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The analysis presented in this paper focuses on the relationship between classroom discourse and mathematical development. We give particular attention to reflective discourse, in which mathematical activity is objectified and becomes an explicit topic of conversation. In the course of the analysis, we differentiate between students' development of particular mathematical concepts and their development of a general orientation to mathematical activity. Specific issues addressed include both the teachers role and the role that symbolization plays in supporting reflective shifts in the discourse. We subsequently contrast our analysis of reflective discourse with Vygotskian accounts of learning that also stress the importance of social interaction and semiotic mediation. We then relate the discussion to characterizations of classroom discourse derived from Lakatos' philosophical analysis.

The purpose of this study was to investigate the patterns of problem solving behaviour displayed by Year 11 students, when attempting to use recently studied mathematics . on problems set in unfamiliar, life-related contexts. The aim is to develop a framework to guide teachers in the type of feedback they give to students. Patterns of behaviour within the categories of engagement, planning and monitoring, use of heuristic strategies and verification skills, knowledge of facts and procedures, and beliefs were inferred from a study of written responses to four questions A Student Response Feedback Framework is proposed and suggestions are offered for a range of uses for this instrument.

This paper reports on the findings of an investigation into the attitudes of primary students toward calculators and their use in the classroom. Through the use of a questionnaire and semi-structured interviews the attitudes of two groups of children - those for whom the calculator is part of their mathematics instructiqn and those for whom it is not - were examined. In particular, the findings highlight the need for teachers to be aware of the diverse attitudes children hold toward calculators.

Studies have shown that many students make systematic errors when expanding linear algebraic brackets. Some of these errors could be classified as bug s (of a procedural nature involving an incorrect routine), but most are slips (of a careless nature). Many slips are caused by difficulties experienced within working memory. This study investigated whether the use of a calculator could reduce the load on working memory and, subsequently reduce the number of slips made. A comparison was made between students, who had use of calculators, and students who had no calculators on bracket expansion tasks. An analysis of errors found that the use of a calculator did not reduce the number of errors or alter the types of errors made.

Drawing from a critical perspective on the discourse of mathematics the aim of this study is to explore an , ethnomathematics' evolving in advanced capitalist society in an area that impacts on the lifeworlds of its members - savings and investment. The focus will be on the literature produced by the superannuation, insurance and unit trust industries for the purposes of client communication. Implications for mathematics education will be considered. This paper provides a summary of the theoretical underpinnings of the study.

An extensive survey of children's mental computation skills in years 3, 5, 7 and 9 was undertaken in the Perth Metropolitan area as part of an international study involving Australia, Japan and the USA (McIntosh, Bana & Farrell, 1995; Reys & Reys, 1993). This paper deals with perceived error patterns arising from the Perth study.

No abstract available.

The lack of full evaluations of curriculum change in NZ has prompted a project to establish a basis for future evaluations. A longitudinal study of the curriculum is being done so that the interrelationships between parts of the curriculum can be identified., and the effect of change in any part can be monitored and/or predicted. Methodological problems of undertaking the project with limited resources is discussed. A new technique of 'icon development' using video material of students is described.

The strategies employed by 130 Grade 5 Brisbane students in comparing decimal numbers were investigated. Nine different strategies were identified, some of which indicated sophisticated understanding while others indicated restricted understanding. Most students had a predominant strategy which determined success or failure on particular items. Predomonant strategy distibution was compared with that of French, USA and Israeli students.

This paper reports on a pilot study. The purpose of this study was to determine what mathematics content a group of adult women would like to cover in an adult numeracy class, situated in a community setting, and why this mathematics content is important. It is based on the belief that there is no one set of mathematics content which is appropriate for a group of adults in an adult numeracy class. Therefore, the aim of the study is to develop a process for discovering the selection of mathematics content.

