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This paper describes a preliminary investigation of some of the beliefs held by preservice primary teachers at the commencement of their mathematics education studies and at the end of the first of a sequence of three mathematics education units. The beliefs of this cohort will be monitored in subsequent years with a view to identifying factors that influence them in a positive direction. Initial results provide promising evidence that mathematics education courses can, within current university resourcing constraints, influence the beliefs of pre-service teachers.

The disjunctures that exist between research and practice and ways to bridge them are examined. An underlying theme of the presentation is a consideration of the roles played by beliefs and values in decision making about school mathematics, and the conflicts that can exist due to unexamined opposing beliefs and values.

This paper describes an ongoing research and professional development project involving 70 Victorian primary schools (1999-2001), seeking to identify processes for supporting and enhancing mathematics learning in the early years of school. The project involves three main components: the development and refinement of a set of research-based “growth points” in mathematical understanding in various mathematical domains; the creation and use of a one to-one, task-based assessment interview with all children twice a year; and a multi-level professional development program. In this paper, the characteristics and effects of each of these three components is discussed. Data is presented on growth in student understanding across the mathematical domains and grade levels (K-4). A discussion of the professional growth of project teachers and the view of the teacher underpinning the research is also given.

This is the report of the establishment and first stages of a major project working with senior secondary students in low socio-economic schools in Auckland, New Zealand. The project is the result of a Scoping Study conducted during 1999/2000, and is planned to involve eight decile 1 & 2 schools in one region of Auckland over a 5-year period. It is aimed at enhancing the achievement and participation of Year 12 and Year 13 mathematics students in their final years at school and promoting their transition into mathematical programmes in tertiary education. This paper outlines the results of the Scoping Study, the research objectives of the project, the methodological principles being used, and the preliminary results of the first 6-months work.

This paper reports on the initial findings of a longitudinal study aimed at investigating the impact on preservice primary teachers’ mathematical beliefs, knowledge and practices of a mathematics education course utilising a situated learning perspective. Other research in this area has found that preservice primary teacher’s beliefs have remained unchanged as a result of their teacher education programs. Preliminary findings from this study contradict these results. It is suggested that the utilisation of a multiplicity of learning contexts may explain this discrepancy.

Mathematics education reforms in numeracy focus on children’s thinking and problem solving strategies. Cognitively Guided Instruction (CGI), developed by researchers at the University of Wisconsin, provides a model for both mathematics pedagogy and the professional development of teachers. In the same way that children’s learning of mathematics in the classroom builds on their previous understanding, the activities of CGI workshops are deigned to build on the previous understanding of the participant teachers. This paper discusses the challenges and changes to participants, both teachers and teacher educators, of a CGI-based professional development numeracy programme.

There has been little research into either the writing process for mathematics programme plans or their content. Ideally the scheme provides a template for the teacher to follow throughout an academic year, giving guidance on topics, level and depth of presentation, and examples of suitable tasks for learning and assessment. In New Zealand schemes are also part of a school’s accountability process. This paper reports some findings of a study that examined the preparation and composition of such schemes at the year 9 level of schooling from a sample of fifteen North Island New Zealand state secondary schools in provincial cities. This paper does not explore classroom teaching or learning; rather it focuses on the mathematics department policies and the documents that guide classroom practice at year 9.

An important component of the algebra needed to do mathematics with a computer algebra system (CAS) is symbol sense, analogous to ‘number sense’ in arithmetic with a four function calculator. This paper presents an assessment of a component of symbol sense: algebraic expectation. We describe the results of 169 Year 11 students including interesting individual items and correlations with other measures. Initial analysis shows the test is successful in monitoring both algebraic skills and students’ certainty in these skills, both of which affect success with using CAS.

