Display Conference Proceedings

As a contribution to honour the foresight of Ken Clements and John Foyster in founding MERGA so many years ago this paper is not a research paper in the usual sense. Rather it sets out to sample the context of Mathematics Education in Australasia and beyond (then and now) and to highlight some challenges as seen by this author. In this personal view I do not intend to expand in detail upon particular strands of research in which I have been involved, although for purposes of illustration examples will be drawn from time to time from this and other work. MERGA is about both people and scholarly activity, and so this paper will make reference to both – for history, culture, and challenge are essential components of the development of any organisation.

The evolution of Singapore’s school mathematics curriculum is in tandem with developments in the education system of Singapore. In the last six decades, economic policies of the government that are necessary for the survival of Singapore in a fast changing world have shaped the aims of the school mathematics curriculum. The present day curriculum can best be described as one that caters for the needs of every child in school. It is based on a coherent framework that has mathematical problem solving as its primary focus.

According to Stenhouse (1984), “research is systematic inquiry made public”. By bringing inquiry into teaching practice we promote learning in three layers: learning of mathematics; learning of the teaching of mathematics; and learning of the processes through which mathematics teaching and learning develop. Through examples of developmental practice from school-based research in the UK and Norway, and research in university-based mathematics teaching in the UK, I discuss ways in which mathematics teachers and mathematics educators can form communities of inquiry to promote development in learning and teaching and look critically at some of the issues involved. These issues raise challenges for promoting development within a philosophy of educational practice and at scale, with reference to the wider dimensions of society, system and culture.

Exploring and developing primary teachers’ understanding of mathematical reasoning was the focus of the Mathematical Reasoning Professional Learning Research Program. Twenty-four primary teachers were interviewed after engagement in the first stage of the program incorporating demonstration lessons focused on reasoning conducted in their schools. Phenomenographic analysis of interview transcripts exploring variations in primary teachers’ perceptions of mathematical reasoning revealed seven categories of description based on four dimensions of variation, establishing a framework to evaluate development in understanding of reasoning.

To support teachers in their quest to incorporate reasoning as a mathematical proficiency as espoused in the Australian Curriculum: Mathematics, a professional learning research project using demonstration lessons was carried out. This paper reports on the impact of demonstration lessons on one participating teacher’s pedagogical knowledge about reasoning. The growth in this teacher’s knowledge was analysed using a phenomenographic framework established to evaluate teachers’ development in mathematical reasoning. The results show that demonstration and subsequent trial lessons contributed to her growth.

Design-based research is being used to develop and refine the principles used in professional learning workshops with teachers from three different Papua New Guinean ecologies: highlands, coastal, and inland in a coastal province. The appropriateness of the design of principles for Papua New Guinean Elementary Schools is tried over several phases and improved with each evaluation. This design-based research approach is proving suitable for the Papua New Guinean context.

Observation of fellow educators conducting demonstration lessons is one avenue for teachers to develop sensitivity to noticing students’ reasoning. We examined teachers’ noticing of children’s learning behaviours in one demonstration lesson of the Mathematical Reasoning Professional Learning Research Program (MRPLRP). The observations of teachers evident in the audio-taped post-lesson group interviews conducted at one school are reported in this paper. The teachers noticed that the children struggled to employ mathematical language to communicate their reasoning and expressed concern about gaps in children’s understanding of key mathematical concepts. The teachers viewed limitations in language and mathematical conceptual understandings as a barrier to effective reasoning.

Papua New Guinea education policy has encouraged the use of local languages and cultural practices in teaching mathematics via the Cultural Mathematics syllabus. However, teachers have not had appropriate or sufficient training to do this effectively. We report on a project aiming to educate the elementary school teachers to identify and use mathematics in cultural activities. A feasible elementary teacher professional learning process is required guided by a design of principles. This takes the form of week-long workshops delivered in regional areas including villages. Technological-enhancement is provided by the provision of laptops with video resources, which also needs to be at a sustainable scale.

Qualitative and quantitative data are both being used to evaluate a large project in remote areas of Papua New Guinea. Results from teacher and student questionnaires are yet to be evaluated. The responses from teachers participating in the project workshops are reported here to be extremely positive towards the content and delivery of the workshop.

The concept of a growth-oriented disposition framed the analysis of theoretical and practical dimensions of pre-service teachers’ mathematics content knowledge. We identify historical hangovers, tacit habits, and pedagogical strangleholds that present challenges to the way mathematics education researchers interact with the mathematics content knowledge of pre- service teachers. We outline opportunities to expand our agency in the enterprise of teaching, learning, and researching school mathematics and that of our pre-service teachers.

In this paper, three elements of primary pre-service teachers’ relationships with mathematics are explored: mathematical achievement, feelings about the subject, and confidence to teach mathematics. At the beginning of their programme, under half of the pre-service teachers did not meet the numeracy requirements and took part in a support programme. By the end of their first year, 95% of the cohort had met the numeracy requirements of the course. Sixty-five percent of the pre-service teachers surveyed liked or felt neutral about the subject, and 38% felt confident to teach mathematics when they graduated.

This paper describes the assessment of primary pre-service teachers’ mathematics content knowledge and the associated support services provided at the University of Otago during 2013. Most pre-service teachers believed that the results from the assessments accurately reflected their mathematics knowledge and gave them useful feedback about specific content knowledge. There was moderate take-up of the four types of support offered, with few making no use or minimal use and few making high use of the support services. Pre- service teachers who had access to all four types of support believed that the face-to-face teaching by a mathematics lecturer and the HOTmaths website were very useful.

Results of a personal number sense assessment completed by 1253 students enrolled in the first year of pre-service teacher education between 2010 and 2013 are reported. The assessment consisted of 10 short questions requiring solutions to addition and subtraction problems, selected to promote mental calculations using strategies that implied the use of number sense. Analysis of data revealed the scores gained by the pre-service teachers were not necessarily consistent with the University entrance requirements for numeracy. Findings suggest that personal number sense could make a difference to the outcome of pre-service teachers’ final grades for the first year mathematics education course.

This symposium is the outcome of ongoing discussion over the past year with MERGA members interested in pre-service teacher education. Interest in this topic is evident from the 2012 special issue of MTED, “Evidence-based approaches to developing content knowledge and pedagogical content knowledge in pre-service mathematics teacher education.” Each of the symposium papers discusses a different aspect of initial teacher education with reference to pre-service teachers’ mathematics content knowledge. The papers focus on identifying and addressing issues, the outcome of support initiatives, and a growth model perspective from which to view the issues.

A design of principles for teacher professional learning was developed to improve the teaching of Cultural Mathematics in elementary schools in Papua New Guinea. The design’s appropriateness for PNG elementary schools is the focus of the research implemented through week-long workshops using technology enhancement. Implementation has been in different ecologies and through workshops with different numbers and diversity of languages of teachers attending. This paper outlines the design of the principles and the structure of the workshop.

Mathematical reasoning is one of the proficiencies in the Australian Curriculum: Mathematics and prominent in curricula around the world. Yet teachers are uncertain of its meaning and practice and struggle to implement it regularly in their lessons. The four papers presented in this symposium report findings arising from the Mathematical Reasoning Professional Learning Research Program [MRPLRP]. The program used two different demonstration lessons taught in two phases of the project involving four primary schools in Australia and one in Canada. The four papers presented provide an emerging framework for action and research in enhancing children’s mathematical reasoning.

Technology facilitated the implementation of teacher professional learning based on a design of principles to improve the teaching of Cultural Mathematics in elementary schools in Papua New Guinea. An offline ‘website’, a set of interlinked resource materials was used in workshops to enhance the professional learning. Appropriate and relevant content was needed together with consideration of the teachers’ backgrounds.

Engaging children in justifying, forming conjectures and generalising is critical to develop their mathematical reasoning. Previous studies have revealed limited opportunities for primary school children to justify their thinking, form conjectures and generalise in mathematics lessons. Forms of justification of Year 3/4 children from three schools in Victoria, Australia will be examined. Evidence from children’s written explanations and their verbal explanations captured in video recordings revealed that some children employed sophisticated mathematical ideas in their justifications. The value of making children’s reasoning explicit through written explanations and verbal communications is highlighted.

This paper reports how the context in which a mathematics item is embedded impacts on students’ performance. The performance of Year 10 students on four PISA items was compared with performance on variants with more familiar contexts. Performance was not better when they solved items with more familiar contexts but there was some evidence that items requiring the second-order use of context were more influenced by an alteration of context than items of first-order use. Recommendations for further study are included.