My intention with this research was to compare mathematics curricula from five countries with populations and areas similar to those in New Zealand but with different languages and cultural backgrounds. After explaining the school systems, the paper discusses the differences between the curricula and looks at them from constructivist and post-structuralist perspectives. Finally some conclusions are presented.

No abstract accessible to the data base.

This paper reports on the responses of 1242 Queensland teachers to a survey on mathematics assessment in terms of teacher gender and teaching level. These responses were noticeably consistent across the different school systems and locality; however, comparison of responses between females and males, primary and secondary, and gender by teaching level, revealed some interesting differences.

Abstract not accessible to database.

This paper reports on the qualitative data gathered during the initial phases of a longitudinal investigation into the attitudes of preservice primary teachers towards mathematics and toward the teaching of this subject. It provides a more wholistic perspective on the change process by employing multiple data gathering techniques, thus allowing the researchers to focus on the underlying reasons for attitudinal shifts.

This paper is a report of students' responses to instruction with concrete representations in solution to linear equations. The sample consisted of 21 Year 8 students from a middle-class suburban state secondary school with a reputation for high academic standards and innovative mathematics teaching. The students were interviewed before and after instruction. Interviews and classroom interactions were observed and videotaped. A qualitative analysis of the responses revealed that most students did not use the materials in solving problems. The increased processing load caused by concrete representations is hypothesised as the reason.

This paper reports a school-based study of a collective argumentation model of learning implemented within a year 6 math classroom. Quantitative and qualitative evidence indicated that children in collective argumentation learning environments generated a higher proportion of logical operations in their group discussions about a logico-physical task and were more adept at generalising acquired knowledge to a novel problem, than children operating in more conventional learning environments.

This part of a continuing study of production workers' uptake of the Production Engineering Certificate in their workplace in Melbourne. I in terviewed twen ty-five' employees in 1993. The preliminary results indicate their vaJuation of mathematics, mechanical knowledge, and communication skills, and concerns about change in their jobs. I suggest that workers' interest in numeracy, an important component of decision-making in any production operation, may depend, like communication skills, on their sense of social agency.

Seventy-two teachers from Tasmanian government primary and secondary schools were surveyed regarding (i) their agreement with statements relating to personal confidence with chance and data, (ii) their views of the importance of statistics in society, and (iii) their confidence in teaching chance and data. Differences across gender and school type were found in measures of individual items and also. combined scales. These results help to specify needs for professional developmen t.

This paper reviews research on teachers' conceptions of mathematics and presents the results of a study which trials the use of a methodology termed "lived experience anecdotes" (Van Manen, 1995) in providing information about teachers' conception of ma thematics.

Recent investigations of mathematical problem solving have focused on issues that affect students' ability at accessing and making flexible use of previously learnt knowledge. We report here the first phase of a study that takes up this issue by examining potential links that might exist between mental models constructed by students, the organisational quality of students' prior geometric knowledge and the use of that knowledge during problem solving. The results suggest that the quality of geometric knowledge that students construct could have a powerful effect on their mental models and subsequent use of that knowledge.

Abstract is not accessible to database.

Case study research focusing on changing teacher roles associated with a grade six teacher's use of innovative mathematics materials is described. Daily observations and regular interviews with all participants provided a picture of professional growth and major influences on this process. The teacher demonstrated increasing comfort with posing non-routine problems to students and allowing them to struggle together. He also increasingly provided structured opportunities for student reflection upon activities and learning. Major influences on this teacher's professional growth are discussed.

A specific research technique is outlined by which the nature of "coming to know" in classrooms might be put on a more empirical footing. In this research, an attempt is made to optimize the use of currently available technology through the synthesis of classroom videotape and interview data in an integrated video and text "document". The analysis of the resultant data is enhanced by the use of an indexing tool with the capability to undertake complex qualitative analyses of textual data in a replicable fashion. Some preliminary findings are reported which employ students' use of the term "right" to offer insight into the process of "coming to know" in science and mathematics classrooms.