The ‘Who and mathematics’ instrument is used to measure the extent to which mathematics is considered a male, female or gender-neutral domain. Data from students in grades 7-10 in Australia and Greece were compared to explore whether a cultural dimension was evident. A small sample of Australian students attending a school with strong Greek affiliation completed a trial version of the instrument that included 20 out of the 30 items on the final version. Findings from these students provided an additional perspective – the role of competing cultures, Greek ethnic background and the Australian milieu.

This paper presents a case study of a single student, documenting changes in her approach to learning mathematics and her beliefs about mathematics, which she attributes directly to her experience of collaborative learning. The context in which these changes took place is described. The evidence is then analysed to tease out possible key factors contributing to desirable change. Important among these are the level of challenge of the task, its intrinsic interest, and group composition. Factors that may inhibit change are also discussed.

Research shows that significant changes at the senior levels of schooling have implications for teaching and learning approaches in the prior years of schooling. In 2000 a new structure was implemented for school based assessment in the Victorian Certificate of Education. This paper draws on data from a survey of senior mathematics teachers focusing on their responses to the impact these changes are making on the teaching and learning in junior level mathematics. Data on reported frequency of investigations, problem solving, modelling and group work is presented. While the majority of teachers reported that no changes have, or will occur, there is evidence to indicate that a trickle down effect is in motion, the implications of which are discussed. Together this data will provide a base-line for future comparative studies.

This paper reports on research into the emergence of communicative practices within a primary mathematics classroom. Transcripts of whole-class talk provide qualitative evidence that students can use areas of mathematics as means of communication when they are operate in a classroom culture that provides them with the support necessary to positively experience the ways in which mature communities of mathematicians communicate. Characteristics of classroom talk which facilitate such positive experiences are summarised and discussed.

This paper reports on aspects of preservice teachers’ statistical knowledge as assessed through an open-ended problem-solving task. This type of task is considered to be a useful and valuable way of assessing the development of data sense. The level of a teacher’s knowledge is known to be critical in relation to effective teaching. This study indicates that the level of statistics thinking of preservice students presents some challenges for teacher educators to address within their courses and programmes.

Improving numeracy for Indigenous students is a high priority in Australian education. One approach is that taken by the INISSS (Improving Numeracy for Indigenous Students in Secondary Schools) project in Tasmania. The INISSS program was evaluated in part through measuring students’ numeracy outcomes using specially developed performance assessment tasks. The results from this process show that the program was successful in meeting its goal of improved numeracy outcomes.

Research has not identified a general hierarchy of difficulty for calculations performed mentally. This study aimed to provide baseline data about students’ mental computation competence across grades 3 to 10. Rasch modelling techniques were used to develop a scale of mental computation competence, based on 1452 students’ responses to 238 mental computation items organised into overlapping tests. Eight levels of competence were identified. Grade based scales were also developed for grades 3 to 8. These suggested possible curriculum effects since particular items behaved differently across the grades.

By using a questionnaire previously used in Australia, we examined students’ attributions of success and failure in mathematics in the People’s Republic of China, and the results were compared with the previous results from Australia. Differences were found in the attribution patterns between students from China and students from Australia. Students from China view environment and effort as important factors of success in mathematics, while students from Australia regard task and environment as important for their success in mathematics. Students in China attribute their failure in mathematics to lack of effort more than to other factors, while students in Australia attribute their failure in mathematics to task difficulty more than to the other factors. Boys and girls both demonstrate between country differences in their attributions. The role of values and beliefs in the two societies is discussed, as are the variables that affect the attribution differences.

A group of pre-service primary teacher students were asked to evaluate the probability of some everyday events, by (i) ranking the events in order of likelihood, (ii) assigning each event a probability word, and (iii) giving each event a numerical probability. Mismatches between ranking and numerical values were found, some students had difficulty estimating values for events with probabilities close to certain or impossible, and the ambiguity of some probability words was revealed. Students indicated that they thought that making such evaluations was associated with numeracy understanding, but not to the same extent as a more traditional computational number question.

