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University lecture rooms are often very stark, with the only wall decoration usually describing how mathematics is used in a variety of (to most students) obscure pursuits. Primary school classrooms on the other hand are often full of resources and activities chosen to reinforce fundamental concepts and skills that relate directly to what the students are learning. In the spirit of a primary school classroom, the presenter has used displays, resources and atmosphere in a University Maths Drop-In Centre to introduce and reinforce important concepts and skills. This presentation describes the success of this approach, and suggests directions for future research in this area.

This paper addresses the reform of mathematics education in the Netherlands and the attacks that presently take place against this reform. The attacks concentrate on primary education and criticize in particular the program for teaching calculation skills with long division as a case in point. The paper gives an overview of what Realistic Mathematics Education (RME) stands for, and what mathematics education the reform-attackers have in mind. Furthermore, attention is paid to possible factors that could have triggered this attack, and what other countries may learn from it.

In this paper I draw on a particular case that encapsulates some of the most extreme elements of educational disadvantage – poverty, remote location, English as a foreign language, cultural diversity and Aboriginality – to provide a lens for understanding the complexity of coming to learn school mathematics. In so doing, I illustrate the need for a greater understanding of the intersection of various factors that limit the opportunities for success in school mathematics. The objective of this paper to provide an understanding of the complexity of teaching in remote contexts that will challenge current practice and move to a more holistic model for conceptualising research, practice and policy in mathematics education that may enable greater access to mathematics and schooling for some of the most disadvantaged students in Australian schools.

The past two decades have seen extraordinary developments of technologies of potential value to mathematics education, including a range of software (such as dynamic geometry systems, graphing software, statistics software and computer algebra systems), a range of devices (such as scientific and graphics calculators, desktop computers, iPods and interactive whiteboards) and a range of environments (such as computer laboratories, microworlds, the Internet and learning management systems), all in various combinations. While there are many hopes, aspirations and opinions on the appropriateness of particular technologies for particular purposes, obtaining credible and helpful evidence on such matters has been difficult; indeed, many researchers have noted the difficulties of studying what is clearly a moving target. In a world in which simplistic views of research abound (as in suggestions or inferences that research will provide the evidence upon which decisions are made), in which decisions by curriculum developers and classroom teachers are subject to a range of influences (including financial, commercial, political and ideological), and in which communications between different educational interest groups are rarely productive, it is hard to see the best way forward. In this presentation, I will attempt to survey some of the achievements and problems of research on technology in mathematics education, in order to understand the limited impact so far of research upon practice and to suggest how we might collectively do better to productively connect technology development, educational research and classroom practice for mathematics education.

The Mathematics in the Kimberley Project is a three-year research and development project that focuses on mathematical pedagogy in remote Aboriginal community schools. The research team has regularly reported on the project at MERGA conferences, and in this symposium we evaluate the pedagogical model that underpins the project. After two years of the project, the data indicate that some aspects of the pedagogical model have been successful, but other aspects have not been particularly fruitful and still require greater thought, research and development.

Play is an essential part of young children’s lives. This symposium highlights the integral role of play in young children’s mathematics learning and examines the teacher’s role in facilitating and extending this. Papers examine key tenets of play, contributing to theoretical understandings and presenting data on teacher’s perceptions of play and young children’s actions in play. Examination of teacher perceptions and young children’s experiences of mathematical play identifies potential for development of mathematical concepts beyond embryonic mathematics inherent in play.

In this symposium, we discuss some preliminary data collected from our problem solving project which uses a design experiment approach. Our approach to problem solving in the school curriculum is in tandem with what Schoenfeld (2007) claimed: “Crafting instruction that would make a wide range of problem-solving strategies accessible to students would be a very valuable contribution … This is an engineering task rather than a conceptual one” (p. 541). In the first paper, we look at how two teachers on this project taught problem solving. As good problems are key to the successful implementation of our project, in the second paper, we focus on some of the problems that were used in the project and discuss the views of the participating students on these problems. The third paper shows how an initially selected problem led to a substitute problem to meet our design criteria.

This paper highlights a teacher‘s perspective when changing her accustomed and traditional way of teaching into a pedagogic approach philosophically inspired by critical mathematics education. The focus here is on the practitioner‘s identities during the teaching process, in a context of change. The research is socio-culturally grounded and involves a methodologically critical ethnography. The teacher‘s learning was demonstrated through her voice in the end as sensing freedom in her teaching, reflecting on new possibilities and analysing the responsibilities different actors have in the mathematics classroom. Her experiences indicate that a critically mathematics inspired teaching approach has the potential to support teachers‘ achievement of agency.

This paper describes part of research conducted with fifteen Numeracy Coaches as they carried out their work supporting teachers in Victorian government schools. There was great variation in the mathematical background of coaches, and this area of the research investigated the changing perception of professional learning priorities to support their work in schools, using questionnaire and interview data. The data indicated that the coaches‘ priority for mathematics content knowledge and pedagogical content knowledge strengthened over the year of the study.

As part of a longitudinal case study on engagement in middle years mathematics, 20 students attending their first year of secondary school in Western Sydney were asked to provide views on their experiences of the transition to secondary school in relation to mathematics teaching and learning. Differences in teacher-student relationships caused the most concern due to the decrease in teacher-student interactions and a reliance on computer-generated mathematics lessons. Findings indicate that a strong pedagogical relationship forms the foundation for sustained engagement in mathematics during the middle years.

This study reports how the difficulty of simple worded percentage problems is affected by the problem structure and the complexity of the numbers involved. We also investigate which methods students know. Results from 677 Year 8 and 9 students are reported. Overall the results indicate that more attention needs to be given to this important topic. Simple unit fraction equivalents seem to be emphasised, at the expense of fundamental definition (“out of a hundred”) and apparently easy percentages such as 30%. The draft National Curriculum gives better guidance on the variation amongst percentage problems.

Young Filipino students are expected to solve mathematical word problems in English, a language that many encounter only in schools. Using individual interviews of 17 Filipino children, we investigated why word problems in English are difficult and the extent to which the language interferes with performance. Results indicate that children could not solve word problems independently when these were given in English. However, appropriate interventions such as presenting problems in Filipino or narrating them led to improved performance. Implications for teaching are proposed.

Two test items that examined high school students’ beliefs of sample size for large populations using the context of opinion polls conducted prior to national and state elections were developed. A trial of the two items with 21 male and 33 female Year 9 students examined their naïve understanding of sample size: over half of students chose a sample size of “10% of the population”, and a quarter chose a sample size of 15,000 – both approaches grossly exceeding the accepted sample size.

This paper presents the findings of an investigation into the influence primary teachers’ knowledge of a researched-based framework describing children’s cognitive development in early number has on their teaching practices. Survey and interview data from twentyeight teachers were collected to determine teachers’ perceptions of their understanding of the framework, their ability to use the framework to assess students’ mathematical development and to plan appropriate instruction. The findings raise further questions about the influence of affective factors, such as teachers’ confidence in their own knowledge, on their instructional decision-making.

We have analysed multilingual mathematics classroom discourse to understand how languages are negotiated in student-teacher conversations under the assumption that language-use is a socially embedded process. We attempt to comprehend in what different ways languages (of instruction and local) are mixed and switched to arrive at better clarity and understanding of the mathematical contexts. We conclude that when teachers cultivate negotiation between languages by reinforcing the practice of code mixing and switching, students' understanding and participation is enhanced.

