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This essay addresses the problem of the nature of curriculum integration, and an attempt is made to lay the basis for a theory of integration. An aspect of the relationship between mathematics and physics is discussed. (Author/MLF)

Focuses on the condition of the private schools in Australia. Increase in the enrollments of private schools; Success of state teacher unions and parents' committees with enrollment impact assessments in preventing funding of new schools or classes; Interpretation of the patterns of specialization in the humanities, the physical sciences and mathematics.

Examines the integration of science, mathematics and technology curriculums among ninth-grade students in Australian middle schools. Identification of one of the most contested areas of middle school education; Factors which influence the integration of these subjects; Methods used to collect data.

This paper reports selected findings from a study of number sense proficiency of students aged 8 to 14 years in Australia, Sweden, United States, and Taiwan. It comments on the meaning and importance of number sense, the development of the assessment instruments, and student responses to the items. Some implications for classrooms of the findings are then discussed. [ABSTRACT FROM AUTHOR]

After the invasion and occupation of their land by Europeans, Indigenous Australians were expected to benefit from a Western education system based on that of the dominant Europeans. Gradually educators realized that Aboriginal children learn differently and that Indigenous culture and pedagogy has validity and strength. Of course, educators also need to be acutely aware of the diversity of Indigenous cultures in Australia and that there is not a monolithic sense of Aboriginal identity or Aboriginal pedagogy. Dispossession and alienation, poor health and few employment opportunities must also affect educational interest, attendance, application and performance. In this paper the characteristics of Indigenous learners are examined and pedagogical strategies to assist in both students' learning and teachers' delivery are explored. The message conveyed in this paper has particular relevance for teaching mathematics to Aboriginal learners. It is also of considerable value in teaching mathematics to nonAboriginal students, in Australia and elsewhere. [ABSTRACT FROM AUTHOR]

Argues that adults' relationship with mathematics has three components: cognitive, affective, and social. Focuses on the affective and social components and suggests that the differences between informal mathematics and formal school mathematics lead to the former not being recognized as mathematics. Believes this situation should be analyzed from three interrelated perspectives: the adult's mathematical skills; the adult's conception of mathematics; and the adults' self-perception in relation to mathematics. (Author/VWL)

An event based on "find the rule" problems has been part of the University of Canberra Maths Day since 1985. In this paper, the authors describe the Swiss event, its context, its aims, its logistics, and gives examples of problems used in past events. The type of problems used, how they are used in an event at the maths day, and how the event evens out the competition and stops strong schools dominating are also discussed.

The term "quantitative literacy" is used in this article to reinforce its importance in catering for reform-based curricula in Australia. The medium chosen for the problems discussed in this paper is the newspaper. The purpose of this article is to tie together traditional views of the importance of problem solving with the current aims of numeracy and quantitative literacy. In doing this, the author considers another angle on the development of quantitative literacy. Watson (1997) suggested a hierarchy for the related field of statistical literacy, which is easily adapted in the wider milieu. The hierarchy suggests three tiers or steps in the development of the goal of quantitative literacy: (1) The terminology needs to be understood; (2) This terminology then needs to be understood within the social (or scientific) context in which it is used; and (3) There needs to be a critical awareness that prompts questioning of claims in context that are made without proper justification. (Contains 5 figures.)

Estimation is an important skill for everyday living. Good estimators usually have a sound knowledge of basic facts, understand place value and use a variety of strategies to make their estimates. This paper describes an activity which is designed to provide students with opportunities to practice their rounding strategies with addition and multiplication. In particular, the activity shows that estimates fall within limits and that sometimes, an exaggerated estimate will not be useful.

In this article, we provide an understanding of the term numeracy as it is used in Australia and a description of numeracy education in this country. In particular, we discuss the role of outcomes-based curriculum frameworks and outline the dominant teaching approaches. The focus is on students with learning difficulties and how they are identified and supported in schools. We create two vignettes based on real students with difficulties in numeracy, which highlight two of the most common problems. We report on the prevalence of learning difficulties in numeracy in Australia and describe some of the initiatives related to the assessment and enhancement of learning in numeracy that are being undertaken in various states in Australia. Finally, we identify some of the future challenges facing the Australian education system in this area. These challenges relate to teacher knowledge, mandated assessment, and the role of parents. We conclude the article by calling for the evaluation of current assessment and intervention initiatives as well as the development of a national program to support the goal of numeracy for all students. [ABSTRACT FROM AUTHOR]

Metacognition has been accorded a role in both mathematical problem solving and in the learning of mathematics. There has been consistent advocacy of the need for the promotion of metacognitive activity in both domains. Such advocacy can only be effective if the advocated process is well understood. In this paper we have four goals: to describe a "multi-method" technique developed to study student mathematical metacognition; to set out the structural elements and configuration of a coherent model of metacognition in the domain of mathematical problem solving; to report on the empirical utility (and validity) of this model; and, to report the insights into student mathematical metacognition arising from the research. Multi-Method Interview Tasks are appended. (Contains 4 figures.)

