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This paper centres on research on equity and mathematics education in Mexican American communities in the United States. This research is grounded on a socio-cultural perspective and encompasses work with teachers, students, and parents. We address questions such as: What are Latino/a immigrant parents’ perceptions of mathematics instruction? What do teachers see as obstacles and advantages in the mathematics education of non-dominant students? How does language policy affect students’ participation in the mathematics classroom? The findings are likely to be relevant to other settings with immigrant students and non-dominant students.

Over the past decade or so there has been much rhetoric about assessment. There are assessment websites replete with ―rich tasks‖, work samples, standards, and definitions. The MySchool website reports data from large scale assessments. Teachers are exhorted to use assessment as a tool for learning. What has all of this activity achieved? Research evidence is scant and conflicting. It is time to assess mathematics assessment and to reconsider the purpose, nature and use of assessment information.

Inquiry pedagogies are often advocated for equipping students with 21st century skills, but teaching mathematics through inquiry is difficult. A longitudinal study investigated teachers’ experiences of learning to teach mathematical inquiry over time. Using the Productive Pedagogies framework, this paper reports on aspects of practice that evolved for twelve primary teachers as they gained experience with inquiry over three years.

In this paper we examine the nature of the instructional coherence across a series of lessons on linear equations. Using video and interview data from a Year 9 class in the New Zealand component of the Learner’s Perspective Study (LPS) we explore how the teacher’s pedagogical strategies associated with the selection and enactment of tasks and the action of ‘sowing seeds’ were key factors in establishing instructional coherence. We provide excerpts from classroom episodes to illustrate how instructional coherence supported students’ learning of mathematics.

This paper reports on the perceptions of mathematics education of in-service and preservice primary school teachers involved in an innovative model trialled in the final mathematics curriculum unit of a B.Ed. program. Questionnaire items asked about the value of time spent in classrooms, the importance of theoretical understandings, and of linkages between theory and practice. Both groups reported valuing time in schools, understanding the theories that underpin practice, and lecturers with recent classroom experience, but there were also interesting differences between the groups at the beginning and at the end of the unit, and some change for each group.

It may seem that improvisational drama and primary mathematics are two diametrically opposed disciplines, the former being based around emergence and uncertainty and the latter based around predictability and certainty. In this paper I argue that creative mathematics teaching and learning requires a certain amount of unpredictability and that, particularly with regard to problem solving, learners‘ solutions have a certain quality of emergence that is not dissimilar to improvisational drama. By examining children‘s solutions to non-routine problems I consider what mathematics education might gain from attending to the discipline of improvisation.

Recent decades have seen growing concern over the lowering levels of engagement with mathematics in Australia and internationally. This paper reports on a longitudinal study on engagement with mathematics during the middle years and explores the influences of teachers on the participants‟ engagement with mathematics. Findings reveal that development of positive pedagogical relationships forms a critical foundation from which positive engagement can be promoted.

Teacher-student relationships can strongly influence academic achievement and motivation, particularly for minority group students. Teaching practices contributing to strong academic relationships are therefore vital to understand. This article describes such practices drawn from observations of 100 Year 10 mathematics lessons involving six teachers and their classes across three mid-low socio-economic schools. For many indigenous (Māori), New Zealand Pacific, and New Zealand European students, evidence emerged that essential caring teacher behaviours include and extend beyond traditional mathematics teaching practices. Findings are presented using an holistic model of health and well-being that encompasses cognitive, social, physical, and spiritual dimensions.

That preservice teachers’ understanding of what constitutes good teaching is partly shaped by their experiences as students in the classroom is well documented; but how they give shape to their recollections is under-explored. In this study, preservice teachers wrote about their perceptions of good teaching in narrative reflections of their experiences as school students. Almost 25% of the cohort chose to write about a mathematics teacher. Narrative analysis was used to investigate the content and the form of the 31 reflections to provide insight into how preservice teachers reconstruct their narratives of experience. Three distinctly different story types were found.

involves identification of comments related to research interests, formation of clusters to group comments and then confirmation of themes in the data related to pre-determined research interests. Descriptions of each participant’s views on each theme are summarised as case-studies. Illustrative examples from teacher interview data on teaching and learning will show how the approach can be implemented. The approach used is based on the work of Chesler who used grounded theory to explore views of a group of professionals.

This paper reports on one aspect of a two-year design study aimed to assist second-grade Filipino children solve additive word problems in English, a language they primarily encounter only in school. With Filipino as the medium of instruction, an out-of-school pedagogical intervention providing linguistic and representational scaffolds was implemented with 17 children. Pre-intervention, children experienced linguistic difficulties and were limited to conceptualising and solving simple additive structures. Postintervention interviews revealed improved understanding of more complex structures, but only when linguistic difficulties were minimised.

The ability to apply mathematical and statistical thinking within context is an essential skill for graduate competence in science. However, many students entering the tertiary sector demonstrate ambivalence toward mathematics. The challenge, then, is to determine how science curricula should evolve in order to illustrate the integrated nature of modern science and mathematics. This study uses a document analysis to examine degree structures within science programs at a selection of Australian tertiary institutions. Of particular interest are the signals these degree structures send in terms of the relevance of the study of mathematics prior to entry to university and the quantitative content within.

It has been established that the use of interactive whiteboards (IWBs) does not of itself imply interactive pedagogy. Indeed it has been argued that precursors for a change from teacher-centred to interactive pedagogy include a high degree of technical IWB competence. Based on the responses of secondary mathematics teachers at one school to a brief professional learning program we suggest that awareness of the potential of IWBs to enhance student engagement and hence learning, and commitment to collaboration and improved teaching, can motivate experimentation with the technology such that technical competence and pedagogical change occur together.

Moving on from primary school provides many different challenges. This paper explores multiple perspectives about preparation for school transition in mathematics. As a qualitative case study it draws on student, teacher, and parent, voices through the use of questionnaires and interviews. Sixty seven students and six teachers from three different schools participated in the study. There were commonalities and differences in beliefs about mathematics learning and teaching that contribute towards successful transition. The results illustrated that facilitating successful transitions requires that attention be given to the perceptions and values of students, teachers, and parents.

