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Memory has received very little attention in mathematics education literature in recent years, except in the negative connotation of rote learning. However since memory and cognition are very closely linked memory has an important part to play in many, if not most aspects of learning mathematics. The relationships between memory and understanding, memory and assessment, memory and culture, and memory and problem solving are discussed and a case is made for a much more positive role for memory in mathematics education research.

The persistent differential outcomes in mathematics education have been cause for considerable research and concern for over 40 years. This paper considers the social context of contemporary mathematics and its implication in the outcomes for disadvanatged students. It is argued that reliance on individualistic models of theory and research need to be considered in conjunction with the social context

Reflecting on a body of research work can sometimes lead to the recognition of areas of opportunity for research that have gone largely unnoticed. In this paper we consider three such opportunities in the area of research on the teaching and learning of probability and statistics: i) Following up on students' initial thinking to watch for future transitions; ii) Investigating students' thinking on variability; and iii) Posing research questions that begin with what students can do rather than pointing out what they cannot do. Situations from research tasks, past and future, are used as starting points the discussion.

The present study was the final phase of a three-year project in which problem-posing programs were developed for the third, fifth, and seventh grades. The aims of the study were as follows: 1. to trace the development of seventh-grade students' problem posing across a range of mathematical situations; 2. to trace the developments of individual children as they participate in a 3-month classroom problem-posing program; 3. to monitor changes in children's perceptions of, and attitudes towards, problem posing and problem solving; 4. to identify links between students' problem-posing and problemsolving abilities.

The implementation of mathematical problem solving in New South Wales (NSW) primary classrooms is being explored. The results of part of a survey that has been administered to a sample of primary school teachers regarding their beliefs and practices in relation to problem solving is explored. Teachers report that they regularly use strategies such as whole class discussion including a focus on suitable problem solving strategies, concrete materials and teacher modelling. They rarely have calculators available for students, allow students to choose problems or spend much time on one problem.

Qualitative data from lecturers and students were used to identify factors which were perceived as making the most important contributions to students' academic success or failure in first-year mathematics courses. A questionnaire based on this information highlighted similarities and differences in the perceptions of lecturers and students about influences on students' success and failure. The results confirm the importance of motivation and suggest further research is needed in the areas of active learning and student effort and workload.

This paper discusses the experiences of nine women in their high school mathematics and their personal theories on gender and mathematics. Interviews with the women showed that while their performance was above average up until Year 10, only one student completed higher mathematics. In general, support from mathematics teachers was seen as very negative. Further, their personal theories on gender and mathematics are the result of interaction between their own experiences and the research knowledge they encountered at university during their completion of a teacher training course.

This paper uses data from an international study of number sense in Australia, the United States, Sweden and Taiwan to investigate students' misconceptions and error patterns in fraction and decimal concepts. Selected items that were administered to two or three age levels were analysed. It was found that misconceptions about basic concepts were prevalent, and these persisted even among 14-year-olds. Results suggest the need for more meaningful treatment of fraction and decimal concepts, and some relocation of these topics in the curriculum.

Ethnomathematics considers the parallels between traditional indigenous mathematics perspectives and western ones. Generally shared truths are revealed, but notable differences also emerge. This paper, drawn from research in progress, examines Fijian notions of education and in particular ways of mathematising which are embedded in our cultural and everyday activities. The data show that Fijian systems for identifying, naming and classifying are coherent and adaptable. They are distinct from, but. complementary to, western methods.

This paper reports on a study that examined the importance of multiplicative structure and whether, after several years of formal instruction in the decimal number system, Year 6 students had acquired an understanding of this structure. To this end, 173 Year 6 students were tested with a penciland- paper instrument developed to assess the decimal-number numeration processes that are normally taught in primary school and from which 45 students (32 high performing, 13 low performing) were selected for interviewing on tasks related to multiplicative structure. The interviews revealed that only the most proficient students (~ 90% for tenths and hundredths in the test) had acquired a structural schema of multiplicativity that enabled access to application tasks.