This is a report of a study in which we aim to characterise the quality of subject-matter and pedagogical content knowledge constructed by a group of four student teachers in the domain of functions. A key feature of the results is that these teachers tended to emphasise the visual representations in their understanding of functions without sufficient attention to their symbolic equivalency. As expected, their pedagogical content knowledge was not well developed. We discuss the implications for subject-matter growth from the framework of modelling and schema development.

This paper reports on a portion of a larger case study of academically talented Year 9 students studying mathematics via Telematics in rural Western Australia, which investigated perceived advantages and disadvantages of such an approach. The paper focuses particularly on student-teacher and student-student interaction during such lessons – a strategy that was actively fostered by the teacher-researcher – and also on students’ responses to these teacher efforts to improve student participation in lessons. This endeavour was generally found to be successful, with most students recognising the benefits of such an approach, even if some were still reluctant to participate actively. Such active participation, while important in teaching and learning in general, is vital in the use of such a medium as Telematics, and it is recommended that the teachers involved be given special training in this regard.

Engaging children in mathematical investigations is advocated as a means of facilitating mathematical learning. However there is limited guidance for teachers on ways to support young children engaged in investigations. This study provides insights into the mathematical literacy required by seven-to-eight-year-old students undertaking investigations. Examples of difficulties are described in relation to problem solving, representation, manipulation, and reasoning. While mathematical investigations can enhance young children’s learning, teachers need to provide guidance to address necessary skills and knowledge.

In order to establish what constitutes current primary practice in Victoria, video and other data were collected from a stratified random sample of ten year 3 and 4 classrooms in Victoria. Three video vignettes, representing the contrasting pedagogical flows captured on the videotapes, were produced to stimulate discussion in three separate Focus Groups of randomly selected teachers, principals, and mathematics teacher educators and consultants. This paper reports on their views of what constitutes current Victorian practice in primary mathematics.

A teaching experiment was conducted with a small group of prep children considered ‘at risk’ mathematically, to explore the effect of explicit instruction on the development of tens facts through visualisation of the ten frame. After the two-week instructional period, children could mentally recall all addition and subtraction tens facts without counting, and this performance was considerably higher than the class average. In this paper, the sequence of instruction is documented, highlighting the influence of instruction upon tens fact development.

This paper addresses the final year of a 3-year longitudinal international study, which addressed the development of 9th and 10th grade students’ statistical knowledge and reasoning processes. The study engaged students in the construction of data-based projects, which involved the processes of designing, analyzing, interpreting, representing, communicating, and thinking critically and reflectively. This paper addresses students’ reasoning on one of the final activities of the program, namely, students’ construction of newspaper articles. The findings highlight the importance of placing special emphasis on students’ abilities to think critically about data and beyond data.

In this paper we report on findings from classroom observations of a series of government, Catholic, and independent, primary and secondary, co-educational and single-sex schools. Analyses based upon pre- and post-lesson interviews together with videotaped lesson observations reveal that intended values may or may not be nominated explicitly by individual teachers. In turn, these may be observed as explicitly taught, implicitly taught, or not at all. This suggests that there are tensions between intended and implemented values.

Different classification schemes are applied to investigate the impact of CAS availability on the 2000 VCE Mathematical Methods examinations. The degree of CAS impact on individual questions is also investigated with specific examples of CAS sensitive and CAS resistant questions illustrated and assessment issues with different brands of CAS calculators discussed. For both examinations, CAS either did not impact or impacted slightly upon a similar combined proportion of the total marks (approximately 60%).

Attitudes towards success in mathematics, and attributions for such success, among tertiary mathematics students, were investigated using a semi-structured writing task. A large majority reported no expectation of internal conflict about success or of deliberately lowered future performance, but a majority, significantly larger among males, did expect problems with peers. Students most frequently attributed success to effort. Problems with peers tended to be seen as resolved if this attribution was made. Females reported resolution significantly more frequently than did males.