In many mathematics courses at school and university—including in all South Australian Year 12 mathematics subjects—students are allowed to make a “cheat sheet” to take into their exams. However, despite their widespread use, there is little research on the effect of making and using cheat sheets—whether on the students’ performance, learning or learning experience. As a preliminary stage in researching this issue, students in several first-year statistics courses at the University of Adelaide were surveyed on their experiences of making and using cheat sheets. The results and implications of this survey are discussed in this paper.

The investigation of teachers’ knowledge that informs practice in the mathematics classroom is an important area for research. This issue is addressed in our larger research program which is aimed at characterising the complexity and multi-dimensionality of this knowledge. A report on an earlier phase of this program (Butterfield & Chinnappan, 2010) showed that pre-service teachers tended to activate more common content knowledge than content that is required for teaching. We build on this previous work by examining the kinds of knowledge that a cohort of pre-service teachers activated in the context of designing a learning task.

An oft-heard comment from adolescents is that “maths is boring”. Such disinterested students are less likely to engage in mathematics related learning tasks than their interested peers and this lack of engagement can result in lower levels of achievement. This study seeks to explore the relationship between interest and achievement in a middle school statistical literacy context. Based on the results of 218 students, a linear regression model indicated that the relationship between interest and achievement is complex and mediated by other factors that include students’ self-competency beliefs. Moreover, the model predicted that interest has a very minor influence on achievement and that factors related to the classroom teacher have much stronger influence.

We studied how three secondary mathematics teachers who had no prior experience teaching with technology used an online mathematics learning system. The teachers received minimal instruction on how to use the system before we observed them over four school terms as they taught with it. We used the Pedagogical Technology Knowledge framework (Thomas & Hong, 2005) to document changes in the teachers’ practice. Results show teachers advanced toward using the technology in more sophisticated ways but the improvements were not uniform. We suggest some reasons to explain the variation.

Over the years there has been a lack of conceptual clarity and explicit definition of the construct mathematics anxiety. This paper describes a process of building, refining, and validating a construct model of mathematics anxiety using a Rasch Rating Scale.

In this paper, we discuss the use of a framework of “growth points” in early mathematics learning and a related, task-based, one-to-one interview in assessing children’s understanding of the measurement of mass. Data are presented from a sample of 1806 children in the first three years of school. An example of a child’s responses is given to illustrate the kinds of thinking revealed by interviewing young children about their developing concepts of mass.

Understanding the relationships among fractions, decimals, and percentages is a critical goal of the middle years of schooling. There are many approaches that teachers might take to help students develop this understanding; some capture general principles whereas others only illustrate specific equivalences. In this study teachers were asked to suggest three ways of convincing students that three-eighths is the same as 37.5%. The data reveal a wide range of strategies and show that different approaches may exemplify different features of the fraction-percentage relationship. The explanatory power of the examples is also considered.

This paper addresses three key distinctions central to educational research: (i) the distinction between convergent and critical synthesis; (ii) between data source and data; and (iii) between the compatibility of different theories and the compatibility of the interpretive accounts generated by different theories applied to a common data source. Our capacity to learn from research is precisely our capacity to synthesise the findings of research to inform our actions in particular educational situations. The realisation of such a goal requires a reconceptualisation of research synthesis as partial, purposeful, situated and critical. Mathematics classroom research provides the context for this discussion.

Knowing basic facts is critical for expediency in computational mathematics. By the time students reach the age of eleven some teachers are finding that groups of students are still counting with their fingers or resorting to the use of calculators, tricks with fingers, charts, or asking someone the answers to times tables. The question to be answered is why, after all the years at school, that students cannot remember 55 simple facts? An intermediate school in New Zealand has been investigating ways to motivate the students‘ learning of basic facts. This paper explores the improvement of student achievement through an action research plan.

It is now acknowledged that children start school with a wealth of mathematical knowledge and experiences (e.g. Aubrey, 1993; Perry & Dockett, 2004; Young-Loveridge, 1989), and that recognition of this rich resource by the new entrant teacher may facilitate the smooth transition of the child into school (Perry & Dockett, 2004). Positive transitions directly impact on children. This paper investigates how the mathematics content, understanding and practices of the new entrant classroom align with the learning children experience within early childhood settings. In particular it reports on the supportive practices provided by two schools for young children‟s mathematical learning as they begin school. Results from the study show tenuous links in mathematical practices between these sectors.

Indigenous language speaking students in remote Northern Territory schools are expected to learn mathematics in English and are assessed in English. Most teachers in these schools have little knowledge of the mathematical concepts with which their students start school. This paper reports on the initial findings of a project which is investigating spatial concepts in Iwaidja, an Indigenous language spoken in the NT. Examples of spatial frame of reference preferences in Iwaidja and related languages are compared with those taken for granted by English speakers. Implications for mathematics teaching are explored in the context of an Australian Curriculum.

This paper argues for a renewed focus on statistical reasoning in the beginning school years, with opportunities for children to engage in data modelling. Some of the core components of data modelling are addressed. A selection of results from the first data modelling activity implemented during the second year (2010; second grade) of a current longitudinal study are reported. Data modelling involves investigations of meaningful phenomena, deciding what is worthy of attention (identifying complex attributes), and then progressing to organising, structuring, visualising, and representing data. Reported here are children’s abilities to identify diverse and complex attributes, sort and classify data in different ways, and create and interpret models to represent their data.

This paper explores what two cohorts of middle school mathematics pre-service teachers (PSTs) report they learned after interviewing two middle school English Language Learners (ELLs) using four measurement tasks. The written responses of the PSTs to the question about what they learned from the experience were coded and classified into three overarching themes—accommodations, conceptions about ELLs, and the role of language in mathematics. Implications of these themes in future teacher preparation are also discussed.