On her death in 1910, Florence Nightingale left a vast collection of reports, letters, notes and other written material. There are numerous publications that make use of this material, often highlighting Florence's attitude to a particular issue. In this paper we gather a set of quotations and construct a dialogue with Florence Nightingale on the subject of statistics. Our dialogue draws attention to strong points of connection between Florence Nightingale's use of statistics and modern evidence-based approaches to medicine and public health. We offer our dialogue as a memorable way to draw the attention of students to the key role of data-based evidence in medicine and in the conduct of public affairs.

This paper outlines the practical aspects of a project aimed to offer access to numerate knowledge for preschool children by providing them with take-home numeracy kits. A Koori preschool in an urban regional area of New South Wales, Australia, was involved in the project. The centre catered for 18 four- and five-year-old children. The two main resources for the project were numeracy-related activities, and interactive adult and peer support. In the first part of the paper observational transcripts of the children playing with the kits at the preschool are analysed according to Foundation and Transition Level outcomes and indicators for number (NSW Department of School Education, 1994). The second part of the paper clarifies and synthesises key aspects of culturally-situated learning: the children's mathematical language and problem-solving; the responsiveness of the teaching strategies; and the congruence between early childhood education philosophies and national numeracy policies.

Service industries are becoming an increasingly important part of our economies. Not surprisingly there is a corresponding interest in statistics about service industries. The challenges in compiling statistics are often very different to other industries. This paper describes the programme for service industry statistics in the Australian Bureau of Statistics. It also describes some of the more interesting developments in Australia – new presentations in statistics such as satellite accounts; globalisation statistics including the activities of foreign affiliates; knowledge based economy and society statistics; direct volume measurement particularly for largely non-market industries such as health and education services; and price statistics for service industries such as finance, telecommunications and computer software services. These statistics are very important for measuring productivity for example. [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 reviews Fisher's research program, showing how it constituted a theoretical basis for Darwin's evolutionary, genetical and experimental work, and identifies those fields where Fisher, through his influence on colleagues and students, caused some of his aims to be carried through in Australia, particularly in experimental design and evolutionary genetics. [ABSTRACT FROM AUTHOR]

Aim: The ability of nurses to perform accurate drug dosage calculations has repercussions for patients' well-being. How best to assist nurses develop competency in this area is paramount. This paper presents findings of a study conducted with undergraduate nurses to determine the effect of three instructional approaches on the learning of this skill., Method: The quasi-experimental study exposed participants to one of three instructional approaches: integrative learning, computerised learning and a combination of integrative and computerised learning. Quantitative and qualitative approaches were used to explore differences in the instructional approaches and gain further understanding of the learning process., Results: There was no statistical difference between the three instructional approaches on knowledge acquisition and transfer measures, other than measures for procedural knowledge, which was significant (F(2,47) = 3.33 at p < .044). A least-significant difference post hoc test (alpha = 0. 10) indicated computerised learning was significantly more effective in developing procedural knowledge., Conclusion: The provision of instructional strategies, which facilitate development of conditional knowledge and automaticity, is necessary for competency development in dosage calculations. Furthermore, the curriculum must incorporate authentic tasks and permit time to support competency attainment.

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]

Traditionally, primary schools place minimal emphasis upon relations and transformations as objects of study. In their research, the authors have found the young children can engage in conversations about equivalence and equations (Warren & Cooper, 2005a) and functional thinking (Warren & Cooper, 2005b). Fundamental to relations and transformations is the concept of the function, that is, how the value of certain quantities relate to the value of other quantities (Chazan, 1996), or how values are changed or mapped to other quantities, referred to in the literature as co-variational thinking. This paper reports on some recent classroom teaching that attempts to examine repeating patterns and use children's understandings of repeating pattern to begin to explore concepts related to functional thinking.