We report on a study involving the integration of technology in the teaching and learning of senior secondary mathematics. Student responses were obtained before and after the second year of the two year program, with respect to attitudes to technology; alternative motivations within collaborative settings; preferences for technology use in mathematical activity; and choices involving strategic preferences for technology use. Some few substantial shifts in position were identified, while other positions were sustained. The students provided self-assessments of their confidence and competence in technology use.

We report on research at two universities into attitudes of students relevant to the integration of mathematical software packages (MAPLE and MATLAB) in first year undergraduate courses. Both similarities and differences were found between the respective implementations. Separate constructs for mathematics confidence and computer confidence were confirmed, as were systematic gender differences between attitudes to mathematics and computers. On the other hand comparison of pre and post responses indicated some differences in the impact of the respective programs. Implications of the findings are considered against a background of increasing use of technology in tertiary mathematics teaching.

Nursing students at universities are often tested on drug calculations through their degree. These are usually pencil and paper tests which may provide an imperfect picture of drug error. A project, based at the University of Southern Queensland’s academic support unit, was developed to investigate the cognitive and metacognitive processes used by students who have difficulty with drug calculations. This paper presents some of the findings of this research, based on group interviews of nursing students. It identifies student strategies, error and reasons for error. The results of this research will provide a framework for future support for nursing students.

A part of the Victorian Early Numeracy Research Project (ENRP), 21 ‘trial’ schools implemented the Extending Mathematical Understanding (EMU) Program for students in the first three years of school who were low attaining in mathematics. This paper reports on the effect of the EMU program for students in their second and third years of school with respect to the Addition and Subtraction domain. Results suggest that Grade 2 children who participate in a small group specialised assistance program make more progress than children who participate in an individual program, and that the program is more effective for Grade 2 students than for Grade 1 students.

In spite of considerable research algebra remains a difficult subject for many students. Classroom teaching approaches still often rely on presentation of one or two procedures based in a single representation for solving a given problem type, often the symbolic algebra domain. The aim of this study was to investigate the value of using a multiplerepresentational environment in which students interact conceptually with graphic calculators (GCs) while solving quadratic equations. While students gained overall from using the GCs, it has been difficult to show specific representational benefits. However, the study has enabled us to describe and exemplify more clearly the nature of some representational interactions.

This study characterises secondary teachers’ mathematical beliefs and instructional practices regarding the teaching and learning of mathematics thematically. The focus of the study is the 1996 Years 9 and 10 Standard course operating in high schools across New South Wales. In general, teachers’ beliefs revealed a slight alignment to the goals of the thematic component of the course. However, teachers’ espoused instructional practices did not reflect the teaching approach necessary to appropriately enact the mathematics curriculum mandating the thematic teaching approach.

Literature at national and international levels argues the importance of including mental computation in a mathematics curriculum that promotes number sense. Characteristics of good mental computers have been documented. However, there is conflicting evidence about what constitutes high performance in mental computation – high accuracy as a result of efficient mental strategies and number sense or high accuracy without accompanying number sense. The purpose of this paper is to present findings of a study that investigated accurate mental computers and the factors that supported accuracy.

The personal beliefs of preservice teachers about the nature of mathematics, and the teaching and learning of mathematics, influence their experience in the Mathematics Education course and their teaching practice. This paper reports a study which indicates that the personal theories of the preservice teachers are typically mismatched with the formal theories that underpin the curriculum which they will be charged to implement. These personal theories are inferred from drawn and described metaphors depicting the mathematics teaching and learning situation.

In a case study of the feedback practices of a senior mathematics teacher there was found to be a close relationship between the classroom culture and the type of feedback that was used in the classroom. Underlying a classroom culture are the values agreed upon by the teacher and students. These values were reflected in the use of feedback. In this classroom the focus on marks, the correct solution and examination strategies demonstrated the value placed on achieving the correct solution during assessment. The emergence of the classroom culture as the major influence on the feedback practices will have a significant influence on the direction of further research. It was found that due to the culture valuing the marks achieved in assessment, the feedback practices focused specifically on these marks, the correct solution and examination strategies.