In a study of Year 2 students, performance on a novel open-ended Make 10 task was one of two strongest predictors of students diagnosed at risk of mathematical learning difficulties (MD) on the Queensland Year 2 Diagnostic Net (Finnane, 2007). Students who performed poorly on this task produced few combinations, gave counting sequences or figurative responses featuring physical embellishments of the numeral 10, compared to a range of flexible responses by normally achieving students. This paper demonstrates the application of the Make 10 task to facilitating the conceptual and skill development of a Year 4 student with high functioning autism who was facing significant mathematics anxiety and pervasive mathematical leaning difficulties.

Although the creation of graphs to display data has been part of the school curriculum for some time, the call in the new Australian Curriculum for “numeracy across the curriculum” provides both the opportunity and challenge to link the skills of graph creating with the understanding of context in order to produce meaningful interpretation of the messages held in graphs. This paper reports on classroom experiences of and follow-up interviews with 12 grade 5/6 students who were introduced to the software TinkerPlots to assist in graph creation. The focus is on their success at graph creation and interpretation in contexts that provide potential links to other subjects in the school curriculum. Implications for the curriculum and teaching are drawn from the students’ experiences.

In this research we explore pre-service teacher knowledge for teaching mathematics by focusing on the development of the conceptual and procedural knowledge of a cohort of pre-service teachers. In the first phase of this study, we found that a previous cohort of preservice teachers utilised procedural rather than conceptual knowledge when completing fraction operations. We aimed to address this imbalance by targeting the development of conceptual knowledge through modelling. This paper reports the results of this approach with a subsequent cohort of pre-service teachers, where our expectation of greater conceptual knowledge was achieved and procedural knowledge was maintained.

Inquiry in mathematics is well suited to address authentic, ill-structured problems that are encountered in everyday life. However, available formative assessment tools are typically not designed for an inquiry approach. An exploratory study using Design Research aimed to understand and improve assessment practices of mathematical inquiry. Data collected from one classroom provided detailed examples of these assessment practices in action. Results from the initial stage and future directions of the project will be presented.

Given the variety existing within mathematical modelling enterprises, it is not surprising that different perspectives have found their way into educational practice and research. A variety of genres, (or variations within genres), has emerged within education communities, who use the term ‘mathematical modelling’ with different emphases, and in some cases with different meanings. This presentation will review the origins and purposes of several articulations of mathematical modelling. Tensions will be identified, and some inconsistencies and misplaced inferences illustrated. Different approaches will be linked to underlying purposes that are not always made explicit, and some specific issues will be highlighted.

Academic numeracy consists of three critical elements: competence, confidence, and critical awareness of students’ own mathematical knowledge and the mathematics used in students’ future professions. This definition is used to frame pre-test assessment in a first year nursing program. Competence and confidence were measured using a paper and pencil test. Critical awareness was measured via students’ reflections on their own performance, their relationship to mathematics, and their understanding of how mathematics relates to nursing. Results show issues related to professional numeracy practices including relatively low understanding of the connection between mathematics and nursing.

This paper reports on a year long, state wide research project that aimed to assist primary and secondary teachers to improve their teaching and learning practices through engagement with a new model of numeracy. Data collection included sequence maps of participants’ development as teachers of numeracy as elements of the model became more prominent in their thinking and planning. Semi-structured interviews were also used to clarify and expand upon teachers’ perceptions of their own development. Findings include a propensity to begin with the dispositions element of the model but responses showed that in most cases all elements were eventually addressed by each teacher.

Five interpretive place value tasks were added to the Early Numeracy Interview (ENI) to gain further insight about students’ construction of conceptual knowledge associated with 2-digit and 3-digit numbers. The researchers hypothesised that even though some students were successful at reading, writing and ordering numbers, interpreting multi-digit numbers for problem solving remained a struggle for them. Analyses of students’ responses showed that the new tasks distinguished students who previously were assessed as understanding 2- digit or 3-digit numbers, but who could not identify 50 or 150 on a number line or state the total of collections reduced or increased by ten. The new tasks assist teachers to identify students who need further instruction to fully understand 2-digit and 3-digit numbers.

As part of the Bridging the Numeracy Gap Project, four Catholic schools in the Kimberley appointed Key Aboriginal Teaching Assistants in Numeracy who, along with a classroom teacher from the school, participated in a 6-day professional learning program aimed at developing their mathematics teaching and leadership. At the end of 2010, audio-taped conversations took place to gain insight about the impact of the Project on learning and teaching mathematics at the school. Analysis of these data demonstrated that Aboriginal Teaching Assistants had clear views about the positive impact of project and of how to improve Aboriginal students‟ opportunities to learn mathematics at school.

Linear algebra is a difficult introduction to advanced mathematical thinking for many students. In this paper we consider the teaching approach of an experienced lecturer as he attempts to engage his students with the key ideas embedded in a second course in linear algebra. We describe his approach in lectures and tutorials using visualisation and an emphasis on language to encourage conceptual thinking. We use Tall’s framework of three worlds of mathematical thinking to reflect on the value of these activities. An analysis of students’ attitudes to the course and their assessment results help to answer questions about the value of such an approach, suggesting ways forward in teaching linear algebra.

This study investigated the fraction content knowledge of a student teacher, and his ability to use that knowledge in a novel situation through use of a scaled elastic strip. Data indicated that using the elastic strip was effective in challenging and enriching the participant’s knowledge of ordering fractions. The results suggest that use of the elastic strip could assist student teachers to develop their understanding of fractional concepts.

Pre-European traditional Māori education in New Zealand was integrated and holistic. With Western influence many Maori children struggled to achieve at school. Māori medium education based on retaining Māori values, language and culture therefore emerged to provide an alternative avenue for education. A key element in this initiative is to increase children’s engagement with, and learning of, mathematics. Views from 61 Year 5-8 children in Māori medium contexts have been sought to provide insights about their mathematics education. This paper discusses some of these views and raises possibilities for future directions to support the momentum of this positive initiative.

This paper draws from a longitudinal study of student achievement in Melbourne’s northern suburbs. It examines Year 12 students’ attitudes to mathematics, their experience of the mathematics classroom, their views of teachers and their expectations of success. Despite a differentiated Year 12 mathematics curriculum, there is evidence of inequity in students’ experience of mathematics. Perceptions of mathematics classrooms and mathematics teachers, and expectations of success, vary according to subject, gender and social background. Implications for pedagogical and curriculum reform are discussed.