An extended Newman interview technique was used to gain additional information on responses to 16 pencil-and-paper questions (8 short-answer, and 8 multiple-choice) by 65 students in three Year 8 classes in three NSW regional high schools. The data suggest that about one-quarter of students' responses could be classified as either: (a) correct answers given by students who did not have a sound understanding of the mathematical knowledge, skills, concepts and principles which the questions were intended to "cover"; or (b) incorrect answers given by students who had partial or full understanding.

Abstract not accessible to database.

This paper reports on the correct responses and correct-response strategies for word problems from a longitudinal study of grades 2 and 3 children's mental computation strategies for 2 and 3 digit addition and subtraction. Children were found to use increasingly powerful strategies across the two years. However, the pen and paper algorithm tended to become dominant.

This paper reports on the latest results of our research into the conceptions of mathematics, orientations to studying it and experiences of learning it of first year mathematics students at Sydney University. Questionnaires were issued to students at the beginning of the academic year and after one semester. An analysis of the results· suggests two qualitatively different patterns of students' experiences of learning mathematics. Differences in' students' conceptions and approaches were related to their examination performances.

We compare some of the results of two surveys of talented mathematics students, one undertaken with Secondary School students in 1992 and the other with Intermediate School students in 1994. In both surveys (i) the mothers of the group studied were exceptionally well educated themselves, some 40% of them having first degrees; (ii) not only were the number of girls in both samples small but girls seemed to be under-represented in the families studied; and (iii) a reasonable number of the families were not 'middle class'.

This paper reports on research in progress on children using calculators as part of their mathematics learning during their first two years at school. An interview was developed and administered to 12 children on entrance to school in 1993, in order to determine the effect of classroom learning on their mathematical knowledge during the two year period. The outcomes of these interviews show that 10 of the 12 children interviewed commenced formal schooling already having knowledge of most of the stated number concepts for prep level.

Traditionally the effectiveness of the strategy draw a diagram as a problem solving tool has been assessed by using end product measures such as frequency and spontaneity of diagram use, performance scores, solution times, and the appropriateness of the diagram drawn. This paper argues that these measures can be unreliable and proposes that the dynamic use of the diagram should be monitored to ensure the validity of the assessment.

The use of concrete media for developing mathematical understandings has been an unquestioned aspect of mathematics education for many years. Whilst the efficacy of such materials for most children is accepted, the different understandings fostered by different media is less well defined. This paper reports an investigation into the various responses of a large sample of eight-year-old children who used three different media for measuring the area of a rectangular space. Discussion focuses on commonalities and diversities revealed.

Many errors in arithmetical computation are systematic; they are learned and have become habitual. This paper investigates two methods of instruction for correcting systematic errors and promoting knowledge growth for the subtraction algorithm in upper primary students: (1) structured reteaching, linking symbolic procedures to concrete/pictorial representations; and (2) the Old Way/New Way (D/N) technique, based on proactive inhibition. O/N was successful in changing computational knowledge expediently and fairly effortlessly while the conventional approach proved less successful.

No abstract

Abstract not accessible to database.

The belief that mathematics is a social activity, in which members of a community of mathematicians engage in systematic mathematical experimentation and reflection is held by many mathematics educators (Schoenfeld 1992, p335) and underpins A National Statement on Mathematics for Australian Schools National Statement (Australian Education Counci11990). Part of teaching mathematics from this viewpoint involves modelling being a mathematician and encouraging students to practice being mathematicians. How does current practice in classrooms reflect this belief? In this paper the author reports on reflections and actions on his classroom practice aimed at creating a classroom environment where students practice as mathematicians. The use of technology, in creating potentially rich mathematical environments for such experimentation and reflection is also examined.

Based on the production system theory, an information processing taxonomy (IPT) model was postulated to extend the production system by including a second level of production of information. The aim of this paper is to . report on evidence from children's thinking to verify the features of the model particularly the extension of the production system. The results of the investigation show that both the written and verbal statements of children working on a ratio and proportion problem support the mathematical thinking features spelt out in the IPT Model.