Aboriginal children generally do not reach their potential in the learning of mathematics in our primary school classrooms. In order to investigate possible reasons for this, Aboriginal students in the last two years of their primary schooling were interviewed about their learning of mathematics. This paper uses extracts from these interviews to demonstrate the need for teachers to reconsider their approaches to this learning so that Aboriginal children achieve their learning potential.

Multiplicative thinking cannot be generalised in any simple way from additive thinking. A premise of this paper is that teachers need to recognise the difference between additive and multiplicative thinking if they are to help children develop the latter. This paper describes an empirical study that investigated the potential of a set of tasks to distinguish between additive and multiplicative thinkers, and illustrates the results through the responses of two children.

The purpose of this study was to identify the testable beliefs of three secondary mathematics teachers, though for reasons of space only two are reported here. The teachers were involved in a collaborative teacher-led professional development program. The aims of this program were to enable the teachers to reflect on their practice, investigate issues of concern and by collaboration alter their instructional practice. The teachers’ beliefs were identified and several inconsistencies highlighted. This study was able to identify testable beliefs for each teacher and a further study intends to investigate whether these inconsistencies once recognised by the teachers can be tested through teacher-led professional development.

Many students confuse area and perimeter and are additive in their thinking of area. This misconception affects their ability to successfully complete area estimation and calculation tasks. In this paper, a simple pen-and-paper test based on Kidman’s (1999) research into area judgement rules is developed and trialed and used to detect additive (and multiplicative) thinking of area estimation. It found that approximately one half of the students’ intuitively judged area additively showing the power and persistence of this form of thinking.

Mathematics is a discipline comprising abstract ideas best accessed and understood through learner engagement in investigative or inquiry based processes leading to the development, justification and use of mathematical generalisations (Cockroft, 1982; Australian Education Council, 1990; National Council of Teachers of Mathematics, 1991). However, as I attempt to demonstrate from analyses of teaching/learning interactions in a Year 6 classroom, where students are investigating the relationships between square centimetres and square millimetres, the nature or climate of such engagements is always problematic and can have positive or negative effects on learner agency and identity. This being so, I argue that contemporary humanist notions of rational, autonomous learners currently framing practice may actually militate against genuine inquiry and engagement on the students’ part, and, in the interests of responsible pedagogy, need to be tempered by the recognition that agency and identity are discursively constituted.

In this paper I examine current pedagogic emphases in preservice teacher education that focus on active, participatory learning as a means of redressing students’ lack of knowledge of, and poor attitudes towards, mathematics. Against taken-for-granted assumptions about student identity and the agency needed to apply new methods in practice, I counterpose a poststructuralist understanding of these concepts which is then used to analyse a mathematics education subject I teach. This analysis makes visible unintended, previously invisible, conservative effects of inquiry based learning in this site. In conclusion, I argue that although preservice teachers do need to know the mathematics, they must also have a sense of themselves as agentic, reflective professionals which is not an individual attribute or disposition but is discursively determined, partly at least in pedagogic interventions in teacher education.

TIMSS items that matched draft Australian Year 7 numeracy benchmarks were identified and the performance of students from Australia and other countries on these items was examined. It was concluded that at least two-thirds of Australian Year 7 students would achieve them in general, and that many would be achieved by at least four-fifths of Year 7 students. Items apparently assessing the same benchmark were spread along the TIMSS item difficulty continuum, indicating a likely difficulty in constructing tests to assess achievement of the benchmarks.

