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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. (Contains 1 table and 3 figures.) [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

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. (Contains 2 figures and 1 table.) [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

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. (Contains 3 tables and 1 figure.) [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

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. (Contains 4 tables and 1 figure.) [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

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. [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

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. (Contains 4 figures.) [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

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. [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

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. (Contains 6 figures.) [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

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. (Contains 2 tables and 2 figures.) [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

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. (Contains 4 tables.) [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

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. (Contains 10 figures.) [For the full report, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

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. (Contains 3 tables.) [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (RD, Fremantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

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. [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

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. (Contains 1 table.) [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

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. (Contains 1 figure.) [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

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. (Contains 2 tables.) [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

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. (Contains 4 tables.) [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

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. (Contains 3 footnotes.) [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

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. (Contains 2 tables.) [The study reported in this paper was supported by an Australian Research Council Linkage Grant: LP 0455320. For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

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. (Contains 4 figures and 1 table.) [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

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. (Contains 3 tables.) [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

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. (Contains 3 tables.) [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

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. [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

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 twenty-eight 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. (Contains 1 figure and 1 table.) [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

This paper explores the impact of the "Bridging the Numeracy Gap Project" on the whole-number learning of Prep and Grade 1 students living in a low Socio-Economic Status (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. (Contains 4 figures.) [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

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. (Contains 4 figures.) [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

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. (Contains 3 figures.) [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

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' need to develop their graphical knowledge and an awareness that knowledge varies substantially across students. Examples from the six graphic languages, their perceptual elements and encoding techniques are shown in the appendix. (Contains 3 tables and 2 footnotes.) [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the tional Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]