Guided by the principles of lesson study as applied to microteaching, this paper discusses the results and conclusions of a series of activities done by some graduate students of De La Salle University, Philippines, in an attempt to test the applicability of the lesson – Sequence and Patterns – to facilitate the transition of seventh graders from arithmetic to algebra. The post-lesson discussion and a posteriori analysis proved the lesson to be a practical means to address the issue as it was able to put forward discourses and elaborations on possible students’ understanding of variables generated through attempts to describe patterns occurring in sequences presented.

Information and communication technologies (ICT) are positioned in policy/syllabus documents as an essential resource in the teaching of mathematics. Given their youth and lifelong experience with technology, early career teachers (ECTs) are expected to excel in their use of ICT; however, we are not clear on the viability of these expectations and the reality of their teaching practices. This paper draws on data from three separate studies to explore how ECTs use technology in their teaching. Although their use of Interactive Whiteboards did not pose challenges, use of iPads did, and the teachers’ mathematical knowledge for teaching appeared to be directly related to how they used their technology.

Increasing pressure is mounting from all areas of society to maximise technology use within educational domains. Whilst curriculum documents call for the utilisation of technology as a teaching tool in the mathematics classroom, the benefits of exploring forms of dynamic mathematical software, such as GeoGebra, are often introduced in the senior years. This study investigates the challenges and understandings of a Year 9 Mathematics class who were using GeoGebra for the first time.

Despite an emphasis on manipulative algebraic techniques in secondary school algebra, many tertiary mathematics students have mastered these skills without conceptual understanding. A significant number of students with high tertiary entrance ranks enrolled in first semester university mathematics were found to have misconceptions relating to pronumerals. School mathematics teaching at all levels must emphasise that pronumerals represent numbers, not objects, labels or abbreviations. Symbol manipulation must be balanced by problem-solving experiences so that the different roles of pronumerals either as variables, parameters, specific unknown numbers or generalised numbers have meaning for students.

If teachers are to adequately support development of their students’ numeracy capabilities then they need to have an identity as a teacher of numeracy. A preliminary evaluation of a conceptual framework (Bennison & Goos, 2013) developed for use in a two-year study that seeks to understand this construct is presented. Initial findings about an early career secondary science teacher are utilised to describe this teacher’s identity as a teacher of numeracy, enabling the conceptual framework to be illustrated and critiqued.

This study proposes a new theoretical framework that incorporates thematic descriptors to form broad conclusions about teachers’ mathematical beliefs and their classroom practices. Narrative accounts provided by beginning primary teachers were used to analyse the relationship between their beliefs and practices through the lens of this newly developed framework. The outcome of this study was a revision to the proposed framework and a challenge to other well-established frameworks that directly correlate teachers’ expressed beliefs about the nature of mathematics and their teaching and learning practices.

Ten years ago the construct, affordance, was rising in prominence in scholarly literature. A proliferation of different uses and meanings was evident. Beginning with its origin in the work of Gibson, we traced its development and use in various scholarly fields. This paper revisits our original question with respect to its utility in mathematics education research. We explore accepted meaning(s), the clarity of operationalising these meanings within research, and how the construct is being used to move the field forward.

With reports of declining participation in mathematics related careers and low female participation rates, the issue of gender differences in mathematics remains relevant. This study seeks to examine the relationship between: children’s sex, parents’ beliefs regarding their children’s education, and, the children’s mathematics performance. Through a secondary analysis of data from the Longitudinal Study of Australian Children (LSAC), responses from 2927 children aged 8 to 9 years old, show that parental perceptions of their children’s mathematics achievement and their expectations for their children are closely associated with the children’s mathematics performance in NAPLAN.

A survey was given to 87 primary students in Years 3 and 4 at a school participating in the Encouraging Persistence Maintaining Challenge project. Its purpose was to give an overview of students’ attitudes and beliefs about learning mathematics, their motivation, and their self-awareness. Findings indicate that most students believe mathematics is important, they feel confident and capable of learning mathematics. Students were also self-aware and identified their motivations to try hard at mathematics as: an interest in mathematics, wanting to please their parents, and feeling capable of being successful. Their learning appeared to be less influenced by peer pressure and classroom culture.

This paper explores the group dynamics among three groups of students involved in collaborative learning in mathematical modelling activities. It reports how group dynamics were established and their influence on the students’ mathematical problem-solving endeavours. Through video analyses, discourse structures were identified to suggest the dominant roles students play within the group. Frequency counts of the discourse structures accounted for the group dynamics that shape the effectiveness of the learning that takes place in the groups. Implications from the findings are discussed.

What teachers attend to, how they make sense of, and respond to critical incidents in the classroom are important for improving teaching. However, seeing and understanding important features of critical incidents can be difficult. In this paper, I propose a notion of productive noticing, which I used to analyse a case study of what teachers noticed about a critical incident that happened during a research lesson. Findings suggest productive noticing can help teachers to focus on important mathematical aspects of critical incidents, and understand how these can lead them to refine their teaching practices.

It is essential that pre-service teacher educators address pre-service teacher numeracy but with careful consideration as it incorporates more than mathematics skills. Numeracy also involves disposition towards mathematics—attitudes, confidence and mathematics anxiety; that is, the level of willingness to use mathematics skills. As part of an emphasis on developing pre-service teacher numeracy, a new first year unit was introduced. Pre-service teachers were given tools to investigate their competence, attitudes towards, confidence with, and anxiety regarding mathematics. This paper outlines the changes that were identified in the numeracy of these pre-service teachers at the completion of the unit.

‘Emoticons’ are simple face icons expressing common feelings such as happiness, interest and boredom and are popularly used in electronic communication. Emoticons were utilised in this study as experience sampling devices. Year 10 students selected emoticons to indicate their emotional states at set intervals during classroom tasks. Marked emoticons provided important information regarding the quality and timing of experienced emotions. As prompts in post-lesson interviews, emoticons were found to elicit rich feedback concerning associations between emotional experiences and task properties. In combination with interviews, emoticons facilitate probing of student emotions.

This paper reports on a study that investigated the nature of the students’ mathematical talk in an undergraduate mathematics study group. Study groups to support the learning of first year mathematics students are encouraged by mathematics educators. From nine recorded sessions, a session with a high quantity of mathematical talk and unfamiliar topics was chosen as a case study. The students used several different interactions but they developed mostly low level cognitive conversations. Four proposed causes limiting the cognitive level of the student’s mathematical talk are the lack of prior preparation, avoidance of high level cognitive questions and the inability to recognise and then develop opportunities.

When students begin secondary school they must learn what it means to be a learner of mathematics in this new context. Certain actions are more valued than others and these can be considered scripts for successful learning. Students may call upon these scripts when enacting their mathematics learner identity. Sixty-four interviews with 22 students and 16 interviews with their Year 9 teachers were analysed using a performance metaphor for identity to explore the role of scripts in developing learners’ mathematics identities. Teachers promote an ‘ask questions’ script and see their students as lacking if they do not do so. Students, in contrast, receive and enact passive learner identity scripts.

Self-belief can directly predict students’ academic motivation and achievement. Research indicates that mathematical self-belief often decreases during the middle years of schooling. This study explored the mathematical self-belief development of 15 Year 7 students. Data were gathered from a survey, a mathematics achievement test and interviews. Results were analysed and interpreted from a multilevel perspective. Findings indicate that student-level characteristics, such as persistence, were the most influential on mathematical self-belief. While class-level contexts, such as ability grouping, were less influential, interpersonal relationships with teachers played a major role.

This article develops three different types of student explanations and studies how teachers respond to these. The data come from five classrooms at upper grade 5-7 (ages from eleven to thirteen) where all mathematics teaching for one week was filmed. These films were transcribed and student explanations identified. Through a close inspection of these, three categories of student explanations were developed. This enabled a closer study of how teachers respond. Typically, teachers respond by pointing out important details, by moving on without further comments, or by requesting students to provide more details.

Japanese lesson study has attracted many international educators who have been impressed by its capacity to foster student learning and sustained professional growth of teachers. This paper reports a study on its cultural orientations that may explain why lesson study works seamlessly in Japan. Hofstede's dimensions of national culture are utilised to identify and analyse cultural orientations that support key practices in Japanese lesson study and raise some questions about a simple transference model to other cultures.