Models explaining gender differences in mathematics learning outcomes incorporate affective variables including students' attributional styles. In the present study, four grade 7 students in two different classrooms were observed as they engaged in mathematics activities. Behaviours reflecting attributions for success and failure were monitored and compared to conventional measures of the students' relevant beliefs. Classroom factors which might influence these beliefs were identified and partial explanations for some of the gender differences noted were inferred. Implications of the findings are discussed.

This study investigated the nature of conceptions of what mathematics is and the intentions of school mathematics through interviews with Years 10, 11 and 12 students and their teachers. Students and teachers held broad views of what is the content or discipline of mathematics, while their interpretations of mathematics within a wider sociocultural context reflected four additional, influential personally and socially derived interwoven factors: social status of . mathematics, utility of mathematics, career aspirations, and interest or disinterest in mathematics. The existence of these· factors indicate that what it means to 'understand' mathematics is related to both a context and individuals' interpretations of a context.

The learning and understanding of negative numbers was part of a broader study carried out to explore the quality of mathematical thought processes (MTP) of 110 first-year mathematics university students. A mathematical item on finding the 'product of two nega.t~ve numbers' was designed specifIcally for this purpose. The quality of the responses was . assessed using the SOLO taxonomy evaluation technique (Biggs & Collis, 1982). Quality is here defined as logic, depth and clarity of MTP. An alarming 94% of the responses equated understanding to learning the 'rule', two negatives make a plus. A 71 % of the responses were categorised as unistructural SOLO level in the conrete symbolic mode. The findings strongly suggest that such learning and knowledge is a function of teaching strategy and that rote learning rules inhibits quality learning.

The study reported here explored mathematical knowledge students brought with them to University by using both qualitative and quantitative methods. These methods provided current, richer and valid information on students mathematical abilities as compared to the traditional 'normalised' tertiary entrance score. The study data highlighted several issues that could contribute to better teaching of students having insufficient background in mathematics: students retain and recall knowledge 'Which they perceive relevant to their current learning; a high quantitative score does not necessarily equate to high level understanding and the learning of calculus does not support the understanding of functional notation.

This paper reports on a study which investigated the beliefs of 142 Year Six students and their mathematics teachers from six Catholic Primary Schools in Melbourne, with respect to the teaching actions perceived to be helpful in facilitating mathematical learning and their relationship to teaching practice in mathematics instruction. The insights of students and teachers add an important dimension to the advice offered by the informed mathematics education community an,d current mathematics curriculum documents in relation to effective mathematics teaching strategies, and may provide a stimulus for teachers to review and change their current practice. Additionally, the results suggest that mathematics teachers' practice is aligned to student beliefs concerning the helpfulness of teacher actions, rather than their own beliefs, the beliefs of the informed mathematics education community or those expressed in mathematics curriculum advice documents This finding is of concern, and has important implications for mathematics education and teacher professional development.

This paper reports on an exploratory study that investigated links between the quality of secondary school students' metacognitive knowledge, their beliefs about mathematics, and their perceptions of school mathematics practice. Two questionnaires were administered to a sample of 170 Year 11 and Year 10 students in three Queensland schools. Analysis of the responses points toward teaching and learning practices associated with empowering beliefs and well developed metacognitive knowledge. In particular, the potential value of mathematical discussion with peers is highlighted.

Previous research on the development of metacognitive skills has used Vygots1cy's notion of the zone of proximal development, concentrating particularly on teacher-student interaction. However, Vygotsky also conceptualised the ZPD as allowing for peer interaction, so that students might monitor and extend each other's thinking. This exploratory study, carried out in a Year 11 mathematics classroom, provides evidence of metacognitive strategy use during informal peer . interaction, and identifies a collaborative discussion style that was the vehicle for metacognitive activity.

