article illustrates how teachers can change when funds are available to assist schools and communities to implement appropriate and effective professional development, to establish partnerships between school and community, to revise teaching approaches and curriculum, and to value family and Aboriginal cultural heritage. The larger study involved four schools in a Stronger Smarter Learning Community in a small rural city, the whole city community, and the interaction among the schools. Interviews with principals, teachers, Aboriginal students, and their community highlighted the increasing interaction between the Aboriginal community and the schools, the increasing warmth and welcome extended both ways, and the impact that these approaches are having on curriculum, teaching, and learning. This article presents the impact in one of the schools involved in the mathematics project. The findings illustrate how the projects facilitated changing teachers' perceptions, skills, and practices and implemented curriculum, and resulted in a culturally responsive, place-based mathematics education. [ABSTRACT FROM AUTHOR]

Learning support in mathematics and statistics has arisen and developed in response to student needs in many universities. After discussing background to such support, this article gives a brief overview of learning support in mathematics and statistics in Australian universities as found in an Australian Learning and Teaching Council project and of the provision in Queensland University of Technology. Qualitative and quantitative data on student usage and student progression are discussed. Analysis of data for students studying mathematics and statistics contributes to growing evidence that such learning support is fulfilling needs across the range of student capabilities, including students choosing mathematics degree programs. The article closes with discussion of the contribution of learning support in the spectrum of learning in mathematics and statistics. [ABSTRACT FROM AUTHOR]