This paper presents data from a two year study on Year 7 and 9 students, who were classified using a new construct of Non-Anglo-Cultural-Background (NACB). This was used to determine results at the individual level which showed for example that the NACB students generally were more confident and less anxious about their school mathematics than were their ACB counterparts. The paper also discusses some of the problems concerned with doing research into cultural issues in mathematics education.

This paper reports on the quantitative data gathered during the second and third years of a 5 year longitudinal investigation into the attitudes of preservice primary teachers towards mathematics and toward the teaching of this subject. Findings indicate that teacher education programs can improve the attitudes of preservice teachers towards mathematics, and that this shift in attitude can continue to improve well into the first year of teaching.

Many students enrolled in first year university mathematics displayed consistent misunderstanding with some essential algebraic skills. Analysis of an algebraic test given to first year university students in 1996 highlighted five major categories of concern. Further algebraic tests were given to 1997 first year university mathematics students, second year university mathematics students and senior secondary students. The five categories were confirmed as major areas of consistent algebraic difficulties. Many of these difficulties did not seem to improve with higher mathematical learning.

This paper addresses negotiation as a social process related to the practices of mathematics (and science) classrooms and associates the need for negotiation with the occurrence of uncertainty. It is our argument that one pathway to knowing is via the resolution of uncertainty, that the process of resolution is fundamentally negotiative, that negotiation is mediated by language, that language presumes intersubjectivity, and that the matter of intersubjectivity is meaning. Data is presented illustrating the role of intersubjectivity as both mediating agent in the resolution of uncertainty, and as product of the negotiative process. Empirical evidence is reported regarding the occurrence of student uncertainty with regard to academic content encountered in classroom settings and the means by which these uncertainties are resolved.

Identified relationships between figures, based on their properties, is an important characteristic of Level 3 thinking in the van Hiele theory. However, there has been no research directed at how such relationships, leading to class inclusion, evolve. This study, involving indepth interviews with 24 secondary students, addresses this issue by considering their attempts at grouping seven different triangle types. The results reveal important features about perceived relationships between figures, and the existence of a developmental path.

Several theories have been proposed to describe the transition from process to object in mathematical thinking. Yet, what is the nature of this "object" produced by the "encapsulation" of a process? Here we outline the development of some of the theories and consider the nature of the mental objects (apparently) produced through encapsulation and their role in the wider development of mathematical thinking. Does the same developmental route occur in geometry as in arithmetic and algebra; what about axiomatic mathematics? What is the role played by visualisation?

Although the use of diagrams is advocated in mathematics, support for this instructional practice appears to be intuitive rather than evidentiary. A case study was used to evaluate the effectiveness of instruction in diagram generation with Year 5 students. The results suggest that although instruction can have a positive effect on students' diagram generation, the success of the program is dependent on the teachers' understandirig of the role of diagram generation in problem solving and how diagram generation can be facilitated.

This paper reports on Years 8, 9 and 10 students' knowledge of percent problem types, type of solution strategy, and use of diagrams. Non- and semi-proficient students displayed the expected inflexible formula approach to solution but proficient students used a flexible mixture of estimation, number sense and trial and error instead of expected schema-based classification methods.

The effectiveness of a highly regarded short-answer pencil-and-paper test (Mathematics Competency Test, published in 1996 by the Australian Council for Educational Research) was investigated. In the study, 182 students-in Years 5 through 8, in 8 classes in NSW and Western Australia-answered the test questions and were interviewed. About 28% of responses were either (a) correct but students showed less than full understanding; or (b) incorrect, but students showed at least partial understanding, of the key concept/s) and skill(s).

In an industry-driven VET sector major educational decisions are made, not by educators, but by representatives of industry. Mathematics curricula for scientific industries have been designed under a positivist, technicist paradigm without an adequate research base. These are unlikely to be responsive to industry needs for a variety of reasons which include the methodologies used by two separate projects which impact on the curriculum framework, the superimposition of CBT requirements, and the failure to address the issue of transferability.