Indigenous languages are used for instruction in elementary schools in Papua New Guinea, but teachers have generally received their own education in English. The challenges of identifying terminology to use in mathematics include many-to-one correspondences between English and the vernacular languages, and different grammatical structures. Guidelines to assist teachers need contextualised examples. Teachers also need sufficient mathematical understanding themselves.

Students explored variation and expectation in a probability activity at the end of the first year of a 3-year longitudinal study across grades 4-6. The activity involved experiments in tossing coins both manually and with simulation using the graphing software, TinkerPlots. Initial responses indicated that the students were aware of uncertainty, although an understanding of chance concepts appeared limited. Predicting outcomes of 10 tosses reflected an intuitive notion of equiprobability, with little awareness of variation. Understanding the relationship between experimental and theoretical probability did not emerge until multiple outcomes and representations were generated with the software.

This paper reports on a recent qualitative case study that explored the numeracy understanding and practices of a secondary school teacher who did not have formal teaching qualifications in mathematics. Results of the study suggest that although teachers may be able to confidently articulate a definition of numeracy, their working understanding, application of numeracy concepts and propensity to facilitate student learning opportunities in numeracy are less certain.

In this study we set out to investigate the errors made by students in logarithms. A test with 16 items was administered to 89 Secondary three students (Year 9). The errors made by the students were categorized using four categories from a framework by Movshovitz-Hadar, Zaslavsky, and Inbar (1987). It was found that students in the top third were less likely to make ‘distorted theorem or definition’ type of errors whereas they were more likely to make errors in the other three categories.

Numeracy is a fundamental component of the Australian National Curriculum as a General Capability identified in each F-10 subject. In this paper, we consider the principles of design necessary for the development of numeracy tasks specific to subjects other than mathematics – in this case, the subject of English. We explore the nature of potential design principles by synthesising generic principles of task design from relevant literature, mapping these principles against an episode of classroom practice sourced from a project concerned with enhancing teaching in numeracy, and interrogating this mapping for elements of design that are complementary to aspects identified in the generic principles.

There is growing evidence that socioeconomic-related differences in mathematical knowledge begin in the preschool years and can become entrenched over time. Children from low-income backgrounds enter school with less mathematical knowledge than their more affluent peers. This paper reports on the use of a tablet-based computer application developed and implemented in a NSW preschool serving a lower SES community. The study sought to: (i) determine the educational effectiveness of the number application in developing children’s early number knowledge and (ii) identify specific features of the application’s design that supported or inhibited early number knowledge development.

At the start of the Kindergarten year in NSW government schools, teachers gather information on several aspects of children’s number knowledge to guide their teaching programs. This includes knowledge of the sequence of words used for counting, numeral identification, and using counting to solve problems. This study investigated the interaction between socio-economic disadvantage in NSW government schools and Kindergarten students’ number knowledge on entry to school in 2013. There is a strong association between the measure of socio-economic disadvantage and the proportion of Kindergarten children starting school with limited number knowledge, underscoring the need for high quality early number programs in these communities.

The World Bank 2007 TIMSS Video Study provided a distinctive insight into the practices of the Indonesian classroom and identified key strengths and weaknesses of current teaching. This investigation considered this evidence in the development of a structured lesson design that specifically addressed the instructional practices of the teaching and the actions of the participants. Watson’s (2008) framework was used to analyse two teachers implementation of the lesson. Findings revealed that the teacher’s initial content-based decisions on how to frame the lesson were most influential in how the lesson was shaped and impacted greatly on the level of student involvement.

In this paper we argue that mathematics teaching can be conceptualised as a form of praxis. Viewing mathematics teaching as praxis foregrounds the moral nature of teaching and the educational practices that are developed in response to the educational needs in particular sites. The case for praxis in mathematics education is then made by drawing on practice theory and, classroom observation and interview data. Finally the implications of a praxis perspective of mathematics teaching are presented.

In recent years there has been an increased emphasis on algebraic reasoning in primary school classrooms. This includes introducing students to the mathematical practices of making conjectures, justifying and generalising. Drawing on findings from a classroom-based study, this paper explores one teacher’s journey in shifting her task design and enactment to develop a ‘conjecturing atmosphere’ in the classroom. The findings affirm the important role of the teacher in introducing mathematical practices. Careful task design and enactment, teacher questioning, and noticing and responding to student reasoning were important elements in facilitating conjecturing, justifying and generalising.

Mathematical knowledge of pre-service teachers is currently ‘under the microscope’ and the subject of research. This paper proposes a different approach to teacher content knowledge based on the ‘big ideas’ of mathematics and the connections that exist within and between them. It is suggested that these ‘big ideas’ should form the basis of teacher planning but it is acknowledged that this represents a ‘cultural change’. The proposal is supported by results from a project that involved pre-service teachers in their final mathematics education unit. Results suggest that a focus on the ‘big ideas’ of mathematics has the potential to change teacher planning and enhance content knowledge.

Research into human decision making (DM) processes from outside of education paint a different picture of DM than current DM models in education. This pilot study assesses the use of critical decision method (CDM) – developed from observations of firefighters’ DM – in the context of primary mathematics teachers’ in-class DM. Preliminary results show that CDM yields significant amounts of data regarding teachers’ cognition during DM and that the process that expert teachers follow when they make decisions may better match naturalistic accounts of DM.

This paper is theoretical in orientation and explores the limitations of the current field of mathematics education which has been dominated by social theories of learning. It is proposed that the field is approaching its limits for these theories and there is a need for shift that moves from the idiosyncratic possibilities of subjective meaning making and identity formation to a more profound position of “knowledge making”. There have been few, if any, advances in equity target group performance so questions are posed as to the viability of social theories for changing the status quo. If equity target groups are to be successful, then success needs to be more aligned with knowledge-making processes.

This study investigated how to improve the teaching of problem solving in a large Melbourne secondary school. Coaching was used to support and equip five teachers, some with limited experiences in teaching problem solving, with knowledge and strategies to build up students’ problem solving and reasoning skills. The results showed increased confidence by all teachers in the range and use of problem solving strategies, and for students increased use of strategies and improved reasoning skills to solve problems.

This paper describes part of a mixed-methods study comparing the effectiveness of an individual, conceptual instruction based, tuition program delivered face-to-face and by personal videoconferencing (PVC) for 30 upper primary and middle school students with mathematical learning difficulties (MLDs). The experimental intervention targeted number sense and fluency with basic facts in mathematics. Results showed significant improvements were achieved in accuracy on basic skills tasks and standardised test results. Implications for students with MLDs living regionally and remotely are discussed.

This paper reports findings from a classroom based study with 5 year old children in their first term of school. A data modelling activity contextualised by a picture story book was used to present a prediction problem. A data table with numerical data values provided for three consecutive days of rubbish collection was provided, with a fourth day left blank. Children were asked to predict the amount of rubbish collected on the fourth day and to explain their prediction. The results revealed children’s intuitive probabilistic reasoning competencies and the influence of task design on their reasoning.

Spatial visualisation is a subset of spatial ability and is exemplified in predicting whether or not a net will fold to form a target solid. The researchers examined video of interviews to explore the schemes of Year 5 students for determining the validity of nets for a cube and pyramid. Findings suggest the significance of imaged actions, shown through gesturing, and the importance of providing physical models during interviews as a means of validation.

Teachers’ knowledge of the early algebra content that is to be taught is crucial for effective pedagogy and ensuring that the students’ understanding of early algebra is not flawed. This article reports the findings of two of the activities that a group of in-service teachers participated in during a professional learning intervention program that was a part of a recent research study in Nigeria. The intervention program amongst other things focused on enriching the teachers’ knowledge of some common students’ misconceptions about the variable, expressions and equations. The teachers’ algebra knowledge and PCK were enhanced as they examined some of the solutions they gave to two algebra word problems.

The aim of this study was to investigate the use of the dual mathematical modelling cycle framework as one way to meet the espoused goals of the Australian Curriculum Mathematics. This study involved 23 Year 6 students from one Australian primary school who engaged in an Oil Tank Task that required them to develop two models in order to solve the task. Results indicate that although some students struggled to fully develop the two models there were students who engaged in both models, deepening their mathematical knowledge and its application when working in real world contexts.

The aim of this study is to investigate if providing mathematics education pre-service teachers with animated library tutorials on library and database searches changes their searching practices. This study involved the completion of a survey by 138 students and seven individual interviews before and after library search demonstration videos were released to them. Results indicate that although students’ confidence in conducting database searches increased, ongoing support will be needed before their searching practices could be considered sufficiently sophisticated to access the depth of literature necessary for teaching and learning primary mathematics.