This paper summarises part of a longitudinal study to investigate the possibility of establishing an Index that would indicate the appropriate starting point for instruction for students entering high school and reports on the first group of students to sit the Index tests in 2005, comparing the predictive nature of the tests with other state and national tests through correlations. The Index tests focus on the number construct and it is envisaged that by identifying the student’s deficiencies or strengths in this construct it may be possible to devise interventionist strategies or extension activities that would increase the probability of success in later years.

A key element in the examination of how students process mathematics through digital technologies is considering the ways that digital pedagogical media might influence the learning process. How might students’ understanding emerge through engagement in a digital-learning environment? Interactive software that has cross-curricula implications and facilitates thinking in rich, problem-solving environments is emerging. Scratch, a free-todownload graphical programming environment provides opportunities for creative problem solving. This paper is part of an on-going study into the ways mathematical learning evolves through these alternative environments. It reports on a pilot research study involving 10-year-old children using Scratch to create mathematical digital learning objects, including games, and examines the ways mathematical thinking was facilitated through this process.

Curriculum documents in Australia are designed around outcomes and related standards. Teachers need to provide opportunities for students to learn the content that will allow them to meet the expectations defined in the curriculum. After undertaking professional learning sessions about the SOLO model, mathematics teachers in six high schools hypothesised developmental pathways for several key mathematical ideas. These theorised pathways were compared with Australian and State curriculum outcomes. The implications of using this approach for supporting teachers are discussed.

This study examines the influence of middle school students’ frames of reference on their assessments of interest for statistical literacy. Based on the responses of 406 middle school students to a previously validated interest measure, the study explores students’ use of external – perceived self-competency when compared with others – and internal – perceived self-competency when compared with other subjects – frames of reference on their interest assessments. The study concludes that students’ assessments of interest appear to be dependent on both comparisons but only for those students who consider that they are worse at maths than their peers. The interest assessments of other students appear to be less dependent on their self-competency beliefs.

Ratio (and associated topics such as fractions and proportion) is known to be an area of mathematics that students find difficult. Multiplicative thinking is necessary, and students benefit from a wide range of strategies and representations for interpreting ratio. This study examined aspects of teachers’ pedagogical content knowledge for teaching ratio, and investigated their knowledge of a typical misconception together with the strategies that they would use for dealing with such a misconception. The nature of the numerical examples that they suggested might be useful in teaching was also examined. Most teachers were able to recognise the misconception, but not all were able to generate examples that might help students to deal with it. Teachers also appeared to have only a limited repertoire of strategies to assist students.

As part of a larger project, Task Types in Mathematics Learning, through the use of a questionnaire, we sought middle years mathematics teachers’ insights into the task types they chose to use in mathematics, the reasons for these choices, and the ways (if any) in which their choices had changed as a result of their involvement in the project. We found that teachers were able to articulate the reasons for their choices, and that both the choices and the reasons given varied considerably across the group. We also found that most teachers had changed their relative use of task types as a result of the project. Of particular note was the increased use of contextual tasks.

This paper reports on students’ ability to decode mathematical graphics. The findings were: (a) some items showed an insignificant improvement over time; (b) success involves identifying critical perceptual elements in the graphic and incorporating these elements into a solution strategy; and (c) the optimal strategy capitalises on how information is encoded in the graphic. Implications include a need for teachers to be proactive in supporting students’ to develop their graphical knowledge and an awareness that knowledge varies substantially across students.

This paper reports on 13 Grade 3 students’ approaches to Equivalent groups and Times as many multiplicative word problems. The findings are part of a larger study relating to children’s development of multiplicative thinking. Of particular interest was the extent to which task level of difficulty influenced students’ strategy choice. The results suggest a relationship between the level of difficulty and strategy choice: the more difficult the task the more sophisticated strategy choice.

This paper reports on two upper primary teachers’ use of particular scaffolding practices, individual discussion and the use of manipulatives. The cognitive and affective impact on four low-attaining students in these classes is described. The teachers and students were observed during eight to ten sequential tasks. “Scaffolding conversations” emerged as a common practice for these teachers whilst the use of manipulatives represented a point of difference.

Teachers play a crucial role in the mathematical learning outcomes of their students. The quality of teachers’ mathematical knowledge has been of interest to key stakeholders and several lines of inquiry have been running in an effort to better understand the kinds of knowledge that mathematics teachers need to acquire and use to drive their lessons. Despite a decade of research in this area, the interconnections amongst the various strands of knowledge required by mathematics teachers is still unclear. In this report we attempt to investigate this issue by focusing on procedural and conceptual knowledge utilised in the assessment responses of a cohort of prospective teachers.

This is the academic numeracy journey of Tania, who participated in a research study that investigated the academic numeracy skills of nursing students. Tania is a mature aged woman, and her story represents many of such mature aged students as they journey into a largely unknown university culture. The data for this research came from student assignments, surveys, interview transcripts, emails and screencasts. To see the development in Tania’s numeracy, this paper utilises the micro- and macrogenetic models from Valsiner, and his approach to dialogic self, We see Tania in different I-positions in particular of becoming a university student, becoming a nursing student and becoming numerate i.e. as being able to use mathematics confidently and competently in a nursing context.

This paper explores the impact of the Bridging the Numeracy Gap Project on the wholenumber learning of Prep and Grade 1 students living in a low SES community. The findings suggest that an approach that includes a specialist mathematics teacher who provides specialised programs for mathematically vulnerable students, and who works in partnership with classroom teachers to design individual learning plans, and classroom mathematics programs that cater for the diverse range of students’ learning needs, has a positive effect on mathematics learning and instruction.

The National Numeracy Review recognised that numeracy development requires an across the curriculum commitment. To explore the nature of this commitment we conducted a numeracy audit of the South Australian Middle Years curriculum, using a numeracy model that incorporates mathematical knowledge, dispositions, tools, contexts, and a critical orientation. All Learning Areas in the published curriculum were found to have distinctive numeracy demands. The audit should encourage teachers to promote numeracy in even richer ways in the curriculum they enact with students.

Standardised testing has received a lot of political and public attention recently in Australia. This paper describes the sense-making of Year 3 students as they interpret items from the 2008 NAPLAN. Results show that student performance changed dramatically when the terminology of an item was modified and subsequently were not a true indication of student mathematical knowledge and understanding. Implications include the need for test designers to carefully consider the terminology included within assessment items and the need for comprehensive analysis of student results.

The professional practice of teachers is shaped and directed by their sense of identity (Beijaard, Verloop, & Vermunt, 2000). All teachers have some conception of themselves as pedagogues, but they also have identities which relate to the disciplines that they are required to teach. Here we report on a project that explored the nexus of these identities with specialist mathematics teachers in secondary schools and generalist teachers who teach mathematics in primary/middle schools. The preliminary findings presented here suggest that when teaching mathematics, teachers often enact a pedagogy that unconsciously reflects their identities as somewhere on the continuum from mathematician to teacher. It appears that ‘excellence’ as teachers may be associated with teachers viewing themselves as educators first and foremostly, but who have a positive perception of the discipline area, and who are confident in the related Pedagogical Content Knowledge.