This paper has grown out of a research project concerned for participants' in and out-of-school mathematics. The project itself is a qualitative investigation into adult basic education students' experiential worlds. It has been designed to generate insights into supposedly innumerate adults' practices both in everyday contexts and in educational institutions. The presentation reports a cohort of educators', researchers' and theorists' responses to a particular out-of-school practice.

Much attention in recent years has been directed towards an intensive study of the way that students learn elementary algebraic concepts and the best way that these concepts should be introduced into the secondary mathematics classroom. This paper will examine how and why algebra was introduced into the secondary school curriculum, especially in England in the Nineteenth Century. The period immediately preceding the First World War will be particularly addressed since many reforms were advocated at this time in the teaching of algebra, but never taken up. The effect of these changes on the developing secondary algebra curriculum in Australia will also be examined.

Abstract not accessible to database.

The aim of this study was to investigate the relationship between mental computation, computational estimation, and number fact knowledge. Clinical interviews were conducted with thirty-two students who were participating in a longitudinal study of mental computation. They were interviewed for mental computation, computational estimation, and number fact strategies. Results showed that proficient mental computers were also good at computational estimation and exhibited mastery of number fact recall. In addition, the data indicated that children in year 4 are capable of inventing their own valid and efficient mental algorithms.

This paper describes the processes, outcomes and issues that arose out of activities in three school-based settings that focused on teachers determining their own needs in relation to professional development. Teachers identified areas of need or change on the basis of a needs analysis questionnaire. The questionnaire asked teachers to identify their strengths, weaknesses, opportunities for change and threats against change occurring. Teachers then worked with the three researchers in various ways to promote change in the school setting. The teachers involved were asked to keep a diary, recording observations on the activities that were tried and answering such questions as: Was the activity successful? How could the activity be improved?

Problem solving has widely been advocated as the way ahead in the teaching of mathematics. While it is an important development in mathematics education, it may not be as easy to implement as at first thought. We consider four aspects of teaching problem solving to show the difficulties involved. These aspects are the problem solving tasks, the nature of solutions, metacognition, and the scaffolding required to enable students to learn. It is important that teachers wishing to use a problem solving approach in their teaching are aware of all of these aspects of problem solving and, in addition, that professional development is provided in order for them to master the problem solving approach.

The analysis and reporting of the research process involved in an ethnographic study depends on the consistent recording of detailed fieldnoteso This paper discusses some of the cLJmponent and temporal issues involved in the analysis and categorisation of a set of fieldnotes written during an ethnographic study which investigated the expressed views of parents, students and teachers towards learning mathematics. Analysis has resulted in a framework of five categories being suggested for the initial analysis of reflective fieldnotes.

Professional development of teachers has been identified as a key area for future curriculum action. This paper examines the present context for professional development and reports on perceived inadequacies within this area of mathematics education. Certain key influences on the evolution of professional development models are identified, and these are illustrated with reference to a number of recent studies into the provision of inservice to teachers and other teacher knowledge base development activities. Alternative models for professional development are canvassed. The paper concludes with a proposed general structure for models of mathematics teacher development (transmissionist models versus meaning-centred models). This structure relates the process of teacher development to assumptions made about the nature of learning and teaching mathematics, and assumptions and beliefs about teacher knowledge.

A set of graphics calculators was used to supplement teaching and learning in an undergraduate mathematics course. Student attitudes to the innovation were collected, through Likert items and optional unstructured written responses. Attitudes were generally favourable, although time pressures and assessment in the course were sources of concern. Classification of written responses provided some legitimacy to a proposed series of metaphors for technology, and suggested an additional metaphor of technology as a nuisance might also be needed to understand student reactions.