Accessing children’s feelings and attitudes towards mathematics is a challenging proposition since methods for data collection may be fraught in terms of bias and power relations. This paper explores a method using iPads and a video diary technique not dissimilar to the ‘Big Brother” room with which many children are familiar. We describe the development of the tool and process when implemented in a primary school setting. We allude to both the enabling prospects of the technique as well as some of the limitations we found when implementing the method.

Interaction and dialogue are seen as essential components of mathematics classrooms of the 21st century. In this paper we explore the pedagogical actions a teacher takes to reposition his diverse learners as active and engaged participants in the classroom. The findings illustrate the need for explicit teacher modelling of ways for students to participate and explain and justify reasoning. We illustrate how teacher actions led to agentic students and a shift from social to sociomathematical norms in the construction of mathematical explanations, justification and generalisations.

In this paper we report trends over time of performance of non-Indigenous and Indigenous students on the Numeracy component of the NAPLAN tests. Possible links between student performance on the NAPLAN Numeracy test and the four components - Reading, Writing, Spelling, and Grammar - of the NAPLAN Literacy test were also explored. While the performance of both groups of students at all grade levels have remained fairly consistent over time, there were differences in the aspects of literacy most strongly related to the numeracy performance of the two groups.

Declining participation rates in advanced mathematics courses and STEM-related occupations has been an issue in Australia for some time, particularly for females. As students continue to disengage with mathematics and complain about its usefulness, it is important to explore what we can do to stem the tide of departing students. One area worthy of investigation is students’ interest in mathematics including whether they are able to name a mathematical role model in their lives. Forty-three students in Years 7 to 9 from three schools were asked to name people they knew who were interested in mathematics. There was a strong bias towards male figures (44 to 17), particularly fathers and male peers.

In early childhood settings narratives that capture children’s learning as they go about their day-to-day activities are promoted as a powerful assessment tool. However, in the New Zealand context there is increasing concern that learning stories currently downplay domain knowledge. Data from teacher interviews and samples of learning stories suggest that many teachers prefer to document and analyse mathematics learning that occurs within explicit mathematics activities rather than within play that involves mathematics.

Understanding the development of pre-service teachers’ mathematical content knowledge (MCK) is important for improving primary mathematics’ teacher education. This paper reports on a case study, Rose and her opportunities to develop MCK during the four years of her program. Program opportunities to promote MCK when planning and practicing primary teaching included: coursework experiences and responding to assessment requirements. Discussion includes the Knowledge Quartet: foundation knowledge, transformation, connection and contingency. By fourth-year, Rose demonstrated development of different categories of MCK during practice teaching.

This paper reports on an intervention program, ‘Prepare 2 Learn’, that was designed taking into account a range of components from other successful intervention programs. The program is focussed on year 6 students from a school in Melbourne, Australia, who are falling approximately 6 months behind with the hope that extra help at an early stage may result in them reaching the required standard and realising their potential. While the students’ academic results moved substantially a more pleasing result was the noticeable improvement in the students’ approaches to their learning.

This study compares Singaporean Grade 6 students’ performance and strategy preference on two graphic-rich mathematics tasks, presented via pencil-and-paper and iPad modes. There were statistically significant differences between students’ performances on the two tasks, one in favour of the paper mode and the other in favour of the iPad. Students who possessed higher spatial ability were more likely to solve the tasks correctly. The implications of the study are timely given the fact that high-stakes tests are likely to be presented in a digital form in coming years.

This paper reports on one aspect of a wider study that investigated a selection of final year pre-service primary teachers’ responses to four probability tasks. The tasks focused on foundational ideas of probability including sample space, independence, variation and expectation. Responses suggested that strongly held intuitions appeared to interfere with understanding probability, which impacted on the pre-service teachers’ ability to identify students’ errors and to confidently provide appropriate teaching suggestions and approaches.

This paper draws on two studies, one conducted by each author, where procedures for gaining insights into people’s beliefs about mathematics and learning were developed or adapted for use by the researcher. In this paper we discuss the use in each study of variations of the procedure called Pupil Perceptions of Effective Learning Environments in Mathematics (PPELEM). The paper demonstrates the flexibility of PPELEM as a data collection tool and shows that, even with a large age difference of respondents, the procedure can be used as a prompt for both adults and primary school children and provides insights into beliefs.

Ill-structured tasks presented in an inquiry learning environment have the potential to affect students’ beliefs and attitudes towards mathematics. This empirical research followed a Design Experiment approach to explore how aspects of using ill-structured tasks may have affected students’ beliefs and attitudes. Results showed this task type and learning environment created situations that exposed and challenged students’ beliefs and attitudes and required them to defend their position. Insights regarding factors that may influence students’ beliefs and attitudes are discussed.

This paper explores how young Indigenous students’ (Year 2 and 3) generalise growing patterns. Piagetian clinical interviews were conducted to determine how students articulated growing pattern generalisations. Two case studies are presented displaying how students used gesture to support and articulate their generalisations of growing patterns. This paper presents a hypothesised cultural learning semiotic model that was a result of the interactions that occurred between the non-Indigenous researcher, the Indigenous students and the Indigenous Education Officers.

The approaches to new technologies available to schools, teachers and students largely concern computers and engagement. This requires adoption of alternate and new teaching practices to engage students in the teaching and learning process. This research integrates youth voice about the use of technology. A major motivation for this research is to increase understanding of student perceptions about their learning and interactions taking place during mathematics classes utilising ICT. The focal point is student experiences online as it applies to middle school aged youth (12 - 15 years old) and the constructs that inform student online experiences.

Large-scale numeracy assessments are intended to facilitate the improvement of educational outcomes; however, it is not clear exactly how this is to be achieved. To move towards the goal of numeracy for all, it is necessary to systematically address issues that are known to be difficult, pervasive and persistent. This paper includes an analysis of an `addition of fractions' item from the Australian 2008 Year 7 NAPLAN assessment and draws insights that may be generalised to improve overall numeracy.

The “flipped classroom” is gaining popularity in a number of settings, including secondary schools, reflecting a belief that the approach is more engaging and effective for students. This paper reports on a senior secondary mathematics class’s experience with adopting a flipped classroom approach. The findings indicate that the teacher and students were positive about the practice and perceived it as being sustainable and transferable to other classes. The study has particular implications for senior secondary mathematics teachers who often find it challenging to cover the syllabus and prepare their students for externally imposed assessment tasks.

This paper describes students’ developing meta-representational competence, drawn from the second phase of a longitudinal study, Transforming Children’s Mathematical and Scientific Development. A group of 21 highly able Grade 1 students was engaged in mathematics/science investigations as part of a data modelling program. A pedagogical approach focused on students’ interpretation of categorical and continuous data was implemented through researcher-directed weekly sessions over a 2-year period. Fine-grained analysis of the developmental features and explanations of their graphs showed that explicit pedagogical attention to conceptual differences between categorical and continuous data was critical to development of inferential reasoning.

An analysis of one-step equations from a cognitive load theory perspective uncovers variation within one-step equations. The complexity of one-step equations arises from the element interactivity across the operational and relational lines. The higher the number of operational and relational lines, the greater the complexity of the equations. Additionally, the presence of a special feature increases the complexity of the one-step equations when the number of operational and relational lines is kept constant.

This theoretical paper outlines the process of defining mathematical giftedness for a present study on how primary school teaching shapes the mindsets of children who are mathematically gifted. Mathematical giftedness is not a badge of honour or some special value attributed to a child who has achieved something exceptional. Mathematically gifted children possess unusually high natural aptitudes for understanding mathematical concepts, and subsequently differ substantively to their peers in the way they view, understand and learn mathematics.

With the advent of new technologies, methods of blended learning are used in online mathematics classrooms to facilitate interactions and provide a richer experience for students. This paper analyses data obtained from practising teachers during their participation in two postgraduate mathematics courses. We conclude that discussion forum interactions are students’ preferred way of online learning. Also, although high levels of interaction do not necessarily correlate with success, they are essential for some students to persist with difficult content.

This case study describes the ways in which problems involving additive differences with unknown starting quantities, constrain the problem solver in articulating the inherent quantitative relationship. It gives empirical evidence to show how numerical reasoning takes over as a Grade 6 student instantiates the quantitative relation by resorting to guess-and-check trials. Although our study focuses on a single case study and a set of limited tasks, analysis of the data brings forth the necessity to give more explicit curricular attention to additive differences.