Despite considerable research with students of calculus, rate and hence derivative, remain troublesome concepts to teach and learn. The demonstrated lack of conceptual understanding of introductory calculus limits its usefulness in related areas. Since rate is such a troublesome concept this study trialled reversing the usual presentation of introductory calculus to begin with area and integration, rather than rate and derivative. Two groups of first year tertiary students taking introductory calculus were selected to trial the effect of changing the sequence; a control group and a group which followed the reversed sequence. Two-sample t-tests undertaken in Minitab on the examination results indicate there is no significant difference between the examination results of the two groups. These results indicate that changing the sequence of delivery was not detrimental to the development of conceptual understanding of introductory calculus.

The results of the National Assessment Program – Literacy and Numeracy [NAPLAN] tests of Australian students in 2008, 2009, and 2010 were analysed by individual question responses (percentage correct) of females and males. The analysis of Grade 3 and Grade 9 data demonstrate that a decline in the achievement of females is evident and these gender differences become larger as students progress through their schooling.

Students’ perceptions of what teachers do and what students themselves do that helps them learn gives an insight into what might be effective in a mathematics classroom. This paper looks at student perceptions in general but also specifically in relation to the teaching and learning of mathematics. Data were collected from students at two South Australian schools via an online survey conducted each year for three years. The students were asked questions relating to what teachers did that helped them learn and what they did that helped them learn Mathematics. The results of the survey will be presented and will highlight areas that students think are most important in learning mathematics.

The Make It Count project aims to provide better mathematical outcomes for Indigenous children, and, to that end, the Swan Valley cluster identified various initiatives. This paper reports on a research project that investigated those initiatives and resultant changes in practice. First, a modified First Steps in Mathematics professional learning program was provided for Education Assistants and Aboriginal and Islander Education Officers to upgrade their mathematical and pedagogical content knowledge. Second, elements of best practice in teaching Indigenous children were investigated. It is apparent that genuine professional learning communities have begun to develop in the wake of the professional learning and that there are clear directions for pedagogical practice that may lead to improved student attendance and engagement.

This paper reports on the language-related misconceptions of a group of post-secondary students when working on problems involving the limit of a real-valued function at a single point. In this qualitative study, 50 post-secondary students took a test and participated in a survey, from which 10 were interviewed after the test. The data revealed several misconceptions held by the post-secondary students about the limit concept that were related to the issue of language. Such language-related misconceptions resulted from incorrect internal representations and the inability to reify the limit.

Australia is a country that has a strong interest in water and swimming with most of the population living within one hour of a body of water. Significant numbers of parents take their under-5s to swimming lessons. Anecdotally, the swim industry believes that swimming enhances many aspects of young children‘s growth and learning. This paper explores the ways in which the swim environment for under-5s offers significant opportunities for learning many mathematical concepts that have transferability to school contexts. However, with the costs of swimming lessons being high, questions are posed regarding equity and the potential of swimming to further advantage the already advantaged.

Drawing on the work of James Gee in literacy, we apply his contemporary approach to not only the knowledge systems of mathematics but also the processes by which school mathematics can be learned through the digital games environment. Using a number of games, and young people working these games, we propose that there are novel ways to learn not only many of the concepts that are integral to school mathematics, but such concepts can be learned in ways that are deep. The games environment offers an engaging environment that is substantially different from that experienced in formal school settings. We suggest that many of the principles that underpin the games environment may create new opportunities for teaching and learning that will (re)engage learners and learning of school mathematics.

This paper explores the learning experiences of 346 year four low attainers in mathematics from Singapore. The pupils were interviewed about their learning experiences related to mathematics lessons in school. An innovative method, using pictures as stimulus, was adopted to engage pupils to talk about their lessons. From the interview data it is apparent that there was a mismatch between how pupils were taught and preferred to be taught. Almost all the pupils experienced teacher-led whole class instruction during their mathematics lessons. A study of three teacher-led whole class instruction lessons showed that these lessons were not unique but had some commonalities. The mathematical tasks used during instruction were routine and repetitive. Teachers also did not stimulate the development of pupils‘ metacognition.

The New Zealand Government recently introduced National Standards in response to concerns about levels of student achievement in mathematics and literacy, and significant investment has been made in the Numeracy Development Project. Principals are responsible for improving teacher practice but most principals were educated in contrasting pedagogies to that of the NDP and have more language arts than mathematics strength. This qualitative case study compared two diverse, primary-sector principals, chosen for contrasting mathematical backgrounds and leadership of mathematical professional development. The results illustrate that a school principal is an influential "cog‟ in the mathematics professional development process and that their direct participation in mathematics professional development is required for effective leadership of mathematics. It provides evidence about the mediating influence of leadership in mathematics professional development and learning in schools. Practical implications for improving classroom practice in a distributive leadership environment will be discussed.

This study draws on Valsiner’s (1997) extension of Vygotsky’s (1978) theory on Zone of Proximal Development that had been further extended by those interested in teacher professional development (e.g., Blanton, Westbrook & Carter, 2005; Millett & Bibby, 2004). These theories were used to guide the constant comparative analysis of interview data collected during a case study involving all teachers and leadership in one primary state school in Queensland. Through this analysis it became apparent that the principal created a Zone of Free Movement and a Zone of Promoted Action that limited teachers’ meaning making of reform in mathematics. Being alert to these actions is important if we are to truly understand how change in mathematics reform may be being implemented in schools.

Although preservice primary teachers’ limited mathematical knowledge has been well documented, little research has been conducted on programs to improve it. We report on first-year, teacher education students’ use of recommended internet resources on different mathematics topics. Our findings suggest that many of our preservice teachers had not previously used internet resources for learning, except to do research. They also saw mathematics learning as occurring only when they are taught by a teacher and so internet resources were of limited value. Ultimately these beliefs, if left unchanged, will have an impact on their teaching of mathematics to primary school students.