The understandings reproduced here arose from three year's involvement in an action research project in pre-service teacher education in mathematics. 1 implemented pedagogical practices based on constructivist tenets of students' active and autonomous construction of meaning in a supportive, though challenging, environment. In this article 1 endeavour to make explicit some concerns I experienced within my practice when I failed to appreciate the full implications of the socio-cultural and political constitution of the students and knowledge within the discourse of constructivism. It became clear that all students are always actively involved in learning, some learning even within constructivist methods of teaching that they have no agency in this supposedly supportive context.

This paper describes a study which sought to understand more fully the thought processes of year 6 students when they estimate measurements and to determine possible gender differences in such thinking. After completing 14 untimed multiplechoice estimation of measurement questions, 100 year 6 students were asked to explain to an interviewer how they had obtained their responses for each question. In general, no significant gender differences were found for performance on specific estimation of measurement questions. Year 6 boys and girls reported using similar strategies.

This paper reports research into kindergarten students' spatial constructions and describes advancements in students' problem solving under adult guidance. In particular, it reports kindergarten students' attempts to match solid shapes with their respective nets and to interpret isometric drawings of stacked cubes.

A sample of 577 secondary pupils in Hong Kong were tested on a set of problems that commonly give rise to the 'reversal' error. Two areas of the test are discussed in this paper: (i) the effect of the syntactic structure of a question with respect to the contiguity of elements in the sentence, and (ii) the effect of the inclusion of subsidiary questions within a problem. The results are discussed with particular reference to the construction of cognitive models based on comparison.

In this paper we describe the ways in which students in Years 9 and 10 perceived problem structures and tried to represent them algebraically. We show that, for some students, different verbal descriptions of the same problem influenced the structures perceived and the non-algebraic solution strategies used. However students who used algebra were not affected by the form of the verbal description. They were able to transform their initial model to the one appropriate for algebra.

This paper reports on the first phase of a national study, currently in progress, designed to investigate factors that influence students' choice of mathematics courses at the upper secondary school level. In this first phase, an instrument was developed and trialled which incorporated a number of "cognitive preference" items based on the Myers-Briggs Inventory of Psychological Type and also the CareerMate counselling instrument. Outcomes of this first phase indicate that several dimensions of· personality appear to be most relevant to students' course selection choices.

Abstract not accessible to the database.

The major purpose of this study was to explore performance on a variety of mental computation tasks using two presentation formats (visual and oral).

Observations of 104 lessons taught by final-year secondary mathematics student teachers were analysed to identify weaknesses in their pedagogical content knowledge. 11 Pedagogical mathematics weaknesses" were found in the areas of meaning and purpose, accuracy and appropriateness, quality of explanation and quality of language. Six "pedagogical mathematics themes" were identified as in need of particular attention. It is argued that teacher education programs need to include more explicit discussion of the purpose, basic concepts, and pupil learning of such central mathematical themes.

60 female students were observed four times during Grades 2 and 3 as they solved the same set of 24 multiplication and division problems with a wide variety of semantic structures. Students used three main intuitive models for both multiplication and division problems: direct counting, repeated addition and multiplication operations with a fourth model, repeated subtraction occurring only in division problems. The most popular model was repeated addition. Children's intuitive understanding of multiplication and division developed largely as a result of their recognising the equal group structure common to all multiplicative structures. The findings are in contrast to those of Fischbein et al. (1985).

The responses of 115 children in Years 1 to 4 to three types of multiplicative word problems were analysed. The representations that children drew to solve or to explain solutions were categorised in terms of structural characteristics and examined to assess if the drawn representation was related to success in solving the problems. There appeared to be a relationship only for the Cartesian product problem. The wording of the problem was found to influence the structure of the drawn representation.

This research determined whether a group of 50 Year 9 students playing a card game that involved probabilistic reasoning demonstrated a type of misconception in the selection of strategy they employed. Earlier research into misconceptions in probabilistic reasoning by the author identified widespread use of the heuristics of availability and representativeness by Year 11 students. The present research identified a misconception of a different nature relating to the concept of mathematical expecta t ion.