This study examined the continued gender imbalance in mathematics participation in senior high, which has implications for adolescents' future careers. It confirms persisting greater male participation in maths-related educational and occupational choices among this sample of Australian youth. Gendered course-taking in maths, along with participation intentions for maths-related careers, were explained using the Expectancy–Value framework of Eccles and colleagues (Eccles (Parsons) et al., 1983; Wigfield & Eccles, 2000). The influences of maths-related self-perceptions, intrinsic and utility values, and perceived task difficulty were assessed using longitudinal data from a sample of 442 adolescents spanning Grades 9 through 11 in Sydney, Australia. Gendered maths-related self-perceptions and intrinsic values were the major influences on gendered educational participation in senior high maths, which subsequently predicted maths-related career aspirations—over and above prior mathematical achievement. Utility value showed a curvilinear relationship with maths-related occupational intentions moderated by gender, whereby girls with the highest utility values planned for highly maths-related careers, while boys with mid through high utility values planned similarly highly maths-related careers. Recommendations focus on ways to enhance participation in maths, especially for girls. [ABSTRACT FROM AUTHOR]

Several researchers have noted how children's whole number schemes can interfere with their efforts to learn fractions. An Australian study found that children who were successful with the solution of rational number tasks exhibited greater whole number knowledge and more flexible solution strategies. Behr and Post (1988) indicated that children needed to be competent in the four operations of whole numbers, along with an understanding of measurement, for them to understand rational numbers. This paper describes a "hands on" approach developed by researchers that focuses on the use of paper folding, fraction walls and number lines to develop an understanding of fractions using a measurement model. (Contains 8 figures.)

Mathematical computation consists of both written computation and mental computation. The strategies for mental computation can be used to check the reasonableness of written computations. Mental computation has two distinguishing characteristics: "it produces an exact answer, and the procedure is performed mentally, without using external devices such as pencil and paper" (Reys, 1984, p. 548). It is important to consider the accuracy and efficiency of various mental computation strategies and this can be useful to discuss with students. Discussion about different strategies will enable students to consider different approaches and work towards development of efficient mental strategies for computation. Utilising a variety of strategies and methods for computation will enable students to develop a better understanding of computation processes and number sense. In this article, the authors put forth a strong case for an emphasis on developing mental calculation strategies with students, and suggest helpful teaching approaches to achieve this. (Contains 4 figures and 2 resources.)

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.)

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]

This project aimed to quantitatively measure the ability of first year science students to transfer their mathematical skills and knowledge to a physical context. An instrument used in earlier studies to measure transfer of mathematical knowledge was modified for this project, and tested with 49 student volunteers. This paper presents the Transfer Index, a novel way of measuring the degree of transfer of the students' mathematics skills and knowledge. It is demonstrated that the Transfer Index is a useful way of quantifying transfer and that it has predictive validity in a natural educational setting. (Contains 7 tables, 4 figures and 5 footnotes.)

Inquiries into the state of mathematics and science education in Australia express the need to make the curriculum more relevant and meaningful to students' lives. However, such a vision requires that teachers understand how relevance can enter mathematics and science classrooms in a meaningful and appropriate way. This paper asks, how is relevance thought of in mathematics as compared with science, and what problems might this pose for teachers moving between mathematics and science? [ABSTRACT FROM AUTHOR]

This article reviews "problem solving" in mathematics in Australia and how it has evolved in recent years. In particular, problem solving is examined from the perspectives of research, curricula and instructional practice, and assessment. We identify three key themes underlying observed changes in the research agenda in Australia in relation to problem solving: Obliteration, Maturation and Generalisation. Within state mathematics curricula in Australia, changes in the language and construction of the curriculum and in related policy documents have subsumed problem solving within the broader category of Working Mathematically. In relation to assessment, research in Australia has demonstrated the need for alignment of curriculum, instruction and assessment, particularly in the case of complex performances such as mathematical problem solving. Within the category of Working Mathematically, recent Australian curriculum documents appear to accept an obligation to provide both standards for mathematical problem solving and student work samples that illustrate such complex performances and how they might be assessed. [ABSTRACT FROM AUTHOR]

In the teaching of calculus, the algebraic derivation of the derivative (gradient function) enables the student to obtain an analytic "global" gradient function. However, to the best of this author's knowledge, all current technology-based approaches require the student to obtain the derivative (gradient) at a single point by implementing differentiation using first principles. This paper shows that the ability of spreadsheets to fit a polynomial to a set of discrete (x,y) points enables students to not just evaluate a gradient at a single point, but at a whole family of points, thus generating the analytic global gradient function of secants without doing any algebraic manipulations. Students can then perform "numerical experiments" to see the effect of taking the limit as the secants tend to tangents of the original function. Finally, students can derive the rules for differentiation through exploration and experimentation, again, without doing any algebraic manipulations. This approach enables the class to focus on the concepts being taught, rather than being hindered by the mechanics of (for example) trying to factorize a cubic polynomial. (Contains 4 figures and 1 table.)