Pat was a 19-year-old attending a Special School for the Intellectually Disabled in Indonesia. She was interviewed by the first author regarding her mental calculation strategies when solving 1- and 2-digit addition and subtraction problems. Results indicate that she was able to see ten as a unit composed of ten ones and was facile in using standard written algorithms: addition with or without carrying and subtraction with or without borrowing. Her mental calculation strategies were influenced by the taught standard written algorithms. These algorithms seem to be counter-productive. However, with appropriate supports, she might have a potential to be an accurate and flexible mental calculator.

This paper reports the findings of research into an educational intervention featuring open-ended mathematical problems situated in “real life” contexts and associated pedagogies. “Money and financial mathematics” is the topic in focus, with tasks termed “financial dilemmas” being trialled by 35 teachers in 16 Victorian primary schools. Drawing on the teachers’ reactions to one task, “Catching a taxi,” the strengths, challenges, and complexities associated with creating and/or selecting meaningful “real life” contexts for mathematics teaching and learning are discussed.

Grades 5/6 students in Melbourne reported the valuing of achievement, open-endedness, relevance, humanism, ICT, and openness most in mathematics learning. Although prior research suggested that students in East Asia valued achievement most as well, there was an observed difference in the nature of this valuing in Australia. Knowledge of what students value reveals the pedagogical potential of values, and also allows teachers to identify values related to effective mathematics learning. Values alignment facilitates further work with these values.

This paper reports on the experiences of newcomers at the 36th Annual MERGA Conference. The paper applies Wenger’s (1998) social learning theory to explore the kinds of feedback that might assist newcomers. Questionnaire responses to describe the experience of ten newcomers and interview responses from five of the ten are reported. The participants identified the stimulating presentations and being immersed in an environment conducive to rich dialogue as important factors that contributed to a positive experience. The newcomers felt welcomed by the MERGA community and were able to contribute, particularly those who had previous experience in research or at other conferences.

The mathematics curriculum leader plays an important role in leading the mathematics curriculum in primary schools. They experience successes and face challenges associated with this leadership role. The perceptions that 25 mathematics leaders held about the successes and challenges they experienced whilst participating in a school mathematics project are reported. Main successes included improved mathematics planning practices using key ideas, transformed cultures concerning mathematics education, and greater use of quality tasks. The main challenge related to sustaining improvements and maintaining the profile of mathematics in school improvement agendas after involvement in the project.

With persistent concerns about student engagement, interest and participation in mathematics, this research investigated the range of practices 31 Year 7 mathematics teachers reported using and how they perceived these practices influenced student engagement in mathematics. In-depth interviews revealed similarities in teachers’ perceptions of student engagement but differences in what teachers did to address engagement through their practices. This paper reports on teacher practices identified as promoting and hindering student engagement in mathematics.

This study reports on the use of formative, diagnostic online assessments for the topic percentages. Two new item formats (drag-drop and slider) are described. About one-third of the school students (Years 7 to 9) could, using a slider, estimate “80% more than” a given length, in contrast with over two-thirds who could estimate “90% of” a given length. While four-fifths of the school students could, using drag-drop cards, choose the 2-step calculation of a reduced price after a 35% discount, only one-third could choose the corresponding 1-step calculation.

As part of a project exploring various aspects of teachers’ choice and use of challenging mathematics tasks, we sought some responses from students on their preferences for the difficulty of tasks on which they might work and also on the ways of working. Despite the common finding that teachers are reluctant to pose challenges to their students for fear of adverse reactions, many students reported that they prefer tasks to be somewhat challenging and many prefer to work on the tasks before having the process explained by the teacher. An important finding was the diversity of student preferences. There are implications for the information that educators offer to teachers on structuring their lessons.

The following is a report of an exploration of what mathematical reasoning might look like in classrooms. Focusing on just one lesson in one classroom, data are presented that indicate that upper primary students are willing and able to reason for themselves, especially in classrooms in which the culture for such reasoning has been established. It seems that the opportunities to reason are a product of the tasks that are posed, the structuring of the classroom, and the willingness of the teachers to allow students to engage with the tasks for themselves.

In this paper I seek to critique pervasive notions of what counts in mathematics education using Heidegger’s notion of the technological enframing. I suggest that early childhood and schooling have become technologies in themselves, casting students and teachers as part of the standing reserve within the inexorable drive for economic advancement. I seek to problematise notions such as evidence-based practice and school improvement by analysing the text in a current state numeracy policy. I then outline an alternative that I term “coming into the world of mathematics” to provoke new insights into the purposes for mathematics in early childhood and school settings.

This paper reports teachers’ beliefs about the extent to which expertise in one-to-one teaching can be transferred to classroom teaching. The study involved 21 mathematics intervention specialists. Data collection involved a structured questionnaire with six open-ended questions. Participants were found to be very positive towards transferring strategies developed in one-to-one teaching to their classroom teaching. The strategies included using material settings, using particular questioning techniques, incorporating assessment into teaching, focusing on dimensions of mathematisation, valuing students’ responses, teaching at the 'cutting edge’, and using mathematical language.

The following is a report of aspects of a project that is exploring the implementation of mathematically challenging tasks and ways of supporting teachers to facilitate effective lessons. Teacher participants indicate that the three-part lesson structure proposed for implementation is valuable. However, they continue to describe the summary phase as complex. The data presented below suggest that repeated opportunities for students to voice their strategies in a cumulative approach may lead to a more purposeful whole-class discussion during the summary phase.

This design-based research project investigated the development of functional thinking in algebra for the upper primary years of schooling. Ten teachers and their students were involved in a sequence of five cycles of collaborative planning, team-teaching, evaluating and revising five lessons on functional thinking for their students over one year. This paper focuses on two aspects of the study related to developing students’ functional thinking by visualising the structure of a growing pattern in different ways.

In small-group workshops, a joint initiative of the researcher and the student counsellor, primary (elementary) pre-service teachers (PSTs) wrote about critical incidents in their mathematics learning, and shared them with the group. Then, PSTs read extracts about mathematics anxiety (maths anxiety), and wrote and shared their reflections (bibliotherapy). Their experiences illuminated factors in their maths anxiety and helped them identify alternative conceptions. The discussion highlights the need for teacher educators’ awareness of perspectives of PSTs, verbalisation and sharing of emotions, and includes recommendations for further research.

This study investigates the relationship between students ability to answer reduced language dependency mathematical questions with their overall numeracy level. It investigates whether a student’s success at reduced language mathematical questions translates into better overall numeracy scores. It was found, students have up to two years advancement if able to correctly answer reduced language dependency questions. This phenomenon was clearly apparent in the overall findings, but was most pronounced at the Year 3 level test, and for female students.

What would the curriculum look like if it were developed from the perspective of measuring? Without formal tools, the Yup’ik Eskimos of Alaska used their body as a measuring device and employed ratios extensively in their daily practices. Math in a Cultural Context is developing curriculum materials based on Yup’ik Elders use of mathematics. This paper describes a hypothesised learning/teaching sequence that is grounded in real life experience and linked to the mathematics in the classroom. Activities that were trialled in classrooms at a K-12 school in interior Alaska are also reported.

This paper focuses on children’s number fact knowledge from a study that explored the impact of using multiplication and division contexts for developing number understanding with 34 five- and six-year-old children from diverse cultural and linguistic backgrounds. After a series of focused lessons, children’s knowledge of number facts, including single-digit addition, subtraction, and doubles had improved. However, they did not always apply this knowledge to relevant problem-solving situations. The magnitude of the numbers did not necessarily determine the difficulty level for achieving automaticity of number fact knowledge.

Recent research suggests some teachers may not have a wide range of teaching and learning strategies for their most proficient mathematics students, which could impact on these students’ learning and ongoing improvement in performance. This paper outlines the different drivers of high achievement and explores the main curriculum differentiation strategies schools and teachers can use for such students. With a toolkit of appropriate strategies, teachers can ensure that class time is productive for their high achieving students and that these students have the opportunity to fully develop their mathematical abilities over the course of the year.

From 2011 – 2013 the VCAA conducted a trial aligning the use of computers in curriculum, pedagogy and assessment culminating in a group of 62 volunteer students sitting their end of Year 12 technology-active Mathematical Methods (CAS) Examination 2 as a computer-based examination. This paper reports on statistical modelling undertaken to compare the distribution of results for this group with the standard cohort, and any differences in student response between the two groups at the item level.