Mathematics educators and mathematics standards of curriculum have emphasised the importance of constructing the interconnectedness among mathematic concepts (“conceptual understanding”) instead of only the ability to carry out standard procedures in an isolated fashion. Researchers have attempted to assess the knowledge networks in students’ minds. A technique that has gained popular use in science education over the past three decades is concept mapping. This paper examines students’ conceptual understanding about triangle concepts using concept maps, and an analysis of the maps using degree centralities derived from social network analysis has demonstrated new insights through this novel technique.

Rate is an important, but difficult mathematical concept. More than twenty years of research, especially with calculus students, report difficulties with this concept. This paper reports on an alternative analysis, from the perspective of multiple representations and context, of interviews probing twenty Victorian Year 10 students’ conceptions of rate. This analysis shows that multiple representations of functions provide different rate-related information for different students. Understandings of rate in one representation or context are not necessarily transferred to another representation or context.

There are concerns about the trends and patterns in enrolments in senior school mathematics. Shortages of suitably qualified teachers and dwindling students’ demand for Advanced Mathematics have led some Western Australian schools to collaborate to provide an otherwise unavailable opportunity for their students to study Advanced Mathematics. It is of research interest amidst the downward trends in enrolment to learn about such students, to hear about their experiences and perspectives. This paper reports parts of the initial findings.

Student transition from arithmetical understandings to algebraic reasoning is recognised as an important but complex process. An essential element of the transition is the development of a rich understanding of variables. Drawing on findings from a classroom-based study, this paper outlines the instructional tasks and pedagogical actions a teacher used to facilitate her students understanding of variables. The findings affirm that younger students can begin developing understanding of variables and use forms of algebraic notation to represent their mathematical ideas. Carefully designed tasks, specific pedagogical actions and extended discourse were all important elements in facilitating student understanding.

This paper adds to a discussion initiated by Askew (2007) about two contrasting views of scaffolding; as a ‘tool for results’ and a ‘tool-and-result’. The study took place in four primary classrooms within a low socioeconomic setting. Two classroom episodes drawn from one of the teacher’s classroom, illustrate the two different perspectives of scaffolding. These are presented and the learning that evolved from each episode is discussed. The paper illustrates that when scaffolding was used as a ‘tool for results’ the learning was restricted but when the students were scaffolded within a tool-and-result perspective the mathematical knowledge and ways of doing and talking mathematics were generative.

This study considered ways of improving mathematical outcomes for urban Indigenous students. It focused on three primary schools in Western Australia and identified factors that were perceived to be having an impact on student learning. These included expectations for students, attendance rates, parent involvement, student literacy levels, student engagement, and test literacy. Base-line data were gathered to identify mathematical needs — conceptual understanding, place value, calculating beyond finger counting, and an action plan for 2010- 2012 was developed to address those needs and to counter factors that may have had an adverse impact on student learning.

This paper reports on two of ten themes that emerged from a study of the impacts of a fraction teaching intervention on the mathematics anxiety and fraction competence of eight Year 8 students. The themes arose from multiple data sources and relate to Student Attitude and Student Understanding. The students identified practical, hands-on activities and group work as impacting positively on their understanding and their confidence in relation to fractions. The influence of improved understanding and confidence was also recorded as positively affecting student attitudes to fractions in particular and mathematics in general. The study highlights the connections between mathematics anxiety among middle school students and their existing understandings of and attitudes towards mathematics.

In remote Aboriginal communities, there are many challenges that confront educators, not the least of which is leadership that challenges the status quo and moves Aboriginal communities forward in their access to, and engagement with, the mathematics school curriculum. This paper draws on data from the Maths in the Kimberley (MiTK) project where the complexities around reforming mathematics were investigated through leadership models. It was considered that the complexities faced by principals in their day-to-day management of schools closed down their capacity for curriculum leadership. A new model of curriculum leadership, based on the Accelerated Literacy model was adopted for numeracy reform. This model, its genesis and its implementation is discussed along with the mitigating context that shapes the need for models of leadership that focus on curriculum reform for remote Indigenous contexts. The implications of this model are discussed in conjunction with the field of mathematics educational research.

This qualitative research study involving 128 students in grades 4-6 was conducted to develop a framework for characterizing upper primary school students’ algebraic thinking. Four levels of algebraic thinking were identified from student responses to tasks involving patterns and open number sentences. Level 1 students failed to understand the tasks or answered with irrelevant data. Those at Level 2 understood the tasks but were unable to proceed further. Level 3 students were able to complete the tasks but were unable to link one aspect of the task to another. Level 4 students understood the relationship among various aspects of data and used all aspects of the data.

This paper explores the infusion of financial literacy into the Mathematics curriculum in a secondary school in Singapore. By infusing financial literacy, a core theme in the 21st century framework, into mathematics education, this study investigated the impact of using financial literacy-rich mathematics lessons by using validated learning environment instruments. This study is part of a larger study to design, monitor, and evaluate an innovative pedagogical approach of using authentic financial literacy examples to reposition mathematics education in schools.

While the notion of numeracy as the capacity to make use of mathematics within contexts associated with personal and public life, as distinct from basis mathematical competence, is broadly accepted, forms of professional teacher learning that lead to the effective teaching of numeracy are still the subject of ongoing research. This paper reports on a small scale study which aimed to investigate the potential for pairs of teachers, working with two tertiary mathematics educators, to improve the quality of their teaching of numeracy through reflection on each other’s teaching practice. While viewing their teacher pair’s lesson via video each teacher identified aspects of the lesson that they could use to improve their own teaching.

A program of Assessment for Learning (AfL) was implemented with 107 Year 12 students as part of their preparation for a major external test. Students completed extended mathematics tasks and selected student responses were used for peer assessment purposes. This paper reports on two of the AfL elements, namely task selection and peer assessment as part of the AfL process. The importance of initial task selection in terms of supporting students in building awareness of quality of mathematical arguments is highlighted.

Gender differences in mathematics learning have attracted sustained attention in Australia and internationally. Over time, female participation in academic fields and careers long considered male domains has improved. Yet recent mathematics achievement data reveal that gender gaps favouring males appear to have re-opened. In our study we explored the Victorian general public’s views on gender issues and school mathematics. In general, boys were considered to be better at mathematics than girls, that is, vestiges of the male mathematics stereotype persist.

2009 was the final year of parallel implementation for Mathematical Methods Units 3 and 4 and Mathematical Methods (CAS) Units 3 and 4. From 2006-2009 there was a common technology-free short answer examination that covered the same function, algebra, calculus and probability content for both studies with corresponding expectations for key knowledge and key skills. There was also separate technology-assumed examinations comprising common and different multiple choice and extended response questions. In 2009 the two cohorts were of similar size, comprising 7000-8000 students each. This paper analyses student performance for both cohorts with respect to these common items.

Studies that investigated students’ attitudes toward mathematics and its relationships with achievement are scarce in Singapore. To address this issue, the mathematics attitudes and achievement of 984 junior college students were measured. Results indicated that students had positive attitudes toward mathematics but lacked intrinsic motivation to do mathematics. Students were extrinsically motivated to study mathematics, but the relationship between extrinsic motivation and achievement was weak. However, there was a significant positive correlation between intrinsic motivation and achievement. This is contrary to the beliefs of many educators and parents in Singapore who believe in extrinsic rewards and punishments to encourage better achievement. This study suggests that Singapore educators and parents should focus more on how to motivate students intrinsically.