Students at the University of Melbourne participated in a larger study that aimed to explore the critical factors contributing to decisions to pursue mathematics at the tertiary level. Of particular interest and concern to the Department of Mathematics was knowing the composition of the student cohort, the students' reasons for choosing to study mathematics, and whether they would continue into higher levels. The findings and their implications are reported in this paper.

Students' difficulty with mathematical word problems such as the 'students and professors' problem has been studied in mathematics education research. The difficulty may lie with the language or with choosing an appropriate schema. Translating these word problems into a language such as Chinese creates a new avenue of research, since the syntax of Chinese is different from the English version. This paper will discuss the results of part of a cross-cultural research masters thesis investigating problem processing of mathematical word problems in Chinese and English. The results suggest that while language appears to be a factor in the processing of relational word problems, the selecting of an appropriate schematic model is also an important factor.

This study documents a school-based professional development activity conducted in a secondary school in the Philippines where five secondary mathematics teachers and the head of school participated in a program of action research. Qualitative research techniques were used to provide rich information on the changes made in teachers' pedagogical knowledge, practices and beliefs. Within the parameters of certain constraints, it emerged that action research as a form of professional development led to important changes.

In this study I look at university students' orientations to learning statistics - how they feel about learning it, their conceptions of the subject matter and their approaches to learning it. I use complementary methods of analysis to understand the relationships among students' appraisals, conceptions, approaches and attainments on assessments. The findings reveal underlying dimensions of the variables and present dramatically different profiles of students' experiences. Students' learning is linked to a complex web of personal, social and contextual factors.

An initial framework to be used as part of a study that is exploring how students construct initial algebraic understanding is proposed. As a starting point, Pirie and Kieren's dynamical model of growth of mathematical understanding is proposed. A qualitative ethnographic case study approach to be used in the research is described.

Communication is a vital part of assessment if student and assessor are to understand each other and not talk past each other. I consider why this misinterpretation should occur and what can be done to attempt to improve student's understanding of the intent of the question writer. Student answers on one question in particular are used to demonstrate some student misunderstandings.

Often students' tendency in approaching calculus is to follow an algorithm or manipulate symbols. Mathematics educators seek to provide a range of experiences that develop mathematical ideas in a cognitive manner so that the learner both knows and understands. In this paper I describe how students used spreadsheets and symbolic manipulators to investigate the processes and concepts of integration, using the modules of work to supplement traditional approaches to integration. They gained a significant improvement in proceptual understanding, especially with regard to misconceptions exhibited in the pre-test.

Secondary education in Victoria began in the 1850s, and the struggle for control of the mathematics curriculum dates back to this time. However this struggle was intensified with the emergence of public secondary education this century. By the 1960s University control was under attack, principally due to two main factors - the attempt to modify course content on the basis of a new mathematical paradigm, and the professionalisation of mathematics. The critical role that the "New Maths" played in these processes is examined.

This paper continues an ongoing research investigation of teacher beliefs towards the learning and teaching of mathematics. The focus is the espoused beliefs of a group of secondary teachers. Analysis of returned questionnaires allows secondary teachers to be profiled according to correlations of their espoused beliefs about mathematics, mathematics learning and mathematics teaching, along a continuum of learning and teaching approaches.

We present data from two children who participated in a teaching experiment to investigate fraction learning and the role whole number knowledge might play in it. A major source for the children's experiences was an operator-like computer program called CopyCat. How these children were constrained in their efforts to succeed with set tasks because of limited facility with whole number sequences, is demonstrated. Analyses of selected teaching episodes are discussed.

Sixteen Form 1 and 2 students worked in pairs to solve problems involving decimal fractions. Their discussions were analysed to see what kind of conflicts led to learning about the meaning of decimals. Useful conflicts arose from those written into the problems, differences between calculator results and expectations, discussions with a peer, and differences between out-of-school experience and calculations. The most profitable conflicts could be classified as those that brought about what Piaget called beta reactions.