In this study we build on Leder and Forgasz’s (2010) examination of the public’s perceptions about the learning of mathematics at school and its role in determining males’ and females’ career preferences. Data were gathered at 12 different sites throughout Victoria and via an innovative recruitment tool, the social network site Facebook. The latter provided a unique opportunity to target a wider audience across Australia. Our finding that younger respondents (under 40) were more likely than those over 40 to question girls’ aptitude for mathematics is of concern.

Improving numeracy performance of all students across Victoria is a government priority. A key element of this initiative lies with tertiary institutions that are responsible for adequately preparing pre-service teachers for teaching primary mathematics. This paper examines data from a larger, longitudinal study of primary preservice teachers‘ mathematical content knowledge and focuses on responses to fraction tasks by nine pre-service teachers in the study who are in the final year of their course. Two dimensions were used to categorise their responses. The majority of these preservice teachers did not demonstrate a fluid and flexible knowledge of fractional numbers; half demonstrating a regression in their knowledge of this topic since the beginning of the course. These pre-service teachers will be challenged when working with students who have a wide range of numeracy experiences and abilities.

This paper examines the piloting of a Written Strategy Stage Assessment Tool designed to identify students‘ ―global‖ strategy stages and provide formative data for teachers. The Year 9 cohorts from two schools were assessed at the end of the school year. Numeracy experts then interviewed a sample, to identify each student‘s strategy stage, using an oral assessment. Results from the written assessment gave relatively consistent measures of stages in terms of the criteria set and a relatively close match to national data. Comparison of the written and oral assessment results showed the stages identified by the two measures to be generally consistent.

This paper explores the development of young children’s understandings about measurement, and the ways in which children represent these understandings. This paper presents a selection of data gathered during a three-year study that examined young children’s engagements with measurement in prior-to-school and out-of-school contexts. In this present investigation, children’s representations in the form of drawings and narratives are analysed in relation to a framework of emergent measurement. Initially, this paper considers the understandings about measurement which children are demonstrating in alignment with the framework, before offering a selection of data which represents a disruption to the framework and contests existing ideas about young children’s measurement understandings.

This paper examines the experiences of teachers seconded as mathematics educators in the Faculty of Education at an Australian University. Data were collected from four participants who responded to a series of questions derived from an existing framework on the transition from teacher to teacher educator. The purpose of the study was to undertake a reflective exploration of the major challenges faced by seconded teachers from their perspectives, with the findings indicating that participants generally felt they lacked the requisite skills and knowledge required to teach in a tertiary environment. The study adds to the limited research in this area and has implications for tertiary providers and teacher educators.

Student engagement in mathematics in the middle years is consistently reported to be a challenging problem. Yet, as this action research study shows, it is possible to engage students in meaningful mathematical learning with the use of relevant investigations. This project with 14 Year 8 and Year 9 mathematics teachers was structured around an action research model with teachers supported to refine capabilities and pedagogical processes to implement mathematical investigations that ‘make sense’. Following implementation, teachers reported that students were more engaged compared to traditional mathematics lessons and that students recognised the value and application of mathematics, which in turn leads to greater engagement in mathematics

Calls have been made for teacher educators to innovate upon well-established teacher education programs. During 2010, a project was initiated that sought to study the impact that a school-university partnership had on building preservice teacher capacity for effective teaching of mathematics. Early findings suggest that a range of factors including observation of lecturers teaching mathematics lessons, and participation with teacher educators in lesson planning, team-teaching, and post-lesson reflections can be helpful in building capacity for effective mathematics teaching.

Research has shown that children can offer the right answer but have mathematically incorrect reasoning (Clements & Ellerton, 2005). One-to-one task-based interviews enabled the researchers to engage in observational listening (Empson & Jacobs, 2008) and uncover the mathematical strategies used by Grade 6 students in fraction pair tasks. Some students’ answers and initial explanations were similar, but different strategies were revealed by further questioning: the correct strategy of benchmarking or the misconception of gap thinking.

It has often been reported that children of Australian Indigenous background do not perform as well as a group as the whole population. This paper addresses the question of whether Victorian Indigenous children have different patterns of responses from the general population. The analysis compares the responses on each item for Indigenous children with the responses for non-Indigenous children both directly and for those who achieved the same NAPLAN scores for the 2008 NAPLAN numeracy assessment for years 5, 7, and 9. The results indicate trends in the characteristics of items which successes or challenges for Indigenous children.

While extensive reference in the literature can be found in regard to professional learning sessions and workshops for teachers of mathematics, relatively little has been reported about engaging parents in learning about mathematics and mathematics education. The importance of home school partnerships is readily acknowledged, with parents being arguably the most influential factor in their children‘s educational success, yet many parents feel uninformed about current educational practices and how best to support their child‘s learning. This paper reports on an initiative undertaken with the parents from a District High School whereby they joined a ―Maths club‖ and attended information sessions designed to familiarise them with current mathematical practices and pedagogy. The results indicated that parents were appreciative of the opportunities provided to them and that they were supportive of contemporary mathematical practices.

The classrooms of Papua New Guinea are multilingual. For many years only the official language of education, English, was permitted for teaching. In the mid 1990s the curriculum changed to declare that multiple languages would be used in teaching in the first three years of schooling. In the next year English is introduced, and gradually over the next few years becomes the dominant language of teaching. This paper examines how eight teachers in the crucial transition year 3 use their multiple languages to teach mathematics, although they seem to use their other available languages to privilege English learning.

This paper reports a 2-year longitudinal study on the effectiveness of the Pattern and Structure Mathematical Awareness Program (PASMAP) on students’ mathematical development. The study involved 316 Kindergarten students in 17 classes from four schools in Sydney and Brisbane. The development of the PASA assessment interview and scale are presented. The intervention program provided explicit instruction in mathematical pattern and structure that enhanced the development of students’ spatial structuring, multiplicative reasoning, and emergent generalisations. This paper presents the initial findings of the impact of the PASMAP and illustrates students’ structural development.