This paper draws on observation of a primary mathematics lesson prepared and taught by a second-year pre-service teacher who lacked mathematical content knowledge. A ‘knowledge quartet’ (Rowland, Turner, Thwaites, & Huckstep, 2009) was used to investigate when and how a pre-service teacher drew on their knowledge of mathematics during primary teaching. Data were collected from field notes, audio recording of part of a lesson, and an interview with the pre-service teacher after the lesson. Discussion focuses on the four characteristics of the ‘knowledge quartet’: foundation, connection, transformation and contingency. Conclusions suggested that pre-service teachers need to continue developing their mathematical content knowledge to assist with future planning and teaching of primary mathematics lessons.

This study investigated pre-service primary teachers’ knowledge and beliefs about mathematics, the curriculum in Hong Kong, and teaching practices. Pre-service teachers from all four years of the program who were majoring in mathematics teaching completed a questionnaire. A sample participated in an interview and provided lesson plans for analysis. This paper reports the data obtained from the beliefs section of the questionnaire. The preliminary results indicated that the mathematical beliefs of the pre-service teachers generally supported the innovative approaches recommended in the revised curriculum. Nevertheless, for some there was a contradiction between their beliefs about the role of mathematics teachers and mathematics learning in classrooms.

This paper presents the results of a survey conducted with students (N=97) whose teachers have used the Web in their mathematics classes. The survey looked at students’ attitudes towards learning mathematics and their responses to the use of the Internet for learning mathematics. Factor analyses were used to determine the constructs that underlie the survey. Indices formed were used to explore their relationships with each other and with other variables. Interview findings were able to support and lend insight into some of these results.

This paper reports on a component of a large yearlong study in three Year 7 classes in three different schools. The aim of this research component was to determine the relationship between students’ number sense and their problem-solving ability by means of paper-andpencil tests, classroom observations, and interviews of students and teachers. The results revealed a strong correlation between these two aspects of school mathematics, with important implications for classroom teachers.

This paper describes the development of an instrument to assess teachers’ views on their geometry instruction and their classroom learning environments in six government high schools in southwest Sydney. The sample consisted of 18 Years 9/10 ESL teachers from participating schools. The study involved completion of a survey form using a modified and expanded What Is Happening In this Class (WIHIC) questionnaire for teachers along with participant interviews. The findings indicated that there were positive associations between the learning environment and teachers’ views on geometry instruction and the achievement of their classroom goals.

This paper presents data gathered during a three-year study that explored the experiences with measurement that children have in prior-to-school and out-of-school contexts, and the ways in which children are able to represent these experiences. In this present investigation, examples of the children’s responses to an open-ended drawing task, collected at the commencement of Kindergarten, are backward-mapped in relation to the draft Australian Curriculum’s Measurement and Geometry strand for Kindergarten, with a focus on the Comparison sub-strand. This data demonstrates that most of the measurement skills described in the Comparison sub-strand of the Australian Curriculum are being exhibited by children at the commencement of schooling, prior to any formal teaching about measurement taking place.

The purpose of this paper is to describe the development of a framework to facilitate the selection and evaluation of picture books that may be useful in promoting and developing mathematical concepts in young children. Three types of mathematical picture books were initially recognised with intercoder reliability of 0.92. Seven categories were identified in the framework: Mathematical content; Curriculum content, policies, and principles; Integration of mathematics content; Mathematical meaning; Mathematical problem solving and reasoning; Affordance for mathematics learning; and Pedagogical implementation.

The educational discourse in recent years in Australia, and in particular NSW has been on advancing the status of the teaching profession through the development of a framework of standards, and by supporting the nature of teachers’ work in addition to improving studentlearning outcomes. The close link between student learning outcomes and quality mathematics teaching has resulted in the call for an increase in teacher accountability and quality. This paper is an exploration of the relevant literature that focused on the professionalisation of the teaching profession in Australia and its potential impact on teaching in Australia.

A challenge for educational employing authorities is the provision of high-quality, sustainable professional development opportunities that will lead to positive growth in teachers’ pedagogical practices. The study reported here sought to devise and implement a model of teacher professional development that would result in such growth by increasing mathematics content knowledge and pedagogical content knowledge. While there were a number of components to the study, including the investigation of a relationship between teacher professional learning and improved student learning outcomes, this paper focuses upon the changes in teachers’ beliefs and practices as reported by the teacher participants, their students, and observed by the researcher. A variety of qualitative methods for data collection were used in order to develop a complete picture of the nature of teacher growth.

This paper reports on change in teachers’ perceptions of important elements of their role as teachers of mathematics at the conclusion of a two-year professional learning project. Analyses of written responses to survey items indicated shifts in four categories describing important elements of their role: teaching skills, knowledge, concepts; developing problem solvers; facilitating learning by providing quality activities, tasks, and resources; and fostering positive attitudes towards mathematics learning. Teachers attributed these perceived changes to the integration of a number of components within the project.

The limited mathematical knowledge of pre-service primary teachers is an international concern. The areas of mathematical difficulties have been well documented, which has led to many universities instituting testing regimes to ensure that their pre-service teachers have appropriate knowledge of primary school mathematics. In this study, the pre-service teachers identify some benefits for being tested, but these were often related to having sufficient knowledge so that they did not loose face in front of a class. It is suggested that these students’ emphasis on performance rather than competence could exacerbate a reliance on procedural rather than conceptual understanding.

This paper focuses on the initial analysis of a study of a professional learning intervention. Using a case study design it was possible to describe one teacher’s involvement in this research. The study revealed how the teacher’s beliefs and pedagogical content knowledge of computational estimation was altered as a result of participating in the research. This development appeared to have an impact on her approaches to the teaching of computational estimation.

Gap thinking has been categorised as one of several whole number strategies that interfere with early fraction understanding. This study showed that this claim is not supported by interview data of Grade 6 students’ gap thinking explanations during a fraction pair comparison task. A correlation with equivalence performance was uncovered, leading to the suggestion that the additive nature of gap thinking may actually reveal the (erroneous) additive nature of students’ early engagement with equivalence concepts.

This paper reports on an investigation into managing cognitive conflict in the context of student learning about decimal magnitude. The influence of prior constructs is examined through a brief review of the literature. A micro-genetic approach was used to capture detail of the teaching intervention used to facilitate development in student thought. A framework for considering cognitive conflict in lesson design is presented, and a case is made for the use of measurement tasks to generate data.

The MERGA website has a list of the titles of the last 10 years of Australasian mathematics education Masters and Doctoral theses, with linked abstracts. After a discussion about the socially-determined nature of document analysis, this paper reports the results of an interpretive document analysis of the web page and the pages of abstracts, with a focus on (a) numbers of theses, by year and by institution; (b) methodological approaches used; (c) countries where data were collected; and (d) theses topics. Begle’s (1979) framework of mathematics education domains is used to categorise 3 descriptors for each thesis.

This paper reports on the use of a reflective technique that incorporated video-stimulated recall to encourage reflection on practice. The author videotaped a series of mathematics lessons conducted by an experienced teacher, which were then collaboratively viewed and discussed, with the aim being to bring about changes in the teacher’s practice. The findings indicated that the video footage was a powerful medium that stimulated deliberate reflection and led to changes in teaching approaches that were consistent with mathematical reform recommendations.