This study examined changes in students' probabilistic thinking and writing during instruction emphasizing writing to learn experiences. A class of fifth-grade students with no previous experiences in writing during mathematics made significant gains in probability reasoning and writing; however the correlation between probabilistic thinking and writing was not significant. Analysis of focus students revealed that their writing changed from narrative summaries to reasoned patterns and generalizations. However some used invented representations without interpretation and were reluctant to write in mathematical contexts.

In this paper airline ticketing desk operations are studied in order to develop a greater understanding of numerical workplace knowledge as seen from a non-essentialist account of mathematical knowledge. In the first part of the paper alternative approaches to knowledge use are discussed and their epistemological groundings noted. Next, transcripts are analysed in order to ascertain the logic of ticket exchange task performance. Methods used for the study include those derived from linguistic philosophy; decisive use is also made of the Vygotsky inspired notion of artifact mediation within task performance. Finally, an attempt is made to find the place of numerical knowledge within the workplace knowledge of the episodes observed.

This paper investigates the use of area integration rules. 36 children in Grades 4, 6 and 8 were given area judgement tasks, using rectangles of varying areas and perimeters. Information Integration Theory procedures revealed both additive and multiplicative judgement rules that determined the children's responses. It was found that judgement rules change intra-individually but there does not appear to be a relation between judgement rule and Grade level. The form of presentation of the rectangle was found to be important.

Delineation of the quantum of influence of extra-cognitive auxiliary inputs like affective factors may help to explain gender differences by illuminating the mechanics of cognitive functioning in early adolescents engaged in mathematics problem solving. Part of the data from a semi-longitudinal study is analysed in this paper to explore the relationship between algebraic problem solving ability and affective factors based on the differential problem solving abilities among junior high school students. The results show that there is a difference in this relationship for female and male students. A transient refractive affective state of high achieving girls could be the reason for compromising any advantage over their male counterparts.

Using detailed information from the certificate records of 5,825 Year 10 students in Tasmania, this study found that the level of mathematics students access -- advanced, intermediate, or low -- is strongly related to socioeconomic background and school attended. Differences across schools, measured using multilevel modelling techniques, are related to the type of school (government, Catholic or independent), enrolment size and social composition. Residential segregation, the uneven distribution of selective schools, and school-level policies are the mechanisms discussed in explaining the origins of social area and school differences.

In the early 80s Mayberry (1981) developed a diagnostic instrument to be used in an interview situation to assess the van Hiele levels of pre-service primary teachers. At the University of New England, a detailed testing and interview program was undertaken, replicating the Mayberry study. The students' responses to the Mayberry items were assessed using two different methods, first by Mayberry's method, and second, using the method developed by Gutierrez, Jaime and Fortuny. This paper presents an evaluation of the two coding systems.

This paper focuses on the affective and cognitive behaviours of a small group of grade 7 students who worked for eight lessons on an extended mathematical task in the classroom. Data sources included videotapes, field notes, students' reactions, self-report affective measures, and interviews. By drawing on these data sets, inferences were made about cognitive and affective behaviours influencing learning and the students' longer term involvement with mathematics five years later, in grade 12.

This paper provides case studies of the attempts of four young children (a high achieving first-grader, a high achieving kindergarten student and two low achieving first-graders) to solve three tasks involving three-dimensional shapes and their two-dimensional representations. Detailed descriptions of students' solutions are provided; these highlight the appropriateness of challenging geometric tasks for young students. High achieving students spontaneously made more frequent use of formal geometric terms when explaining their actions.

This paper compares the perfonnance of first-language Chinese and English secondary students in Hong Kong on a set of items requiring the students to express simple relationships algebraically. It is suggested that the different types of response produced arises from the distinct syntactic structure of a given expression when translated from English into Chinese. The results are discussed in terms of the construction of mental models and evidence is also considered from interviews conducted with a small sample of the students.