Kayla was a 15 years old girl with Down syndrome attending a special education school in Indonesia. A modification of Wright et al.’s (2006) approach to assessment documented her number knowledge and arithmetical strategies. This paper discusses the assessment process and the results focusing on her ability to solve number problems. Results show that Kayla’s stages in early arithmetical learning and base ten arithmetical strategies are the same as those of typical developing students of a much younger age. This supports the notion that a student with Down syndrome may be capable of learning arithmetic similar to that learned by typical developing children, but their speed of learning appears to be much slower.

This paper reports on one phase of a long-term project investigating mathematical content knowledge of pre-service teachers. A cohort of second year PSTs conducted a diagnostic assessment and a series of associated tutoring sessions with a primary aged child. The focus here is on the PSTs’ ability to make appropriate task choices following the diagnostic process. Results of the study suggest that PSTs are capable of making sound choices of tasks and associated resources based on their mathematical and pedagogical content knowledge following a targeted diagnostic assessment process.

This paper presents insights into the transformation of teaching practices in an undergraduate engineering mathematics course. Adopting a developmental design research approach, the second author introduced mathematical modelling and group work into his teaching of the course, while the first author offered peer observation and feedback to support pedagogical change. The paper uses a sociocultural framework to examine how the peer observation process supported the mathematics lecturer in implementing the teaching innovation. A previously developed adaptation of Valsiner’s zone theory is used to analyse the productive tensions experienced by the lecturer and the observer’s role in promoting change.

Network analysis may be used to enrich understanding of conceptual relationships in mathematics and their development over time and is used to examine spatiotemporal connectivity of learned concepts, or outcomes, and concepts inherent in multiple choice items. The network representations derived from this analysis show the connections between concepts for individuals completing multiple choice assessment tasks in years 3 to 6 in a large-scale testing program. The longitudinal relationships described in this analysis of measurement items offer a way for teachers to address poorly learned concepts that may have compounded over time, particularly for the design of revision and intervention.

Leung (2002) suggests the high TIMSS performance of Singapore, Hong Kong, and Taiwan, which have high proportions of Chinese students, may be influenced by cultural and family values. However, comparative studies of Chinese students’ mathematics performance often focus on what Chinese families do to support children’s learning, with few studies examining why. Using an ethnographic case study, this research focuses on six Chinese families living in Sydney to explore how their cultural identities influence their children’s mathematical learning. Initial findings suggest parents perceive mathematics as an important, yet not difficult subject, and believe their children can be trained to improve.

This study describes the importance of context analysis in designing professional development guidelines to support Ethiopian mathematics teacher educators to integrate technology in their teaching. The study was conducted at departments of mathematics in two Colleges of Teacher Education using a combination of qualitative and quantitative data. Sixteen mathematics teacher educators completed a questionnaire as part of a larger study. The data were analysed using descriptive statistics and theme grouping of the qualitative data. The study showed that analysis of the learning context and teacher educators’ context are found to be important to suggest relevant professional development guidelines.

This presentation examines how a Critical Commentator (CC, the author) facilitated reflection amongst seven Singapore primary mathematics teachers during a school-based professional development programme. Laboratory class cycle involving planning, observing and critiquing mathematics lessons was used as a framework for the programme. With the aid of a questioning framework, the CC was able to help these teachers improve the quality of their reflections, moving from Level 1 technical reflection, to the Level 3 critical reflection. The difficulties in recalling exact details of the observed lesson which prompted the teachers to embrace video technology for their reflection were also examined.

There has been increasing interest in the use of mathematical modelling to better prepare students for the 21st century. However, established rubrics that assess students’ ability to apply their mathematical skills in mathematical modelling tasks are scarce. This study proposes to develop a set of mathematical rubrics based on four standard mathematical modelling steps of formulating, solving, interpreting and reflecting. Validity and reliability of the rubrics will be assessed with 200 high school students from Singapore. The rubrics will then be used to investigate the effects of using a mathematical modelling teaching package on students’ ability to solve real-world problems.

This presentation is based on a literature review (Williams, 2012).The puzzle of why "able children are unable to learn arithmetic" (Butterworth & Laurillard, 2010, p. 536), has different names. It affects the ability to count hence the ability to do arithmetic but not the ability to do higher levels of mathematics. The incidence of dyscalculia is about 5%. However, there is a high degree of co-existence between all learning disabilities. For example, over 50% of students with dyslexia are likely to have dyscalculia. Another issue for dyscalculics is time. They often have working memory problems so need extra processing. References Butterworth, B., & Laurillard, D. (2010). Low numeracy and dyscalculia: Identification and intervention. ZDM Mathematics Education, 42, 527-539. Williams, A. (2012). A teacher's perspective of dyscalculia: Who counts? An interdisciplinary overview. Australian Journal of Learning Difficulties, 2012(Oct), 1-16. doi: 10.1080/19404158.2012.727840

The past decade has seen an increase in the attention given to education in prior-to-school settings, and as a result, two areas of interest have emerged: (1) the intent and nature of this phase of education, and (2) the identity of the educator in these settings. This paper presents data from a project seeking to identify how teachers in this phase identify themselves as teachers of numeracy, and how they articulate their role in the implementation of early childhood mathematics curricula.

This presentation describes a project designed to enhance mathematics and science teacher education in regional Australia. Iterative processes are used to develop and trial enhancement and feedback modules, involving pre-service teachers, mathematicians and educators in targeted interactions designed to ground pre-service teacher education in contexts relevant to daily life. The feedback module, designed for self-evaluation, involves pre-service teachers analysing critical affective states recorded while teaching. The aim is to improve performance through an investigation of the contribution of competence, developed via the enhancement and feedback modules, to pre-service teacher confidence.

The role and status of interactions (student-content, student-instructor and student-student) are considered foundational to current online learning theory (Anderson & Elloumi, 2008). This research investigates these interactions in fully asynchronous online mathematics courses taught in the US public higher education context. It reports on problems with human interactions in general and evidence for a de-emphasis on student-student interactions and an emphasis on computer-based student-content interactions. Findings are discussed in relation to current theory and prior research with concerns raised concerning the quality of associated learning. References Anderson, T., & Elloumi, F. (2008). The theory and practice of online learning. Alberta, Canada: AU Press.

This presentation reports on an intervention study aimed at improving middle year (Years 5-7) students’ engagement in mathematics. Motivation and engagement levels in mathematics were assessed prior to and at the completion of a year-long intervention for two different cohorts of students in 2012 (N=339) and 2013 (N=319) using the Motivation and Engagement Scale (Martin, 2008). While 2012 data found downward shifts in student engagement were generally abated and even reversed for some aspects, 2013 results revealed a greater mix of ‘ups’ and ‘downs’ in student engagement levels. Reasons for the variation in findings of the two cohorts are explored. References Martin, A.J. (2008). The Motivation and Engagement Scale. Sydney: Lifelong Achievement Group (www.lifelongachievement.com).

We investigated the strategies used by Year 7 students in answering a problem solving question. The strategies mostly used by students were Estimation and Check (46%) and Drawing Pictures (19%). A total of 125 students, from the 650 responses collected overall responded using a ‘Drawing Pictures’ strategy while another 299 students opted for ‘Estimation and Check’ strategy. Here we attempt to categorise further these specific strategies to help us analyse the level of students’ problem solving proficiencies. It has been found in previous studies that student’s solution strategies are indicators to show students’ level of proficiency in problem solving skills.

LUMOS is a two-year Ako Aotearoa-funded project that aims to identify, observe, and report on the full spectrum of desired learning outcomes for undergraduate mathematics, that is, not only content-based outcomes. The project includes the development of three innovative delivery methods for undergraduate mathematics. As we enter the second year, we can report on the first and second trial of an innovation that places the responsibility for learning onto students, but also offers them authentic mathematical experiences.

The development of a strategy teaching model associated with the New Zealand Numeracy Development Projects is presented and examined against a Design Research framework. The development while informed by literature, multiple forms of feedback from practitioners, and a clear intent to make it workable for teachers, was a responsive and organic process. It can appear not to have been the result of research or been formally researched overall. However, this examination of the development of the Numeracy Development Projects Strategy Teaching Model suggests otherwise indicating that it is the result of a research process albeit an informal one.