This paper provides an interim report of a large empirical evaluation study in progress. An intervention was implemented to evaluate the effectiveness of the Pattern and Structure Mathematical Awareness Program (PASMAP) on Kindergarten students’ mathematical development. Four large schools (two from Sydney and two from Brisbane), 16 teachers and their 316 students participated in the first phase of a 2-year longitudinal study. Eight of 16 classes implemented the PASMAP program over three school terms. This paper provides an overview of key aspects of the intervention, and preliminary analysis of the impact of PASMAP on students’ representation, abstraction and generalisation of mathematical ideas.

This paper investigates the impact of group dynamics on metacognitive behaviours of students (aged 13-14) during group collaborative problem solving attempts involving a design-based real-world applications project. It was discovered that group dynamics mediated the impact of metacognitive judgments related red flag situations and metacognitive failures. The existence of partial metacognitive blindness was also discovered and two contrasting phenomena could result from this because of differing group dynamics.

This paper collates some of the systematic ways that different cultural groups refer to space. In some cases, space is more strongly identified in terms of place than in school Indo-European mathematics approaches. The affinity to place does not reduce the efficient, abstract, mathematical system behind the reference but it does strengthen its connection to the real world of place. This review of research uses a critical approach to develop an ecocultural perspective on spatial referencing. It refers to studies on the Polynesian Wayfinders; the Garma project at Yirrakala in the Northern Territory of Australia identifying Yolgnu sense of position; original field data mainly from Papua New Guinea; and on the work of linguists who have recorded and analysed the ancient languages of the Pacific region. The paper provides the mathematics educator with a richer perspective on position and a way of understanding the thinking of students with language and cultural backgrounds other than English. The Indigenous languages of Australia form a basis for ways of thinking spatially for specific groups of Indigenous students.

This paper originates from a larger qualitative study exploring how teachers incorporate the affective domain into the primary mathematics classroom. This paper analyses teacher’s experiences of mathematics and explores, using activity theory, how these experiences impact their teaching. An important factor to emerge from the data was teacher’s own experiences learning mathematics and how this shaped their mathematical identity.

If the ability to reason proportionally seems to be a good indication of likely success in further mathematical pursuits (Lamon, 1999), how do children develop this ability, and how can teachers facilitate this? In this present study, six ratio/rates task-based assessment questions were trialled on ten students from Grades 5 to 9 in an attempt to describe the developing understanding of students within this construct of rational number. Tentative points of growth (or stages of understanding) are suggested, with some implications for the classroom teacher.

This paper is aimed to describe an ethnographic intervention study of supporting a Low Use Internet (LUI) teacher to use the Internet for his professional development. Five characteristics of effective professional development were identified and applied. This description is followed by a reflection on the process to get a deeper insight about factors that could support and restrict teachers in making positive changes in his mathematics teaching.

This paper explores the notion that the discourse of the mathematics classroom impacts on the practices that students engage when modelling mathematics. Using excerpts of a Year 12 student’s report on modelling Newton’s law of cooling, this paper argues that when students engage with the discourse of their mathematics classroom in a manner that promotes the communication of ideas, they employ mathematical modelling practices that reflect the cyclical approaches to modelling employed by mathematicians.

An assessment approach from Mathematics Recovery was used to document the number knowledge of 20 first-graders and 20 second-graders in an Indonesian school. Sixteen firstgraders were at the advanced-counting-by-ones stage and fourteen second-graders were facile. As well, fifteen first-graders and eleven second-graders were at the level of an intermediate concept of 10. Other findings were nine of the second-graders used the erroneous ‘subtract smaller from larger bug’ and five first-graders used Jarimatika (Chisanbop). Results are discussed in light of the literature.

This paper seeks to establish a research framework for an investigation into the extent to which pupils are able to visualise figural cues in multiple ways within the context of pattern generalisation. Enactivism, along with the constructs of knowledge objectification and figural apprehension, are identified as forming an ideal theoretical framework for such a study. Although largely theoretically driven, this paper also presents results from an initial pilot study in order to contextualise the theoretical milieu.

Through reporting on an initiative in South Africa that aimed to provide epistemological access to teachers and learners of mathematics (and science) through translating mathematical concepts into two indigenous languages, this paper argues for the urgent development of mathematical registers in indigenous languages for mathematics and science. The pilot research reported on in this paper indicates that the use of a multilingual concept literacy book impacted noticeably on the code-switching practices of selected teachers who switched between English and Xhosa in their teaching of mathematics.

Curriculum reforms in the teaching of mathematics have encouraged a move away from sole memorisation of facts to the construction of deeper levels of understanding. With this reform, teachers of mathematics are called to act as facilitators of the construction of mathematical knowledge. However, some research suggests that students believe that their teacher’s role is one that would be more aligned with the transmission of knowledge. This paper reports an aspect of a small-scale pilot study that sought to illuminate the beliefs that students hold about their preferred mathematics learning environments. It also highlights the role that ‘concept cartoons’ played in making known these beliefs.

There are now strong arguments for building closer links between children’s understanding of numbers and number operations and the beginning of algebraic (relational) thinking in the primary school years. Rarely, however, do Australian mathematics textbooks give enough guidance for teachers to use good activities in the classroom to promote algebraic thinking. By contrast, Japanese mathematics textbooks introduce students to relational thinking about number sentences, starting from the first grade. The idea of a learning trajectory – or trajectories – seems a fruitful way of looking at how this is achieved and what it might mean for the teaching of Number and algebra in the primary years.

As part of a larger project, we examined how students describe their ideal mathematics lesson. We found that the students’ comments were similar to the characteristics that are often used by researchers to delineate the features of effective teaching. In particular the students liked clear explanations, they recalled lessons that used materials that allowed connections to their lives, felt the mode of grouping to be important, and many liked to be challenged. There was diversity in the types of lessons that they described indicating that variety is also important. Teachers are encouraged to pay attention to opinions of students on the pedagogies they value.

This paper presents a comparison of the solution strategies used by two groups of Year 8 students as they solved linear equations. The experimental group studied algebra following a multifaceted variable approach, while the comparison group used a traditional approach. Students in the experimental group employed different solution strategies, namely balancing method, working backwards and guess and check for solving different linear equations, whereas students in the comparison group tended to use a single, procedural approach. It is concluded that the multifaceted approach developed students’ concepts not only of variables but also of equations.

incorporating interactive technologies. This musical analogy suggests pre-planned manipulation of events to generate ‘performance’ leading to learning. However, in two recent projects we have observed how effective teaching and learning is often based on serendipity and improvisation – characteristics more often associated with jazz. This paper explores how a jazz analogy can be useful when analysing classrooms in which serendipitous events were exploited and performances were improvised.

This paper reports on the structure and impact of a one on one numeracy intervention project conducted during 2009 with students in years 1, 4 and 8. The project was built on a Reading Recovery model, using research into how the brain learns mathematics and ideas of threshold concepts. Teachers were provided time to work individually with students at their point of need. The results suggested that the model was effective in both cognitive and affective terms, and that the learning gained through the project is beginning to result in whole school improvements in mathematics pedagogy.

Pre-service primary teachers have been identified in several research studies as having poor self-conceptions of themselves as mathematics teachers. Many express feelings of anxiety when faced with mathematics tasks resulting in poor dispositions and understandings. This paper reports on beginning pre-service primary teachers’ (N=106) recollections of critical moments in their mathematics education at school. Interestingly, their graphical ratings of their dispositions suggest a slightly positive recollection of their mathematical experiences. In contrast their justifications and recount was generally negative.