Over 1995 and 1996, the researchers conducted a study of the factors which influence Australian students' selection or non-selection of mathematics subjects at the upper school level. Some 6 000 students from Western Australia, Queensland and Victoria responded to a survey seeking to determine such factors. This paper describes the outcomes of the survey and suggests that students' cognitive style orientations have a significant role to play in the subject selection process.

An evaluation of a statistical training program.

Group tests of Number Sense were devised and administered to students aged 8, 10, 12 and 14 in Perth, Western Australia and in Missouri. The development and structure of the tests are described, and some results are presented. Research building on this work and conducted in Sweden and Taiwan is described, and implications for research and teaching are discussed.

Despite controversy, the van Hiele levels continue to be used as an important framework for developing geometry teaching programs and for interpreting students' understanding of geometrical ideas. However, as they stand, the level descriptors offer a restrictive base. These cause problems when questions are posed outside of the direct notions of properties of figures, class inclusions· and deduction about which the Theory is explicit This paper is an initial attempt to broaden the level descriptors in a way that is consistent with the original ideas of the theory but which allows for more inclusive criteria. To assist in this process ideas drawn from the SOLO Taxonomy are employed.

Individual interviews were used to explore 128 seven-year-old children's understanding of place value, to see how this related to the strategies that they used to solve written addition problems. Children who understood the place value of two digit numerals were more successful at solving written addition problems, but a surprising number of children with face value understanding could also solve the problems. The variety of strategies (successful and unsuccessful) that the children used are described, and the implications for teaching algorithms are discussed.

This paper discusses some characteristic ways of reasoning within the discipline of statistics from the perspective of someone who is both a practising statistician and teaching statistician. It is conjectured that recognition of variation and critically evaluating and distinguishing the types of variation are essential components in the statistical reasoning process. Statistical thinking appears to be the interaction between the real situation and the statistical model. The role of variation in statistical thinking and the implications for teaching are also discussed.

The difficulty in teaching and learning place value concepts is well documented. One suggestion to overcome this is to use computer manipulatives to help students "bridge the gap" between symbols and concrete materials. A teaching experiment investigated Year 3 students' place value learning using either conventional or computer-generated place value blocks. Observations of one lower-achievement student using computer software indicate that well-designed mathematics software offers advantages to teachers for overcoming students' misconceptions not possible with conventional materials.

There have been many policy recommendations for students to become more active in their learning of mathematics, and to make sensible choices of computation method. Year 5-7 students were asked to choose among calculator, written and mental computation methods to answer a series of multiplication questions, with a teacher either absent or present. Findings indicate that the students made choices based on what they believed the teacher "really" wanted, rather than on valid mathematical factors.

This paper reports on a study which investigated the effects of a computer algebra system, Derive, on the learning of, and attitudes towards mathematics amongst engineering students in Papua New Guinea. The study compared the traditional course approach to an experimental approach integrating Derive. The findings indicate no statistically significant differences in achievement performances between control and experimental groups, nor in students' attitudes towards mathematics. However, positive indicators of enjoyment, motivation and usefulness of mathematics observed with the experimental group are considered educationally significant.

This paper reports on research using the Questionnaire on Teacher Interaction (QTI), and provides validation data for the first use of the QTI with a large sample of mathematics classes. The effect of teacher-student interpersonal behaviour on the students' attitude towards their mathematics class was investigated and the dimensions of the QTI were found to be associated significantly with student attitude scores. The paper also describes how mathematics teachers could use the QTI as a basis for reflecting on their own teaching.

The paper considers the way that a cohort of prospective primary school teachers engage with a mathematics education subject in their initial teacher education program. They appear to do so through the medium of three selves. This metaphor of the three selves is explained, and the implications of using this metaphor to promote positive interactions in mathematics education subjects are discussed.