This paper presents results from the Resourcing Talking in Maths project. The project aimed to review the resourcing, management and orchestration of collaborative mathematical tasks with young children (6 years old) and to examine the tensions involved in developing tasks that are accessible but also provide a challenge. It was found that the level of explicitness of the attended focus of the task needed to be balanced and that this balance was informed by the precision of the teacher’s explanations and the definition of the mathematical relations as presented in the use of resources.

Mathematics pupils in Singapore are not performing to expectation. Pupils fail to apply learnt concepts, and new concepts are learnt in isolation instead of through a 'build-up‘ based upon known older ones. This ongoing study investigates relating students‘ prior knowledge of the topic Ratio to new concepts. Case Based Reasoning and Cognitively Guided Instruction are used in this research. Their frameworks are combined, creating categorisations, where items are grouped based on the concepts.

This paper provides a critical analysis of the probability questions in the 2009 & 2010 NAPLAN numeracy tests for Years 3, 5, 7, and 9 from a number of perspectives. The analysis revealed that probability is under-represented in recent NAPLAN tests, with only one probability item included in each year level in the 2010 test. The items reveal a limited focus regarding type of task and response method. There is poor coverage of the National Statements on Learning in Mathematics, and weak alignment with the constructs in the Probabilistic Reasoning Framework (Jones et al, 1997).

Goldin (2003) and McDonald, Yanchar, and Osguthorpe (2005) have called for mathematics learning theory that reconciles the chasm between ideologies, and which may advance mathematics teaching and learning practice. This paper discusses the theoretical underpinnings of a recently completed PhD study that draws upon Popper’s (1978) threeworld model of knowledge as a lens through which to reconsider a variety of learning theories, including Piaget’s reflective abstraction. Based upon this consideration of theories, an alternative theoretical framework and complementary operational model was synthesised, the viability of which was demonstrated by its use to analyse the domain of early-number counting, addition and subtraction.

University students’ evaluations of mathematical presentations are examined in this paper, which reports on part of a pilot study about different types of presentations, regarding different topics, formats (oral or written), and discourses (process- or object-oriented). In this paper focus is on different formats; oral lectures and written texts. Students’ written comments about what is good or bad about given presentations are analysed in order to examine what students focus on when evaluating the quality of presentations. In addition, evaluations given about written and oral presentations are compared in order to examine if and how format affects students’ evaluations regarding quality.

This paper describes how one teacher‘s attempts to promote powerful positive affect in her mathematics classroom gave rise to concerns and tensions related to her practice. The paper shows how using a combination of Activity Theory and the Stages of Concern provides a helpful lens for researchers to understand the challenges of change and professional development. It is argued that the identification and resolution of these tensions is crucial to understand and facilitate the efforts of sustainable pedagogical change.

Using children’s literature in mathematics is not a new idea. Although resources have been produced to support teachers in using literature in their mathematics programmes, there is little research to show this approach is successful. One debate associated with using children’s literature in mathematics teaching/learning is how much support is required for children to recognise the mathematics in the literature. The research that is available has focused on very young children interacting with stories being read to them or identifying adaptations needed to the text and/or illustrations to allow children to recognise the mathematical information inherent in the story. This paper presents the results of a study that used book reviews as a tool to identify the extent Year 7 students could identify the mathematics in children’s literature.

During 2009-2010, the South Australian Department of Education and Children‘s Services implemented a mathematics learning and teaching program for educators in preschools and the first year of school in response to national curriculum agendas. The Early Years Numeracy Pilot Project (EYNPP) used an inquiry model of professional education led by early childhood educators who were designated as numeracy leaders. This paper analyses the impact of EYNPP on the knowledge, skills, confidence, and pedagogical approaches of these numeracy leaders and on the development of powerful mathematical pedagogy in their own settings and those of the colleagues whom they were leading.

After an introduction to the current conceptions of play in early childhood settings, we consider what The Early Years Learning Framework and the Australian Curriculum say about play and mathematics learning in the home and preschool, and the early years of school. We analyse similarities and differences in the two documents with regard to their philosophies about play as pedagogy for the learning of mathematics. We use the construct of a Numeracy Matrix to illustrate how playing with mathematics can be utilised to provide curriculum and pedagogical continuity between preschool and school.

As part of an investigation into statistical literacy for the teaching workplace, this research paper uses a framework for professional statistical literacy to examine teachers’ perceptions of the complexity and value of such reports. Although teachers identified aspects of the data as useful for their work, many features were described as being difficult to understand. Even tertiary educated adults may not be well prepared for dealing with quantitative data in their workplace. There are lessons, too, for the presentation of statistical information.

This paper investigates students’ emerging inferential reasoning about samples and sampling through observation of 13- to 14-year-olds, challenged to infer aspects of an unknown population in an inquiry–based environment. This paper reports on how students working with TinkerPlots focus on changing aspects of the samples as the sample size grew larger. Students made connections to key statistical concepts during the process of growing samples and quantified the level of confidence about their informal statistical inferences. They generally recognized the relationship between the sample size and the confidence interval for a given confidence level.

The relationship between the development of the teaching of mathematics and the classroom teaching of mathematics is of considerable interest to teachers and university academics. This article reflects upon the nature of the participation of teachers and university academics as they participate in research communities of practice that use inquiry as a tool to engage with change and development. Conclusions are drawn in terms of the nature of the relationship of university academics to classroom teachers within a research community of practice.

For the past three years, the authors have been using questionnaire items to assess the pedagogical content knowledge (PCK) of primary teachers involved in a multi-faceted professional learning program in Catholic schools in Victoria. We will describe the challenges of developing and coding items which assess PCK in mathematics, levels of performance on various items, and the extent to which change over time was evident. We will also share insights about areas for which professional learning programs might give greater emphasis, arising from the data.

Encouraging students to articulate their thinking when doing mathematics is a means by which teachers ascertain understanding. Reported here are the results from a content analysis of the written reflections of 67 undergraduate students who incorrectly simplified a rational expression. Although asked to write about the thinking that led them to their solutions, most did not. Instead, they recounted what they had done or had not done. Of those who did write about their thinking, most wrote of their confusion or uncertainty; only a few provided a rationale for the procedures they used. Nevertheless, insights into student thinking were gleaned.