A Numeracy Strategy was trialled in 30 at-risk schools in Fiji. A Training Needs Analysis and a review of the Fiji Islands Literacy and Numeracy Assessment helped decide on the focus of the trial. Teachers were introduced to Classroom Based Assessment and child centred pedagogy, which they used over a four-week period. Students showed considerable improvement in their mathematics knowledge and attitudes. Teachers’ knowledge and confidence in using classroom based assessment to improve students’ numeracy also improved.

Student centred approaches to teaching and learning in mathematics is one of the reforms currently being advocated and implemented to improve mathematics outcomes for students from low SES backgrounds. The models, meanings and practices of student centred approaches explored in this paper reveal that a constructivist model of student centred teaching and learning is being promoted and implemented with some success. The ways in which teachers and leaders are being supported through network and school based professional learning are described.

Poor results in Queensland Year Three NAPLAN Numeracy tests have provided a focus to critically review the classroom practices of lower primary mathematics teachers. This paper outlines how pedagogical content knowledge can be strengthened by emphasising conceptual understanding, by utilising dynamic classroom discourse, by an awareness of bidimensional thinking and with an improved understanding of children’s typical learning trajectories.

Teacher mobility is often viewed as a limitation of longitudinal analyses of teacher learning in communities, in which membership changes. I introduce an analytical tool developed to address the continuation of the learning of such communities across changes in membership. In the case analysis, I examine whether changes in membership should be framed as induction of new members into a single community that evolves across the years, or instead as the emergence of a new community each time the membership changes.

This paper engages general debates about the production of knowledge and, within that, more specific debates about the place of the researcher in the research process. There are two main objectives: one is a theoretical interest that involves examining the issue of subjectivity and how intersubjective negotiations take shape in research encounters. A second objective is to speculate from my own data what these understandings of the researcher’s subjectivity tell us about the production of knowledge. It is also to understand the part that emotions and unconscious interference play in research.

The gap between young Indigenous and non-Indigenous children’s capability within mathematics is widely acknowledged. This gap is conjectured to exist at all levels of schooling, including pre-school, and widens as children mature. Most of these findings are based on research relating to children’s understanding of number and space. Little is known about what knowledge Indigenous students bring to early years settings with regard to patterning, an area that is widely acknowledged as fundamental to the development of concepts, process and knowledge of mathematics. One on one interviews were conducted with 35 Indigenous children (average age 4 years and 4 months) as they entered kindergarten. The results indicate that these children do enter these settings with some intuitive understanding of repeating pattern, and that this knowledge is at odds with the hypothesised learning trajectory (Samara & Clements, 2009) for repeating patterns.

As part of an interview protocol investigating teachers’ pedagogical content knowledge (PCK) in statistics, 40 teachers were presented with a newspaper article reporting a phonein survey about the legalisation of marijuana. The article and a question about the reliability of the sample had earlier been used in student surveys, and three student answers to the question were also presented to the teachers. Teachers’ PCK was assessed based on responses to questions about the big ideas in the task, potential student appropriate and inappropriate answers, and how teachers would intervene in relation to the three student answers. The wide range of responses provided evidence for the potential of the task in a cross-curricular secondary classroom.

This paper reports partial outcomes from a three-year project that provided professional learning opportunities in mathematics for middle school teachers in rural schools in Tasmania. The educational environment for the study was one of significant system transition. Student change is reported here and was measured with survey instruments reflecting the basic elements of numeracy considered essential to students’ development of critical quantitative thinking and preparation for study of further mathematics. Student improvement was significant across grades in the project.

The 2009 Counting On program has evolved from a series that began in 1999 and which continued to expand and change until the current manifestation. The program has always had a twin learning focus upon both students and teachers. Thus it seeks to improve student mathematical outcomes while building capacity within the teachers by improving their professional situated mathematical knowledge which is the knowledge teachers need to effectively teach the early mathematical concepts to their students in a classroom context. Counting On 2009 was evaluated and this paper will use the findings of the evaluation report (White, 2010 in press) to examine whether the program was successful in changing student learning outcomes.

This paper discusses an attempt to examine pre-service teachers’ mathematical modelling skills. A modelling project investigating relationships between temperature and time in the process of cooling of coffee was chosen. The analysis was based on group written reports of the cooling of coffee project and observation of classroom discussion. Findings showed that pre-service teachers were able to model the process of cooling of coffee as a decreasing exponential function. Difficulties with interpretation of the constant rate of cooling and reinterpretation of mathematical model were identified.

This study draws on data from a broader video-stimulated interview study of the role of optimism in collaborative problem solving. It examines the activity of a Grade 5 student, Tom, whose initial constructing activity resulted in a ‘Partially Correct Construct’. Insistent questioning from another group member pressuring for clarification led to Tom developing a ‘more correct construct’ with further potential for revision. This paper raises questions about influences that can stimulate or inhibit construct refinement.

Mathematics anxiety in pre-service primary teachers is an important issue in teacher education. This leads to the question of how pre-service primary teachers with mathematics anxiety perceive their mathematical identities. The paper explores the potential to develop a research-based model to identify the process whereby pre-service primary teachers with mathematics anxiety could develop more positive identities as learners and potential teachers of mathematics. It indicates emerging themes from previous research using subsequent preliminary data analysis and argues that a grounded theory approach to building a theoretical model for this process would make a valuable contribution to teacher education.

The paper reports some findings about how pre-service students engage with the mathematics and statistics section of the New Zealand Curriculum (2007), when writing a yearly long-term plan in this curriculum area. This authentic task for pre-service students provided opportunities to seek out information about relevant curriculum knowledge including reviewing and revising mathematical content. This paper is part of a larger study, which focuses on the needs and concerns of final year primary pre-service teachers as they anticipate teaching mathematics in their first year of teaching.

Algebraic thinking is a crucial and fundamental element of mathematical thinking and reasoning. It initially involves recognising patterns and general mathematical relationships among numbers, objects and geometric shapes. This paper will highlight how the ability to think algebraically might support a deeper and more useful knowledge, not only of algebra, but the thinking required to successfully use mathematics. The paper will highlight how a deeper analysis of mathematical problems can instigate student discourse, providing meaningful experiences that can developing algebraic thinking.

Learning pathways capture the development of competence in a mathematical domain. They have been developed from empirical studies in the areas of mental computation and emergent numeracy concepts. These pathways afford teachers the opportunity to identify students’ current levels of understanding, antecedent understandings and the steps that are likely to result in students achieving a more sophisticated level of understanding. A pathway of the skills and knowledge that students acquire in developing conceptual understanding of fraction equivalence was developed through the assessment of 649 students from Grades 3 to 6 attending six primary schools. The assessment, analysis of data and hypothesised pathway for area models are described in this paper.

This paper reports on three primary school students’ explorations of 3D rotation in a virtual reality learning environment (VRLE) named VRMath. When asked to investigate if you would face the same direction when you turn right 45 degrees first then roll up 45 degrees, or when you roll up 45 degrees first then turn right 45 degrees, the students found that the different order of the two turns ended up with different directions in the VRLE. This was contrary to the students’ prior predictions based on using pen, paper and body movements. The findings of this study showed the difficulty young children have in perceiving and understanding the non-commutative nature of 3D rotation and the power of the computational VRLE in giving students experiences that they rarely have in real life with 3D manipulations and 3D mental movements.