As a new technology, the uptake of iPads in Australian schools is increasing. As part of a current case study, numeracy and literacy teachers from an Independent school in Victoria, Australia in which iPads had been introduced were interviewed and their views on teaching with iPads were explored. A number of concerns arose related to the use of this technology, including teachers expressing the opinion that their teaching had not changed, not seeing benefits for students and concerns about assessment. A discussion of these concerns and possible educational implications is presented.

Increasing numbers of students enrolled in primary pre-service teacher (PST) Education degrees in Australia enter university with insufficient mathematical content knowledge and low confidence levels about their ability to teach and do the mathematics required for their intended role as classroom teachers. Mentoring of PST’s by highly capable and experienced classroom teachers within the framework of a structured and well-planned mentoring programme, has the potential for developing the confidence, and thus alleviating the mathematics anxiety exhibited by PST’s. This study examines a novel approach to mentoring outside the pressure-cooker of the professional experience block.

Middle Years students often do not see the value and usefulness of mathematics while the Australian Curriculum: Mathematics aims for students to be “confident and creative users and communicators of mathematics” (ACARA, 2012). This paper discusses how a group of middle year students have used mathematics to communicate a local issue. The data were analysed in terms of the ‘working mathematically’ moments, in particular problem negotiation, formulation, and solving. The paper will show how these students have made a difference in their local community by using mathematics to communicate the young people’s view.

The focus of this presentation is to report on an exploration of what teachers observed when watching modelled lessons. Focusing on two modelled lessons in one school, data are presented that indicate that observation of teaching practice raises many questions related to the meaning of explicit teaching, the structure of lessons, catering for diversity and the implementation of the Australian Mathematics Curriculum. It seems that a modelled lesson and subsequent inquiry into the teaching practice being modelled can provide an opportunity to challenge teacher beliefs as well as demonstrate what is possible.

I advocate for a shift from the traditional role of the teacher in developing computational proficiency through a single method model-and-practice teaching approach to a pedagogy that promotes learning through diversity. By examining mathematics through different lenses, alternative ways of thinking may be nurtured in the learning environment. Drawing on the lived experiences of immigrant secondary students I present some perspectives that diverse learners have of learning mathematics in their classrooms. In an attempt to understand different ways of solving mathematics problems, I present alternative multiplication strategies from India, Japan and Scotland.

This paper reports on teachers’ experiences of being out of their comfort zone in their mathematics teaching. We describe examples of experiences that the teachers considered “scary”, their reported responses to those situations, and the longer-term effects of such experiences. Implications for the acquisition of knowledge for teaching mathematics are discussed, and questions raised about the possible impacts of confidence and experience on the interaction between discomforting experiences and teacher learning.

This is a presentation of an evaluation and assessing method in mathematics using the concepts of scaffolding, formative assessment and writing to learn intertwined. The scaffolding formative assessment approach is a product of over ten years of development of teaching and assessing mathematics in both compulsory school and secondary education. The aim was to make learning visible and make students reflect on their own learning, what strategies they might use and what needs to develop further. Furthermore, a way of using tests in mathematics as an additional learning opportunity was considered by using summative tests in a scaffolding and formative manner.

The study examined multigroup invariance of Mathematics Self-efficacy and Attitude Scales (MSAS) and examined gender differences of MSAS across gender. The analysis of invariance was conducted to examine whether the items in the MSAS were operating equivalently between Year 9 female and male students in the state of Aceh, Indonesia. The analysis discovered the evidence of multigroup equivalence of the MSAS across gender (p value is not statistically significant or ∆CFI ≤ 0.01). An independent t-test found that attitude toward mathematics was significantly different between female and male students. Females had a more positive attitude toward mathematics.

SPOT (Structures Perceived Over Time) diagrams (Yoon, 2012) are analytical tools for visualising changes in the mathematical structures students create, attend to, and manipulate over time. SPOT diagrams use animated networks to portray relationships between mathematical objects and their attributes, as well as changes in these structures. In this presentation, I show how SPOT diagrams can be used to analyse the role of a participant’s Partially Correct Construct (PaCC) (Ron, Dreyfus and Hershkowitz, 2010) as she developed a method for determining relationships between a function, its derivative, and its antiderivative References Ron, G, Dreyfus, T. & Hershkowitz, R. (2010). Partially correct constructs illuminate students’ inconsistent answers. Educational Studies in Mathematics, 75, 65-87. Yoon, C. (2012, July). Mapping Mathematical Leaps of Insight. Regular Lecture presented at the 12th International Congress on Mathematical Education, Seoul, Korea.

To teach mathematics in the 21st century, and more specifically to teach early algebra, the teacher should bring to the classroom a particular cluster of skills, understandings and knowledge. Early algebra is crucial for students’ success in higher mathematics. While a written curriculum is needed for teaching, a teacher’s beliefs and knowledge are also important determiners of the algebra content taught in the classroom. In this cross-cultural study, we examine the similarities and differences found in two recent and concurrent mixed methods research projects in both Australia and Nigeria. The two research studies showed teachers’ beliefs had a meaningful influence on the teachers’ practice.

This paper presents an argument in support of the proposition that a poetics of mathematics classroom interaction is necessary to the effective design of mathematics curricula. Drawing on an account of the ‘interaction order’ (after Goffman, 1983), which is one aspect of a theoretical investigation of the tools needed to systematically describe mathematics classroom interaction (Kusznirczuk, 2012). I argue that an educator’s ‘critical literacy’ with respect to the rhetorical structure and function of the interaction that realises a ‘mathematics period’ amounts to a ‘poetics of mathematics classroom interaction’ and that the effectiveness of mathematics curriculum design depends on such poetics. References Goffman, E. (1983). The interaction order: American Sociological Association, 1982 Presidential Address. American Sociological Review(1), 1. doi: 10.2307/2095141 Kusznirczuk, J. (2012). In search of the zone of proximal development: Introducing a map used to navigate a confusion of categories and things. Paper presented at the Contemporary Approaches to Research in Mathematics, Science, Health and Environmental Science Symposium, Melbourne. http://www.deakin.edu.au/arts-ed/efi/conferences/car-2012/

A mathematical modelling framework called MODEL (Meanings, Organise, Develop, Execute and Link) was designed to assess students’ application of abstract mathematical knowledge into real-life situations. A pilot study was conducted aimed to identify the level of mathematical modelling skills of 183 pre-university students in Brunei Darussalam. Test items were employed and students’ responses were evaluated using the MODEL framework. The results revealed that the maximum level attained by the students was at the Execute (E) level only. They managed to obtain mathematical solutions and contextualised their solutions but all had failed to justify for validation at the Link (L) level.

The Flipped Classroom Model is an approach to blended learning that is currently being trialled in many settings from mathematics teacher education to the primary mathematics classroom. This literature review offers a general introduction to the model, a discussion of key components of the model including analysis of the opinions of both critics and proponents of the model, and lastly a series of recommendations/ areas for further research.

This study is an exploration of the ways in which experienced mathematics teachers recognize and learn about issues that shape their own professional practice. In a school-based professional development program teachers collaboratively analyzed their teaching practice in order to recognize and interpret concerns and teaching needs, as well as link them with corresponding decision making and teaching actions. Findings indicate that by systematically “unpacking” teaching and students learning and making rationalizations about their practice explicit, the teachers came to articulate, re-interpret and challenge what they need to know about teaching in order to orchestrate meaningful classroom practice.

Critical mathematical thinking is the ability to reason and make judgments to solve mathematics problems. In order to identify young children’s critical mathematical thinking processes, mainstream classroom teachers may ask higher-order, open-ended stimulus questions to elicit the thinking of these children. This research focuses on teachers’ understanding of critical mathematical thinking and their current processes of identification. The study will use purposively constructed mathematical stimulus questions with children, which focus on a range of mathematical conceptual understandings. The focus children are in their first year of formal school (Kindergarten) in a NSW setting.

Recent studies suggest that, similar to secondary school teaching, appropriate mathematical and pedagogical content knowledge (MCK; PCK) and pedagogical technology knowledge (PTK) may also be necessary in order to make informed decisions about curricular values in undergraduate mathematics. There are a growing number of studies that examine these teacher competencies at the secondary school level, but there are few such studies in undergraduate mathematics. This paper discusses the design of a study that looks to examine university lecturers’ PCK and PTK, as a basis for a curriculum-wide examination of relative content value in first year undergraduate mathematics courses.