The purpose of this study was to examine relationships between different forms of problem representation and students’ performance on a number of mathematics measures including problem solving, spatial ability and numeracy sense. Participants (58 Grade 6 students) solved mathematics problems and reported their solutions. The participants mode of representation, which included problem-solving success and representational preference, was placed along a visual-nonvisual continuum. The mode of representation did not influence problem solving or numeracy performance. However, when students at the extremes of the continuum were investigated, students who predominantly used visual methods performed better on these measures.

This presentation deals with the common but largely unnoticed and undocumented experience of misperceptions (as opposed to misconceptions) in the contexts of mathematics and music. While learners may possess an accurate conceptual understanding of specific tasks, misperceptions may hinder successful problem solving. Using the study’s computer software, this presentation will demonstrate misperceptions existing in these subjects, show how misperceptions confound learning problems diagnosis, how they sabotage the process of conceptualisation in learning, and how synergy between the disciplines might enhance learning.

In this paper, I explore the effectiveness of numeracy intervention within Australian primary schools. As a mathematics educator and researcher my central concern is that millions of dollars are being spent in this area, but are we seeing the benefits of it for students in primary school? Unlike most of the work being done in the area which is founded in psychological literature, I am undertaking a sociological analysis of numeracy intervention. In presenting this paper, I raise a number of dilemmas associated with this type of approach to understanding the pitfalls of interventions.

Teacher-education students were given the task of drawing two graphs, one to represent categorical data, the other to represent numerical data. A statistical-thinking framework was used to evaluate the graphs produced by assigning levels of thinking to the graphs and comparing the levels associated with the two types of data.. The levels of thinking associated with the categorical data were higher than those associated with the numerical data. More students were able to reorganise the categorical data compared to the numerical data. The levels of thinking were not related to the order of presentation of the data.

The reluctance of many mathematics teachers to embrace the use of computers in their teaching has been well documented. This paper report on a study that attempts to identify and describe the major factors that have effected some teachers’ decisions to use or not to use this innovation. Rich case study data has been summarised in a concept map. This map illustrates that central to teachers responses are their beliefs about mathematics, beliefs about students, pedagogical knowledge, knowledge about using technology in teaching, cultural press and perceptions of assessment. The interactions are complex. The findings indicate that a pronged approach to syllabi reform and professional development is recommended.

This paper describes the evaluation of a program for teaching measurement in the early years of school. The Program, Count Me Into Measurement (CMIM) is based on recent research findings that indicate the importance of students’ knowledge of the unit iteration structure. The CMIM Program was implemented in thirty-nine schools across NSW in the second half of 2000. The results of the evaluation were extremely positive, with teachers reporting that they liked the contents, structure and practicality of the Program. Many of them also commented that the Program had changed their approach to teaching measurement.

A NSW teacher professional development project has concentrated on teaching early primary school students about Space. The project uses a research-based framework organised around two key ideas: Part-Whole Relationships, and Orientation and Motion. Within these two areas students develop and exhibit a range of strategies. Teachers are provided with background notes, task-based assessment interviews, and plans for classroom learning experiences for each area. A questionnaire, discussion groups, and lesson observations have been used to assess change and how teachers are now teaching Space lessons.

Counting On is a NSW mathematics program for first year high school (Year 7) students who have not achieved Stage 3 outcomes when they commence high school. In 2000 it was implemented in 40 schools and the authors conducted an evaluation of the program. This paper briefly describes the program and considers certain aspects of the evaluation, particularly in terms of the changes in students’ conceptual levels in the areas of place value and multiplication and division.

Using advanced calculators to do mathematics changes the focus of what students need to learn. For arithmetic number sense is important, for algebra, symbol sense. Both concepts apply to the whole problem solving cycle. This paper is concerned with algebraic insight, the subset of symbol sense which is needed to solve a problem already formulated mathematically. Students need algebraic insight to enter expressions correctly, monitor the solution process and interpret the output as conventional mathematics. A framework for algebraic insight is described and illustrated with examples.