This study was concerned with finding what characteristics of data, such as direction of skewness, degree of skewness and degree of kurtosis, affected students' ability to use histograms and boxplots for detecting non-symmetry in the parent poplation. The study found that while there was no consistent difference between boxplots and histograms in the proportion of students detecting non-symmetry in the parent popUlation, the direction of skewness did have a significant effect, with more students detecting skewness when the data was displayed in a left -skewed orientation than when the same data was displayed in a right-skewed orientation. This result is consistent with research reported in the psychological literature where many, but not all, studies have shown an over emphasis on the left hand field of view for normal subjects. Other findings of the study are given and suggestions for further research made.

Following a previous attempt to develop a theoretical framework for research into values in mathematics education, a further attempt is made using the three domains of values, culture and mathematics education. The valuing process is examined and the distinction between beliefs and values defined. The four dimensions of culture are linked with the valuing process and the elements in the teaching/learning act to construct a framework which could be the basis for further research.

To what extent are calculators used in primary school classrooms? Data sources are scarce and somewhat dated for judgements to be made. This paper outlines some of the findings of a recent survey undertaken in Western Australian primary schools. Data related to the issue of young children using calculators will be discussed. Initial findings suggest that integrated calculator use is rare with most use being extra to mathematics learning and trivial in nature.

There is a need to find ways to assess performance of students in mathematics which also provide some assurance to the community of the quality of the work of the students. As part of a larger project which sought to develop assessment tasks, we found that tasks could be used to assess the level of students' mathematical knowledge, that teachers could make holistic judgments on students' responses. We also argue that it is necessaty to use a range of tasks to assess mathematical performance on particular aspects of the curriculum.

This paper focuses on better understanding children's early space and measurement knowledge. Five Year 1 students from each of two schools and five Kindergarteners from one of those schools, were given an initial and final assessment in arithmetic, space and measurement. Students' advancements in arithmetic and space were not accompanied by advancements in measurement. Arithmetically more able students were found to be more able on space and measurement tasks and there was great variation in students' space and measurement knowledge.

This paper is a quantitative review of research on cooperative learning in secondary mathematics. Results from the analysis demonstrate that cooperative learning has an overall positive effect in the cognitive domain as well as the social and affective domain. The paper also identifies several potential moderators of the effects and makes implications for further research reviews in the field.

If students are to successfully tackle tertiary mathematics, one prerequisite is the mastery of a number of basic concepts. Despite the best efforts of teachers, many students develop mathematical misconceptions. Is it possible to eliminate these misconceptions? In this study, a strategy based on Piaget's notion of cognitive conflict was employed for this purpose. The method used was found to be successful in reducing, and in some cases totally eliminating, the frequency of misconceptions exhibited by a class of students.

This paper describes on-going action research into the collaborative professional development of the authors themselves. It was based on data collected through story telling and weaving. The results suggest that this is an effective tool for self initiated professional development.

A review of the politics of mathematics education in Australasia was completed in 1996 just as there was a change of government in Australia. In the year since cautious optimism in Australia has become deepening concern as more and more problems confront the mathematical sciences in schools and universities. This paper examines recent political developments in Australia and their effect on the mathematical sciences. Particular attention is paid to mathematics education research and to issues concerning participation.

There appears to be a lack of information about what teachers at large believe and understand about assessment and how this may impact on their instruction in mathematics and subsequently on students learning of mathematics. In an effort to address this issue, this paper explores views about assessment held by a small sample of secondary teachers in St. Vincent. The results indicate that the teachers perceived limitations in traditional assessment methods.

This paper argues that the two models of curriculum development currently used to interpret Australian mathematics education history-the Colonial Echo model and the Muddling Through model-are both deficient, and proposes a more complex model-the Broad Spectrum Ecological model. This considers the physical, social and intellectual forces operating within a specific environment. One small aspect of mathematics education history, the introduction of probability teaching into Australian schools, is used to illustrate the superiority of this model.

This paper addresses the broad issue of relating research findings with pedagogical practices by analysing the responses to questions set in an undergraduate statistics examination using Eisner's connoisseurship and criticism approach, supported by general pedagogical and psychological principles. Comparisons are made between responses to the same course given in two different countries to assess similarities, differences, and weaknesses in order to indicate possible ways in which future courses might be modified to improve student learning.