The relationship between socio-economic background and completion of senior secondary mathematics study leading to various post-schooling pathways has been an area of keen interest to researchers, school systems and policy makers for some time. This paper briefly considers some aspects of this relationship using recent Victorian data relating to the index of relative socio-economic disadvantage (IRSD), enrolments and study scores for Victorian senior secondary mathematics students and On Track destination data.

This paper explores the impact of almost two decades of mathematics education reform in New Zealand on the attitudes of pre-service teacher education students training to be primary teachers. More students were positive towards mathematics and fewer were negative compared to Biddulph (1999). In the present study, more students were positive about the prospect about teaching mathematics than about mathematics. Only 47% of the students were positive about both mathematics and the teaching of mathematics. However, students’ reasons for their ratings revealed that a negative attitude towards mathematics sometimes resulted in enthusiasm about helping children to have better experiences than they themselves had had at school. Some students with positive attitudes towards mathematics worried about the responsibility of providing high quality teaching experiences in mathematics for children. The study showed that this issue is complex and attitudes towards teaching mathematics may be different from attitudes towards mathematics.

This paper explores the differences between middle school students‘ interest for the statistical literacy acquired in mathematics classes, their interest for mathematics in general, and their interest for the statistical literacy acquired in other school subjects. Based on the responses of a sample of 425 Australian middle school students, it appears that such students have no more interest for the statistical literacy in mathematics classes than the mathematics that they encounter. The same students, however, have more interest for statistical literacy when it is encountered outside of mathematics classes. Follow up interviews with 17 students are used to explore the reasons for these differences. The results suggest that students‘ interest for statistical literacy is strongly associated with the perceived relevance of the context in which the statistics is embedded. Moreover, a number of students dislike the inherent uncertainty that is associated with statistics, preferring instead problems with clear solutions.

Recent debates on students' learning outcomes in mathematics have shifted the focus to better understanding the types of knowledge that teachers need in order to support children. In the present study, we examined the quality of knowledge of a cohort of prospective teachers along the dimensions developed by Ball et al. (2008). We found support for the contention that beginning teachers tend to have built a body of content knowledge. However, that knowledge remains less germane to teaching children. Implications for translation of this knowledge for teaching are presented.

One component of an ongoing New Zealand study investigating instructional leadership in numeracy, an online survey, was completed by 44 primary school leaders – numeracy lead teachers, principals, deputy and assistant principals, and syndicate/team leaders. Patterns identified in an analysis of the responses showed that numeracy lead teachers often had a multiplicity of roles, and suggested that numeracy lead teachers who were also a member of the management team had greater influence than those who were not. Implications for the future leadership of numeracy will be discussed.

The Aboriginal Independent Community Schools (AICS) Numeracy Strategy is a DEEWR funded action research project providing support to independent Indigenous community schools in Western Australia. Over the next two years, the Strategy will work towards making significant improvements in Indigenous students’ understanding and skills in numeracy. The project uses a cycle of discovering what students know, focusing on the mathematics they need to learn and implementing effective pedagogy. Consultants will make regular visits to the schools, working shoulder to shoulder with teachers, Aboriginal Education Workers, and principals. Professional development workshops will be run within schools and at conferences, with resources being developed to support the implementation of the Strategy. Progress will be monitored using standardised assessment and classroom based assessment tasks.

The University of Adelaide’s Maths Learning Service offers a bridging course as an alternative pathway to university. This self-paced course is for some students a form of distance education. The course appears to be unique in Australia because of the self-paced nature, with students able to take as much or little time as they require, and the fact that students are not graded but rather only progress once a certain level of understanding is achieved. This communication will discuss the experience of teaching in this mode and the effectiveness of the individual feedback on learning.

The relationship between females’ attitudes to calculator technology and their achievement and participation in higher-level secondary school mathematics was investigated in this small pilot study. The sample comprised nine females who had recently completed secondary schooling. Most believed that technologies such as graphics and Computer Algebra System calculators were obstacles to higher-level mathematics learning and did not enable them to gain a better understanding of mathematical concepts. Several indicated that mathematics was not particularly useful or relevant for them except as a vehicle to university entry. More research is needed to determine the representativeness and significance of these findings.

Research has found marked differences in student performance with various algebraic problems (e.g., word problems, word equations, equations) (Koedinger & Nathan, 2004). In addition, research has shown that students’ understanding of variable is fragile (Booth, 1984; Carraher, Schielmann, & Brizuela, 2001; Stacey, 1989). Often, the teacher/researcher’s introduction of literal symbols assumes that students make connections between their informal symbolisations and formal conventional symbolisations (Kaput, 2008). This cross-sectional research project explores the influence of problem type and variable representation for United States Grade 4 – 6 students as they transition from informal representations of variables to formal conventional representations.

Lesson study is a professional development process whereupon teachers collectively and systematically examine their own practice in order to improve their teaching (Fernandez & Yoshida, 2004; Stigler & Hiebert, 1999). The focus of this report is on how involvement in a lesson study cycle focused on primary mathematics lessons supported teachers to develop reflective practice. It will outline teacher perspectives of their experiences in the project and examine how their reflective skills and investigation into their classroom practices developed. Conclusions will be drawn of the factors which facilitate or inhibit lesson study as a process of professional development and research.

Process, one of the important components to attain the aim of the Singapore Mathematics curriculum, is often given less emphasis as its mastery seem less tangible in an assessment context. This paper describes a preliminary study to determine Singapore pre-service teachers’ ability to articulate mathematics concepts succinctly. The findings show that they were not able to communicate their teaching ideas and concepts effectively. Effective mathematics communication skills using accurate mathematics language and various strategies were then integrated into their pedagogy module so as to equip them better with the necessary repertoire of knowledge and skills for effective mathematics teaching.

In 2005, the National Academy of Sciences and National Academy of Engineering together commissioned the report “Rising Above the Gathering Storm” (Committee on Prospering in the Global Economy of the 21st Century, 2007). The report recommended the UTeach teacher preparation program at the University of Texas at Austin as one that should be scaled up across the nation to address the declining population of high school mathematics teachers. Cleveland State University is now one of 20 universities replicating UTeach, and will accept first year students in August 2010. In this session, I will outline the major differences between this program and traditional programs, and discuss issues I have dealt with during the pre-implementation phase.

In preparation for the collection of baseline data for doctoral research, two assessment instruments – one for students, the other for teachers – were trialled in 2009. At the start of 2010, the final student questionnaire was completed by Year 3 to 6 students in seven schools to gauge their implicit theories of intelligence and their mathematics self-efficacy. Data from a separate assessment of the students’ mathematics achievement were also collected (n = 364). The students’ teachers (n = 24) completed a questionnaire to identify their theories of intelligence and self-efficacy for teaching mathematics. Initial findings will be presented.

This presentation provides some preliminary findings from a large scale survey of 964 Singaporean Senior Secondary mathematics students regarding the use of graphics calculators. Based on Geiger’s (2005) framework of four metaphors for technology use – Master, Servant, Partner and Extension of Self – an instrument was developed (Tan, 2009). It was administered as part of a PhD study on students’ learning preferences and their ways of learning and using graphics calculators. The findings are compared to those in the pilot study presented at MERGA 32 (Tan, 2009). The relationship between students’ use of calculators and their mathematics self ratings are discussed.