There are well-known problems with using patterns as a means of introducing algebra. This paper presents empirical data to support the view that it is inadvisable to try to introduce students to algebraic conventions by moving directly from patterns into algebra notation. These data also support the logical claim that students need familiarisation with the language of basic algebra prior to being expected to express pattern generalisations in symbolic form.

This investigation describes the beliefs and understandings that a beginning teacher developed as she engaged in two case investigations that were part of her undergraduate degree. The study also compared her perceptions about teaching mathematics at the end of her first term of teaching. Although the participant’s identified beliefs and observed practices were consistent with constructivist principles, the case-study analysis indicated that contextual constraints influenced the way in which she was able to teach mathematics. It would appear that school-based structures and constraints need to be considered more at an undergraduate level, and concomitantly, teacher educators need to work to a greater extent in partnership with pre-service teachers to develop a range of strategies to address such constraints.

A large study tracked four primary teachers during their first year of teaching. From their reflections on mathematics teaching, four dilemmas arose that they attempted to manage throughout the year. Discussion with the beginning teachers highlighted issues relating to the noted mismatch between pre-service education, research, and recent recommendations for teaching on the one hand, and on the other hand the realities of classroom practice. Support in the form of a ‘fellow worker’, amongst other things, is needed to help beginning teachers survive their first year and move towards a less teacher-centred approach to teaching.

Many researchers have used the task of comparing the size of pairs of decimals to reveal students’ thinking about decimal notation. This paper reports data from 315 Japanese and Australian students on a modification of this task, comparing decimals involving zero. Many students think decimals are less than zero. Some students who otherwise appeared to be experts exhibited difficulties executing comparison strategies that involved adding zeros to the end of decimal strings. Students believing that the decimal number system is discrete were identified.

This paper describes the development of a new research tool, the cognitive demand profile, from Chick, Watson and Collis’ task analysis maps and Taplin’s cognitive structure of mathematical tasks schema. The cognitive demand profile is to be used for the analysis of applications assessment tasks. Its application to two mathematically equivalent abstract and contextualised tasks is demonstrated.

The increasing availability of substantial sets of complex data (particularly video data) makes imperative the identification of the precepts on which such syntheses of primary and secondary analyses can be conducted. In this paper Methodologically Inclusive Research Synthesis (MIRS) perspective, as conceived by Suri (1999), is used to explore the adaptability of the axioms and procedures of naturalistic inquiry to the process of the recently-published synthesis of the analyses conducted within the Classroom Learning Project (Clarke, 2001).

This paper reports on a study conducted into the feasibility, difficulties and potential of including authentic peer assessment in an online teacher education course. As well as confirming a number of findings reported in the literature, several surprising results surfaced. These included a degree of confusion, a feeling of inadequacy, and a sense of liberation among some of the 44 students who participated. As part of the peer assessment process, course members went beyond their proposed criteria to reflect on the impact on themselves of the report being assessed.

The state of mathematics education research is inextricably linked to other areas in the mathematical sciences as it cannot be separated from the teaching of mathematics nor the discipline itself. There is a crisis in the supply of mathematics teachers and no discipline can afford the losses documented across university schools of mathematics in Australia since 1995 and maintain a vibrant research presence. These factors, combined with other political forces, suggest an uncertain future for mathematics education research.

In this paper, the experiences of lower achieving mathematics students in two secondary mathematics classrooms in which computers were regularly used are described. A year 8 and a year 9 mathematics class from one secondary school participated in the ethnographic study. The results show that in these two classrooms the learning relationships and power relationships did not, in general, support the learning and engagement of lower achievers in mathematics. Research into computer based teaching methods that engage low achieving students in computer based mathematics is needed.

In their own words, ten children whose mathematics careers were tracked from the beginning of their third year at school, to the end of their fifth, describe their experiences of learning of mathematics within the social world of the classroom. Their statements contain both cognitive and affective dimensions. A model linking these two domains, demonstrates impacts of everyday mathematics routines. Suggestions are made for changes in teaching practice to more effectively meet children’s social and cognitive needs in learning mathematics.