This paper explores some observed confusions held by pre-service teachers about concepts of probability and statistics. The writer uses information about confusion and misconceptions held by pre-service teachers gained by examination of teaching assignments written by her tertiary students. It considers some other research in this field and makes some suggestions about what steps may be taken to provide pre-service teachers with a better understanding of stochastics.

This paper presents some of the findings of a pilot study concerning gender differences in behaviour in a secondary mathematics classroom that used computers. Analysis of interactions between students and the teacher and engagement with the task, the computer and the mathematics suggest some evidence of gender difference. A number of factors were hypothesised as relating to behaviour and this paper discusses the preliminary findings in relation to students' experience with computers and their style of interaction with computers.

This paper takes seriously the claim that postmodernism has undermined our 'modem' understandings of mathematics educational research. It therefore seeks to reinterpret this understanding with particular reference to curriculum implementation in a manner that confronts the challenge that postmodernism has posed. In order to do this the paper clarifies how postmodernism discredits the assumptions on which curriculum implementation has been erected. It argues for a reconstruction of the relationship between curriculum inquiry and the truths of curriculum reform.

In response to misconceptions students hold with understanding the concept of a variable new teaching approaches have been introduced into many Australian Schools. These approaches entail generalising from visual patterns and tables of data. While recent research has reported many of the difficulties students experience with these new approaches, it has failed to delineate why these difficulties are occurring. It seems that these approaches call on an array of reasoning processes that, in the past, have not been considered as important to the algebraic domain. This paper delineates some of these processes and pinpoints particular characteristics of successful students.

In task-based interviews 48 Kindergarten to Year 6 children were asked to choose between two jars containing different mixes of red and yellow toy bears, with the aim of giving themselves a better chance at drawing out a red bear. The children applied a variety of strategies, ranging from idiosyncratic reasons to proportional reasoning. These strategies are examined in relation to the ratio pairs presented in each jar and are compared to other strategies reported in the literature.

A sample of 480 students from grades 2, 4, 6 and 8 were interviewed concerning their recognition of abstract angles in nine familiar physical situations. The major factor influencing students' interpretation of an angle situation was not the number of arms of the abstract angle visible in the physical situation. Even by the end of grade 8, many students had difficulty recognising angles in situations where both arms of the angle were not visible. Implications are drawn for the teaching of angles.

Throughout introductory tertiary statistics subjects, students are introduced to a multitude of statistical concepts and procedures. One such term, significance, has been given considerable emphasis in the statistical literature with respect to the topic of hypothesis testing. However, systematic research regarding this concept is very limited. This paper investigates students' conceptual and procedural knowledge of this concept through the use of concept maps and standard hypothesis tests. Eighteen students completing a first course in university-level statistics were interviewed twice during a 14-week semester.

This paper contains observations of the mathematics curriculum in action of two schools, one Australian and one Japanese, both situated in Victoria, Australia. While school structure and mathematical content in both schools were substantially similar, there were notable differences, for example, continuous school based and government testing in the Australian school compared with the relatively few but highly significant examinations set by Japanese institutions as student entrance requirements. Permeating these differences were divergent mathematical histories, and social and cultural factors in the two countries.

The influence of goal orientation beliefs upon mathematics achievement was investigated over almost three years. Task involvement, ego orientation and achievement in mathematics to achievement.were measured with an sample of 243 primary and lower secondary students. While task involvement correlated with achievement at a low but significant level, regression analyses revealed that this factor did not predict achievement over and above the prediction from the earlier Progressive Achievement Test in Mathematics score. At no stage did ego orientation relate.

This paper describes the development of a procedure for assessing numeracy at school entry. What began more than decade ago as a research tool consisting of a collection of tasks to assess children's numeracy, has developed into a classroom assessment device in which various numeracy tasks are embedded within a shopping game, with the potential to assess a broad range of mathematical understandings in addition to those included in the game itself.