This paper draws from a pilot study about a teacher education program that focused on building preservice primary teachers’ confidence and abilities in teaching and learning mathematics. The cohort involved on-campus [n=82] and off-campus [n=420] participants. The qualitative study was based on developing three aspects of mathematics teacher education: (1) Content knowledge; (2) Pedagogical knowledge; and (3) Knowledge of the learner. A problem-based learning environment was created to build students’ self-efficacy and to encourage the beginning teachers’ willingness to engage in the unit content by providing authentic teaching contexts, and to develop a richer conceptual and procedural understanding of mathematics.

This paper reports on a recent research study that investigated Victorian year 10-11 mathematics students’ attitudes and beliefs on the impact of handheld CAS calculators on students’ mathematics achievement. Students were surveyed using the Mathematics and Technology Attitudes Scale, which was used to monitor five affective variables relevant to learning mathematics with CAS. Principal component analysis, t-tests, correlations, and MANOVA were used for the analysis of responses. Students’ responses indicated that there is a positive correlation between their attitudes towards CAS and their prior knowledge and experience. The results also reflected the common finding that boys express greater confidence than girls in technology use in mathematics learning.

Many researchers advocate the use of history of mathematics in education. However, empirical research in this area is scarce. To address this issue, a quasi-experiment is used to investigate the relationship between the use of history of mathematics, and the attitudes and achievement of junior college students in Singapore. Multivariate analysis of covariance and analysis of covariance, with pre-test scores as covariates, and post-test scores as dependent variables, suggest that history of mathematics can improve students‟ attitudes and achievement in mathematics.

Student beliefs about mathematics are difficult to access and categorize. This paper discusses one method used in an attempt to mitigate this issue. As part of a larger study into Year 5 and Year 6 students’ beliefs about the nature of mathematics as well as their self beliefs about the domain, a subgroup of 185 students completed a drawing task. The metaphors used in these drawings are explored as a way of accessing, grouping, and understanding the range of beliefs held by these students.

This exploratory study involving Australian and Chinese teachers seeks to characterise teachers’ capacity to help students connect arithmetic learning and emerging algebraic thinking. The study is based on a questionnaire given to Australian and Chinese teachers, comprising seven students’ solutions of subtraction sentences. Teachers’ responses to the questionnaire were analysed in terms of four categories: knowledge of mathematics, interpretation of the intentions of the official curriculum documents, understanding of students’ thinking, and capacity to design appropriate instruction in the short and long term. These four categories form the basis of our construct of teacher capacity.

Given the diversity of achievement in most classes and the other pressures on teachers, it seems unrealistic to assume that class teachers, as part of their everyday teaching, can provide whatever support is needed by students who have fallen a long way behind. The following is a report of a specific initiative aimed to investigate the potential of an out of class student support intervention, the goal of which is to prepare students for the mathematics lessons they will experience subsequent to the support.

Students’ ways of using handheld calculators were investigated and compared on a sample of 964 Singaporean and 176 Victorian (Australia) senior secondary students. A survey instrument was developed based on four metaphors of technology use proposed by Geiger (2005): Master, Servant, Partner, and Extension of Self. Factor analysis found three factors: Master, Servant, and combined Partner and Extension of Self. Victorian students were found to have significantly lower scores on calculator as Master and as Servant, compared to Singaporean students. Males in both regions exhibited higher fluency of calculator use, compared to females.

Assessment systems should place more emphasis on the thinking process, not academic achievement alone. This study focuses on comparing Australian and Malaysian teachers’ views on the practicality of implementing the Mathematical Thinking Assessment (MaTA) Framework. It involved eight mathematics teachers from Australia and Malaysia. All teachers implemented the MaTA Framework in their schools to assess students’ mathematical thinking using a Performance assessment to elicit students’ thinking processes during problem-solving. They also used a Metacognition Rating Scale, a Mathematical Dispositions Rating, and a Mathematical Thinking Scoring Rubric. Teachers were interviewed and their views towards implementing the MaTA Framework were reported in this study.

Since 2000 gender differences in mathematics achievement in Australia have reappeared. In this paper we report on the achievement outcomes of girls and boys in a longitudinal study of reform in low economic school communities. Analysis of student data to inform teaching was one element of student centred approaches implemented by teachers. Teachers targeted students’ next point of learning and more girls than boys participated in mathematics intervention programs. Growth in achievement was greater for boys than for girls in the primary years, and so the achievement gap that favours males widened. It is concluded that student centred approaches need to be gender inclusive.

In this paper we report our learning as researchers from a 5-year professional development design experiment. At its completion, we identified five strands of support as being essential to mathematics teachers’ learning. However, when planning the design experiment based on prior research, we only explicitly considered two of these strands—Building Mathematical Competence and Focus on Student Reasoning. The significance of three more strands of support became evident during the course of the experiment. We document the emergence of one of these strands, Understanding the Institutional Context of Teaching, by focusing on pivotal episodes from the experiment.

The Early Years Generalising Project involves Australian students, Years 1–4 (age 5–9), and explores how the students grasp and express generalisations. This paper focuses on the data collected from clinical interviews with Year 3 and 4 cohorts in an investigative study focussing on the identification, prediction and justification of function rules. It reports on students attempts to generalise from function machine contexts, describing the various ways students express generalisation and highlighting the different levels of justification given by students. Finally, we conjecture there are a set of stages in the expression and justification of generalisations that assist students to reach generality within tasks.

This paper considers the change in teachers’ confidence, beliefs, and knowledge with respect to mathematics teaching across a 3-year collaborative intervention, which although planned in a reform-based learning environment, took place as the reforms were rolled back and a new view of curriculum introduced. Of 86 middle school teachers involved at some time during the project only 19 completed both the pre- and post-profiles and of these only 11 had been in the project since its beginning. Teacher change appears more likely to have been related to the length of time in the program than to the state-wide curriculum changes.