This paper is about politics and the part it plays in research. My curiosity is not directed at how we attend to a culture of profit and competitive edge, but at how we structure our conceptual categories and what political effects they engender. Unpacking poststructuralist ideas on truth, interpretation and representation, I discuss what their implications for data analysis might be. I revisit my classroom study to reveal an unwritten chapter in which I elaborate the conceptual decisions that were made and the dilemmas which confronted in producing the narrative.

In this paper the question of teacher identity is at issue. Central to the analysis is the preservice teacher and the part which the teaching practicum plays in the ‘making’ of a teacher. Within the context of educational changes, the interest is in the meanings which the beginning teacher gives to the engagement of pedagogical work. Meanings of practice, both conflicting of, and affirming with, the preservice teacher’s own personal theories, are revealed. The tensions recorded have implications not only for teacher education programmes but also for professional development programme development.

In individual interviews, twenty students in each of grades 3, 6, and 9 responded to a task involving chance measurement, then viewed video recordings of other students’ conflicting responses and decided which response they preferred. Seven students improved their levels of reasoning and seven agreed with higher-level prompts without expressing reasoning. Only two students agreed at some point with lower-level prompts, and both reverted to the level of their original response in conclusion. Educational implications are noted.

The method of Teaching for Abstraction was applied in Grades 2 and 4 to individual teaching interviews focussing on the angle concept. Responses of 3 students who successfully matched different physical angle situations are compared to responses of 3 that did not. The teaching method was generally supported, but it appears that more emphasis needs to be given to the examination of within-situation and within-context similarities before matching across contexts, and hence abstraction of the angle concept, can proceed.

Interactions between two Year 8 mathematics students were studied to identify factors that contributed to concept creation. Three cameras recorded the behaviours of: (a) the class; (b) the teacher; and (c) a pair of focus students. A mixed video image stimulated discussion in post-class student interviews. The use of non-routine tasks in a classroom environment that encouraged student autonomy led sometimes to student engagement in the exploration of discovered complexities and student creation of new concepts.

Four 3rd-grade students were individually interviewed and each interview was videotaped for subsequent analysis. The interviews involved presenting addition and subtraction tasks involving 1- and 2-digit numbers, and early multiplication and division tasks. Detailed descriptions of students’ strategies are provided. Three of the students all used just one kind of strategy, that is counting by ones and using fingers to keep track. The fourth student used a range of strategies including adding through ten and using a known fact.

Streaming is a well used practice in mathematics classrooms premised on a pragmatic belief that it supports the teaching of mathematics. This paper draws on interview data from Year 9 and 10 students who discuss their experiences in streamed classrooms. The students’ responses indicate that streaming enhances the learning for the high stream students and restrains the learning of students in lower streams. It is proposed that streaming in mathematics classrooms has the potential to widen the gap between groups of learners rather than to offer more inclusive learning environments that meet the needs of the learners.

School mathematics has two sets of criteria for judging competence¾one that is mathematical, explicit, and founded in psychology. The other, the focus of this paper, is concerned with the hidden criteria for competence in school mathematics. Using the theoretical tools developed by Basil Bernstein, it is proposed that aspects of school mathematics are socially biased and enhance or hinder the potential for success for some students. Two aspects of school mathematics are considered: written texts and classroom interactions.

This paper describes an investigation on semantic characteristics that make an arithmetic word problem difficult for children. Five semantic characteristics were delineated for investigation. They are (1) type of semantic relations, (2) number of semantic relations, (3) number of types of semantic relations, (4) presence of simultaneous unknowns, and (5) nature of unknowns. 436 year three and 116 year five children were given pairs of word problems that differ in one of the five semantic characteristics. It was found that the presence more types of semantic relations and of simultaneous unknowns significantly increases the difficulty of arithmetic word problems.