Abstract not accessible to the database.

This paper reports on a study which attempted to translate research on learning from a constructivist perspective into a teacher ed uca tion classroom environment. The study implemented a social constructivist view of learning mathematics for the purpose of analysing the practice of teaching and learning mathematics. Learning opportunities that emerged from the students' experiences in the classroom environment not only helped to facilitate the students' own mathematical development but also provided insight into the role of the mathematics teacher in the classroom.

Prospective primary school teachers enter their mathematics education subject sequences in their teacher education programs with a number of chains fettering them to the past. These constraints are analysed and their implications considered. Suggestions for the formation . of more flexible links are proposed. Awareness of what students and teacher educators bring to their teacher education courses allows for negotiation of powerful ideas.

In this study, examples of student expository writing in mathematics were examined in order to develop a method of describing the nature of the writing in terms of the way the central idea was elaborated. The aspects of mathematics and the language types being used are described. The writing examples demonstrated the restricted written mathematical genre with which these students are familiar.

Following several reports by the author and a colleague, this paper attempts to synthesise some aspects of research pertaining to beliefs and attitudes in mathematics education. Possible constructs that contribute towards the development of values in mathematics education are suggested and a brief account of valuable methodologies for the study of mathematics values is given. An application of a modified repertory grid technique is described and reported as a case study of two graduate students' beliefs and values. Models for research in different aspects of· values in mathematics education are recognised and implications for the classroom suggested.

No abstract available.

In this study, samples of the mathematical writing of preservice teachers were categorised using a system developed by van Domolen. Further information related to the teachers' understanding ofa major concept involved in the writing was obtained by the use of a Link-sheet activity. The information gained from the two activities was compared. The Link-sheet examples suggest that these teachers possessed poorly developed concepts relating to decimal fractions, whereas the. writing examples demonstrated the limited written mathematical genre used by these teachers.

No abstract available.

The purpose of this study was to compare the structure of mathematical word problems which first year pre-service teachers were able to solve easily, with those that they found difficult. The aim was to identify a hierarchy of problem types to which student teachers should be exposed if they are to develop their mathematical problem solving skills. Task an,zlysis maps of twelve word problems given to fifty-eight student teachers suggested a progression in the required level of processing, the nature of the information stated in the problem, the extent of demand on the working memory, and the type of concepts and processes required.

This research project has examined the development of spatial concepts in preschool aged children.

The paper examines the responses of more than 300 non-naive students of first-year Business Data Analysis to a question asking what information is provided by a value of r in a certain context. It shows that few students appreciate that they can find information about both association and variance from this parameter. Many responses were either incomplete or aberrant, and a summary of the most significant responses is provided.

One of children's views about 'what controls a Random Generator' has been defined in the literature as animism. This paper investigates and attempts to tabulate some of the definitions and explanations given by children in my current study, in an attempt to clarify their interpretation.

In both Australia and New Zealand since 1950 stochastics has become an increasingly important part of the mathematics curriculum at primary, secondary and tertiary levels. This paper looks at the ebb and flow of research over the teaching and learning of stochastics in both countries, assesses its influence on pedagogic practices and argues that there has been both a mismatch and a failure of communication between the two.

This paper discusses new directions for mathematics in school, emerging with use of technologically advanced tools. The data are observations made during work with function graphers in the Technology Enriched Algebra project. There are three propositions. Students will use a wider range of notations, mixing them more than at present. Differences in tools will promote the development of different concepts. The variety of approaches to problems will increase markedly, due to apparently small differences in the design of software tools.

This paper presents an analysis of two questionnaire items which explore students' understanding of the concept of luck in relation to the development of ideas of formal probability. The items were administered to 1014 students in Grades 3, 6 and 9 in Tasmanian schools. The analysis was based on the multimodal functioning SOLO model. The results lead to a hypothesised structure and implications for curriculum and teaching practice.

No abstract