With increased accountability attached to students’ results on national testing in Australia, teachers feel under pressure to prepare students for the tests. One approach is to use evidence from school and student results to identify areas for targeted teaching strategies to improve students’ understanding. Using NAPLAN results lower secondary mathematics teachers in one school implemented mental computation and estimation approaches as well as a strategy to address the literacy demands of typical test items to support student learning before and after the NAPLAN test. An analysis of the professional learning identified approaches to enhance both students’ learning as well as teaching practice.

Increasing numbers of young people experience disruption to their education owing to chronic illness. Many seek to continue their learning despite absence from school for prolonged or accumulative periods of time. The need to consider ways to support them arose in the context of a project called Link ‘n Learn funded by the Australian Research Council (2008-2010). This paper reports on one aspect of a collective case study of students absent from school with diverse types of chronic illness and their mathematics teachers. It highlights that students focussed on their desire for interaction to continue study whereas their teachers were concerned about issues of illness.

Pre-service primary teachers‟ mathematics anxiety affects their future teaching of mathematics. This makes them less likely to engage with mathematics, impacting on the attitudes and performance of their future students. Hence, teacher education is a crucial site for further research. Bibliotherapy, incorporated into a fourth-year pre-service teacher‟s action research during her final practicum, helped identify the impact of previous experiences on her mathematical identity. With each cycle of her action research, supported by the bibliotherapy process, the pre-service teacher was able to develop greater insight, leading to a more positive projection into her future as a teacher of primary mathematics.

This paper reports on an ongoing research project investigating how problem solving can prepare students to think algebraically. The student examples presented highlight how investigating and solving mathematical problems from a structural and generalised perspective can develop the thinking associated with algebraic reasoning.

The latest curriculum development effort of the Math in a Cultural Context, a long-term Alaskan project, includes Indigenous knowledge (IK). Collaborating with Yup’ik elders, MCC has identified a powerful set of mathematical processes used in constructing everyday artefacts. The knowledge of elders provides a unique way to teach Rational Number Reasoning. Measuring the efficacy of curriculum developed from IK requires a reliable and valid assessment instrument, which captures the mathematical content and learning trajectory established by Indigenous knowledge. An appropriate assessment instrument was unavailable; hence adapting questions from other instruments was undertaken. This paper describes the process of adapting an Australian fraction assessment for use in this Alaskan context.

Exceptional performance, or giftedness, in mathematics is complicated by the variety of conceptual approaches to studies of giftedness as well as the broad and diverse nature of mathematics as taught in modern educational institutions. This paper outlines approaches to giftedness in mathematics that are based in studies of cognition within the discipline of educational neuroscience, approaches that conceptualise giftedness within a context that is sensitive to modern biology and, at the same time, inclusive of modern research in the social and behavioural sciences. Based on such approaches, exceptional performance in mathematics is discussed in relation to cognition and performance as a product of internal processing and environmental connectivity of the human organism. Such approaches have facilitated the development of an overarching framework for learning and memory that may enable a view, within the constraints of empirical science, of educational concepts related to exceptional performance. This framework may provide useful insights into the identification and education of students who may be gifted in mathematics.

What is important to teach students within the mathematics discipline? Identifying the fundamental concepts (or big ideas) of mathematics is being looked at in the development of the Australian National Mathematics curriculum. But what do lecturers at university consider to be the “big ideas” in the mathematics courses they teach? Seventeen lecturers were interviewed about thirteen mathematics courses to establish what they considered were the key areas of learning within these courses. This paper reports on the interviews conducted with lecturers from two large first year classes. Their responses indicate that teaching mathematics involves a lot more than mathematics alone.

This study extends a previous study on spoken mathematics (Clarke & Xu, 2008) and seeks to compare the discursive practices in classrooms from Seoul, Shanghai, and Tokyo, with a particular focus on meta-discursive rules (Sfard, 2001) that regulate exchanges between the teacher and students. The analysis centres on the events when the topic of linear equations was introduced. The similarities and differences of the three classrooms suggest that while the shared macrocultural values and beliefs frame the social activity of the classrooms in similar ways, the meta-discursive rules of classroom microculture determine the opportunities for student learning in mathematics.

This paper investigates views of mathematics/science teachers and higher education faculty interacting in professional development projects adding a community of practice component. Knowledge acquisition in a community of practice relates to ongoing interactions among members as they perform their roles and responsibilities. In particular, the paper reports each group’s perceptions of community and discusses implications for state-level programs funding professional development projects.

This paper reports an investigation of primary school children’s understandings about ―square‖. 12 students participated in a small group teaching experiment session, where they were interviewed and guided to construct a square in a 3D virtual reality learning environment (VRLE). Main findings include mixed levels of ―quasi‖ geometrical understandings, misconceptions about length and angles, and ambiguous uses of geometrical language for location, direction, and movement. These have implications for future teaching and learning about 2D shapes with particular reference to VRLE.

The study investigated interactions between nine teachers and their Year 5–6 students during a lesson on the ―equal additions‖ strategy for subtraction problems involving difference. Two quantities were compared (e.g., $445 vs. $398), a quantity was added to both (rounding up the subtrahend), and students asked about the two differences ($447– $400 and $445–$398). Teachers‘ use of so-called ―indicator words‖ was analysed. Those using words such as ―difference‖ and ―how much more‖ frequently had more students who chose the equal additions method to solve post-test problems. The findings reflect the challenges of bringing about deep and lasting change in teaching (and learning) mathematics.

Applications and mathematical modelling have been a distinctive part of the senior secondary curriculum in Queensland for over two decades. Findings related to technology use from an on-going longitudinal study of this initiative are reported. Twenty-three teachers and curriculum figures from across the state were interviewed and artefacts related to technology use were collected from teachers. Teachers’ understanding of the nature of modelling and the potential for technology to be used at various junctures in the modelling cycle affected the extent of technology use in teaching and assessment. The culture of the classroom was perceived as being very different by teachers who made significant use of technology during modelling. Technology was also seen as being essential for the future successful teaching of applications and modelling.