This project investigated how teachers used the HOTmaths learning system in laptop learning environments. It took place in 8 Year 9 classes at three Catholic secondary metropolitan NSW schools. Each school used laptops in a different configuration, and selected teachers in two schools were provided with extensive professional development. Data on the implementation were collected via classroom observations, interviews with teachers, and pre- and post-testing using the ACER PATMaths test. The results indicated significant improvements in student performance of the intervention groups as compared with the non-intervention groups.

This study will evaluate the effectiveness of an online professional development model using communication pathways developed for a web-based mathematics learning system. Upper primary teachers from Catholic and government schools in NSW and Victoria will engage in a four-stage online professional development program employing web-conferencing software (Adobe Connect). Professional development will focus on new pedagogies using technology, and promote collaborative reflection and analysis of teaching and learning. Data sources will include digital recordings of a representative sample of lessons, transcripts of PD sessions, data generated by the online mathematics learning system, online surveys completed by students and teachers, and online interviews with teachers.

This presentation reports on a study that investigated the professional and pedagogical beliefs of effective mathematics lessons that were co-valued by the teacher and students. This study contributed data to an international pilot study that investigated how different interpretations of effectiveness incorporate traditional, cultural or indigenous views of mathematics education. The conceptualisation of this study was stimulated by previous research findings which found that students’ learning of mathematical ideas appeared to be regulated by the teachers’ valuing of professional and pedagogical beliefs (Seah, 2007; Seah & Ho, 2009). Data from photos of “effective learning moments” taken by students during the lesson observations in one primary school will also be presented.

The session started will start a few minutes' reflection from panel members about issues associated with the implementation of the K-10 National Curriculum. This will be followed by input of ideas from participants. Gaye Williams will highlight aspects of MERGA Feedback on the Draft K-10 National Curriculum as they become pertinent to the conversations arising. The purpose of the session is to raise awareness of issues associated with National Curriculum implementation, and invite contributions from participants about future directions for research and teacher education in the light of this.

The round table discussion will begin by presenting the findings from a small study investigating possible misalignment of student data from three different assessment tools. It will also look at how any misalignments impact on making overall teacher judgements about student achievement. The three tools used in this case study were AsTTle (Assessment Tool for Teaching and Learning), GloSS (Global Strategy Stage Assessment) and IKAN (Knowledge Assessment for Numeracy) some of which are widely used across New Zealand schools. With the introduction of National Standards in New Zealand, teachers will become more accountable when making overall teacher judgements (OTJ). An essential aspect of OTJ is that teachers effectively select, use and analyse different assessment tools such as those mentioned above. The small study focuses on helping teachers understand the misalignments within the assessment tools thus helping teachers to use data effectively in order to set clear learning goals. In the Round Table we hope to stimulate discussion with Australian, New Zealand and other international colleagues about: • How do other countries address misalignments of various assessment tools? • Challenges when selecting appropriate assessment tools. • Feedback and advice on how to extend this small case study further by formulating a research question. • How to best utilise overall teacher judgement with a range of assessment tools?

Make it count: Numeracy, mathematics and Indigenous learners is a national, four year project that is developing whole school, evidence based, sustainable practices to enhance Indigenous students’ learning. Community engagement is key to the project’s success and various communities of practice are being built to support the work of the project. Eight clusters of schools across Australia are working together to build their evidence base so teachers will know whether they are doing things better or not; so they have certainty around what they believe, and clarity about why things have worked (or not). Contributing to this is the emerging role of the clusters ‘Critical Friends’ – mathematics and/or Indigenous education academics – who are working in collaboration with the schools in their particular focus. Adding to the evidence base is the overall project evaluation which includes both quantitative and qualitative longitudinal data about change. The project staff is also identifying direct and indirect evidence. Our challenge is to provide an evidence base of ‘stuff’ that works. How do we marshall the different layers of this ‘stuff’ into the evidence base and, at the same time, evolve the various roles of those contributing? Do we need something more? The aim of this round table presentation is to open up discussions about participants’ experiences and knowledge that can maximise the evidence base from a layered, school-based project like this and to inform the work of the project with new thinking, learning and knowledge.

Using collaborative problem solving to develop a “learning community” among mathematics teachers is an established approach to professional development within the field (Lachance & Confrey, 2003; Ryve, 2007). However, the question of whether an online environment adequately facilitates the development of a learning community among teacher-learners remains unanswered (Kim & Bonk, 2006). Any answer to that question will be partial and temporary for two reasons. First, teacher-educators can currently choose from an array of web-based conferencing software of variable quality and capabilities. Second, the rapid pace of innovation of educational technology creates both opportunities and challenges for teacher educators: what some technologies constrain today, other technologies enable tomorrow. Despite these conditions, this roundtable discussion will focus on how one online approach to professional development used by the faculty of Metropolitan State College of Denver (Metro) both promoted and impeded community building and collaborative problem-solving among a group of elementary mathematics teachers in rural Colorado and how other schools may be working through these issues. The growth of online mathematics education and the need for teachers in rural schools to obtain certification in mathematics suggest that mathematics teacher-educators can use Metro’s study and the discussions at this roundtable to structure and conduct online professional development courses in ways that conform to the principles of reform-based instruction.

In 2007 “Targeted Learning Groups” were set up in Otago and Southland, New Zealand to support students with their development of knowledge about numbers and to help students become numerate flexible thinkers (Holmes & Tait-McCutcheon, 2009). Since then many schools in New Zealand have trialled the intervention and adapted, where appropriate, to suit the audience in their areas. The purpose of this round table is to outline how the mathematical intervention has been implemented in some of the low socio-economic schools in Auckland, New Zealand. The discussion will focus on the impact of this intervention on student mathematical knowledge and problem solving skills. Data collated from sample schools have indicated that if there is a delay in strategy learning, it is often due to a deficit in one or all of the four knowledge domains: numeral identification, number sequence, place value, and basic facts. In order to bridge the knowledge deficit this intervention provides teachers, parents and teacher aides with a structured and sequential framework of knowledge teaching. The repetition of any learning enables students to master and retain new knowledge (Nuthall 2002) and the consistent nature of the intervention knowledge lessons provide a foundation for students to develop confidence to problem solve. This round table forum will afford an opportunity for international colleagues to share their experiences of mathematical interventions that have effectively raised student achievement. The discussion will be open to support, critique and/or add to the existing intervention and to seek further research ideas.

At a recent professional development session where I spoke, the principal, a former high school head of mathematics, welcomed participants and reflected on the importance of mathematics for children’s futures. He spoke of the relevance of mathematics and its power to model reality. The following exemplar was proposed: “Imagine you are the general of three army divisions. The first is winning handsomely, the second is holding its ground, and the third is suffering huge losses. You have sufficient support troops for only one division. Where would you deploy them?” The answer, he said, was simple, and based on mathematical modeling, “To the winning division, naturally”. He provided a second example: “Imagine you are charged with placing landmines for maximum effect. How would you arrange them?” Again, he claimed, mathematical modeling would enable this decision to be easily made. I left the session disturbed and perplexed. Both examples used to epitomise the power of mathematics were in military contexts, and enabling deaths (collateral damage) was not considered problematic. The principal seemed insensitive to any conceivable wrong in what he had put forward. Contemporary mathematics curricula urge teachers to ensure that students are exposed to “real world” mathematics. I have no argument with this. But, do teachers reflect on the implications of the contexts in which the examples are set? Do they consider if there are covert messages that reinforce stereotypes, or have moral, ethical, or political implications? At this round table, these issues and the research opportunities offered will be explored.