This paper reports initial findings from an intervention study evaluating the affordances of a variety of interactive multimedia tools on kindergarten students' representations of fractions. The study engaged 21 kindergarten students in a whole-class technology-based mathematics intervention conducted over 12 weekly teaching episodes. A comparison group of a parallel kindergarten class of 22 students maintained their regular mathematics program. Dynamic visual tools, including the interactive whiteboard (IWB), digital learning objects (DLOs), interactive CDs and "constructive" software were utilised by the intervention class to promote concept development. The intervention students' pre- and post-intervention drawings indicated substantial growth in cognitive infrastructure and symbolic notations. Qualitative analyses of the intervention students' digital screen recordings and drawings provided complementary evidence of more advanced, flexible and alternative representations of fraction concepts than those displayed by the comparison group. (Contains 10 figures and 1 table.)

The article focuses on Robert Fleming and his works. It states that Fleming received his Bachelor in Science degrees in mathematics and physics from Queen's University in Belfast, North Ireland in 1958 and 1959. He also finished his masteral degrees in physics from the same university in 1962 and 1985, respectively. He was employed as an Assistant Lecturer at Queen's University from 1962 to 1964 befor he left fot the Royal Military College of Science in Shriverham, Great Britain. In 1976 Fleming he became a Senior lecturer in the Department of Physics at Monash University in Victoria, Australia. He retired in 2000 as Reader and he remains as an Honorary Senior Research Fellow and still manages a laboratory.

Aligned with recent changes to syllabuses in Australia is an assessment regime requiring teachers to identify what their students `know' and `can do' in terms of the quality of understanding demonstrated. This paper describes the experiences of 25 secondary science and mathematics teachers in rural schools in New South Wales as they explore the changing nature of assessment and its implications on their classroom practice. To help reconceptualise these changes, teachers were introduced to a cognitive structural model as a theoretical framework. Throughout the 2-year study, teachers attended a series of professional development sessions and received ongoing consultative support. Each session was taped and transcribed while interviews were conducted with each teacher at the end of both years. Analysis of these data using a grounded theory approach identified seven major components of teacher practice impacted by the study. The core component was questioning while the six contributing components were teachers' pedagogical practices, attention to cognition, teaching strategies, assessment linked to pedagogy, classroom advantages for students, and classroom advantages for teachers. These findings represent a major shift in teachers' perceptions of assessment from a focus on the accumulation of students' marks to one of diagnosis as a means of directing teaching to enhance students' scientific and mathematical understandings. [ABSTRACT FROM AUTHOR]

Recent international studies have highlighted the success of students from Hong Kong in mathematics and problem-solving, and have begun to suggest some of the factors associated with this success. Other studies have suggested that Hong Kong students are averse to risk-taking, favouring memorisation and imitation in their solution strategies. Year 5 students in Hong Kong and Australia were given mathematics assessments of different types: orally presented mental computation problems, and a performance task that was undertaken in normal classroom conditions. Observations of the students' approaches to these tasks in the classroom and analyses of their responses revealed similarities and differences between the two countries. The implications of these findings are discussed in light of the curriculum diversity and differences in metacognitive skills. [ABSTRACT FROM AUTHOR]

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.)

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.)

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]

Information graphics have become increasingly important in representing, organising and analysing information in a technological age. In classroom contexts, information graphics are typically associated with graphs, maps and number lines. However, all students need to become competent with the broad range of graphics that they will encounter in mathematical situations. This paper provides a rationale for creating a test to measure students' knowledge of graphics. This instrument can be used in mass testing and individual (in-depth) situations. Our analysis of the utility of this instrument informs policy and practice. The results provide an appreciation of the relative difficulty of different information graphics, and provide the capacity to benchmark information about students' knowledge of graphics. The implications for practice include the need to support the development of students' knowledge of graphics, the existence of gender differences, the role of cross-curriculum applications in learning about graphics, and the need to explicate the links among graphics. (Contains 8 tables and 1 figure.)