This paper addresses the question ‘what specialised knowledge is needed by teachers to teach mathematics effectively using digital learning resources?’ It outlines how a specific theoretical framework (the Technological Pedagogical Content Knowledge or TPACK framework) may help us understand the complexity of teaching mathematics using technology. The framework is used to analyse a 100 minute video of teaching “comparing fractions using an exploratory type of website”. The findings suggest that the effective integration of technology in mathematics teaching is determined by a teacher’s TPACK and strong TPACK may not be possible without adequate PCK, TPK, and TCK.

The aim of this presentation is to analyze the extensions of the students in a mathematics lesson. The method is the following. Firstly we review the media theory (McLuhan, 1994; Tokitsu, 2012) to extract a viewpoint for mathematics lessons. Secondly we plan and implement a mathematics lesson (Okawa, Ozasa, & Matsuzaki, 2013). Finally we discuss what the students can do or cannot do bodily, and mathematically, by focusing on the viewpoint. References McLuhan, M. (1994). Understanding media: The extensions of man. London, UK: The MIT Press. Okawa, T., Ozasa, H. & Matsuzaki, A. (2013) The integration between mathematics and physical education for connecting two representations: Through the ICT having motion capture function and the dance create activity. Proceedings of the 46th Annual Meeting of JSSE (pp.361-362). Tsu, Japan: Mie University. (in Japanese) Tokitsu, K. (2012). A consideration about the construction of educational practice by media: Focusing on communication media and material, Departmental Bulletin Paper of Hiroshima Bunka Gakuen University, 2, 29-39. (in Japanese)

This short communication reports on the use of an iPad application for mathematical assessment in New Zealand primary and secondary schools. This iPad application enables the user to make notes, while recording sound in real time. Students’ voices are recorded as they work and explain how they solved a mathematical problem – at the same time as recording anything they write down. This study builds on a pilot study (Williamson-Leadley & Ingram, 2014) that found this feature enabled three primary teachers to gather detailed evidence of how their students solved mathematical problems. References Williamson-Leadley, S., & Ingram, N. (2014). Show and tell: Using iPads for assesment in mathematics. Computers in New Zealand Schools: Learning, Teaching, Technology, 25(1-3), 117-137.

The use of metaphor as a reflective writing tool to explore attitudes towards mathematics has been embraced by researchers in recent years. In this study, first year pre-service primary teachers incorporated inventive concepts and contexts in a personal mathematical metaphor to create strong and meaningful images articulating how they felt about mathematics. The findings reveal the complexity of their attitudes and that despite a perception that these pre-service teachers generally had negative attitudes to mathematics there existed a preparedness to approach mathematics in a reasonably positive manner.

Picture books have been shown to provide opportunities for developing mathematical concepts in young children. Twenty-seven professionals (academics, teachers and preservice teachers) completed 118 evaluations of 36 mathematical picture books for opportunities of mathematical concept development using a seven category likert scale. This presentation highlights the range of scores in identifying mathematical content, connections to the curriculum and application to problem solving. It appears that without a good understanding of mathematics and ways to implement problem solving within the classroom, opportunities to use picture books for rich mathematical learning experiences are lost.

Cross-grouping (or streaming) in mathematics requires students to be grouped by ability. Schools differ as to whether there is a fixed or flexible view of ability (Wiliam & Bartholomew, 2004). The notion of a ‘fixed ability’ jeopardises the education of many when these decisions are frequently made very early in a child’s educational life (Boaler, 1997). Ability is a very ambiguous concept and factors related to class, gender, ethnicity and behaviour can be seen to have an influence on decisions made. This paper will look at the potential difficulties involved in deciding exactly what ability means in the mathematics classroom. References Boaler, J. (1997). Experiencing school mathematics: Teaching styles, sex and setting. London: Open University Press. Wiliam, D., & Bartholomew, H. (2004). It’s not which school but which set you’re in that matters: The influence of ability-grouping practices on student progress in mathematics. British Educational Research Journal, 30 (2), 279-239.

In this presentation the importance of developing both fractional number understanding and algebraic reasoning will be articulated. I argue that arithmetical thinking about fractions necessarily involves multiplicative thinking as opposed to additive thinking. However in moving from arithmetical thinking to algebraic thinking involving fractions, a necessary intermediate stage for middle years’ students is effective representational and relational thinking of fractions. The aim is to identify the key stages and develop a Screening Test of algebraic readiness.

Assessment has been perceived as a key to educational reforms. Teachers often mediate their curriculum interpretations and pedagogy based on their understanding of current assessment formats. In-depth research into the existing beliefs and assessment literacy of mathematics teachers has implications for the review of curriculum-pedagogy-assessment alignment and teacher education programmes. This exploratory study aims to develop a preliminary framework of teacher competency on assessment literacy specifically for primary mathematics teachers. It intends to examine teachers’ beliefs, identify possible levels of assessment literacy, and document effective strategies displayed by teachers in their mediation attempts between curriculum, pedagogy, and assessment.

Mathematics learning can be seen as a multi-factored, human-designed system and complexity theory appears to be useful in explaining phenomena within this system (Davis, Sumara & Luce-Kapler, 2008). The poster proposes a model for understanding and interpreting complex interactions in the mathematics learning of exceptional students. The model uses approaches based in studies of metapatterns and complex systems (Volk & Bloom, 2007) and the multi-mediator approaches used in White and Levin (2013) to represent the emergence of a complex mathematics learning system. The model allows inclusion of social, cultural and environmental factors which may affect mathematics learning for exceptional students. References Davis, B., Sumara, D., & Luce-Kapler, R. (2008). Engaging minds:Changing teaching in complex times (2nd ed.). New York & London: Routledge. Volk,T., & Bloom, J. (2007). The use of metapatterns for research into complex systems of teaching, learning and schooling. Complicity: An international Journal of Complexity and Education, 49 (1), 25-43. White, D.G., & Levin, J.A. (2013). Navigating the turbulent waters of school reform guided by complexity theory. Paper presented at the meetings of the American Educational Researcher Association, San Fransisco, CA. paper accessed from http:/tinyurl.com/White-Levin-AERA2013.

A Leximancer analysis will be conducted on the corpus of research conducted by the members of MERGA since its inception to discover the research interests of this group of Australian mathematics education researchers from 1977 to 2013. Papers over this time period will be organised into equal piles before analysis. This analysis will not only provide a large scale view of the research interests of mathematics education researchers in Australia but also possibly point to directions for future research.

This poster reports on a study of a group of mathematics teachers’ learning experiences in an explicit professional development (PD) program. In order to recognize and interpret the complex processes underlying teacher learning, the Interconnected Model of Professional Growth (ICMPG) of Clarke and Hollingsworth (2002) was used as a tool for communication between the participating teachers and the researcher. Findings indicate that the teachers identify learning outcomes and their own learning trajectories, however they also emphasize various elements apparently connected to concrete challenges they each experience in their professional work. References Clarke, D., & Hollingsworth, H. (2002). Elaborating a model of teacher professional growth. Teaching and Teacher Education, 18, 948–967.

New Zealand along with many other countries has an ongoing concern with a ‘tail’ of low achievers. Many of these low achievers attend schools in low socioeconomic areas and are comprised of a disproportionately large group of students of Pāsifika ethnicities. One project which has been successful in significantly increasing achievement outcomes for this group of students is the Pāsifika Success Project. This project extended aspects of the New Zealand Numeracy Project, built on and used subsequent research evidence, and included providing explicit attention to aspects of culture, language and identities of the Pāsifika learners. Over the past three years the Pāsifika Success Project has consistently resulted in greater than expected improvement in Numeracy results and stanines when normed tests are used. However, the project has only been in a small number of schools and involved one researcher who led professional development days and worked closely with teachers in classrooms co-constructing mathematical inquiry communities. This year the project has widened to include involving twenty-eight schools over a two year period and two full time facilitators. Through this round table we invite other researchers to discuss their experiences with working with teachers to co-construct mathematical inquiry communities in low socioeconomic communities. We seek other researchers’ input in possible development of further work in investigating ways to support minority students (for example, Pāsifika students) in learning proficient mathematical practices within inquiry communities.

Good lesson planning is an important part of effective teaching, but it can be very challenging to plan lessons that focus on working with students’ reasoning In this project, we aimed to sharpen teachers’ focus on facilitating students’ mathematical reasoning by making teachers’ mathematical noticing more productive. The key question guiding the inquiry was: How teachers could notice students’ reasoning more productively? The project took place across two groups—a lower and an upper secondary group; involving 11 teachers at a Secondary School in Singapore. Guided by Choy’s (2013) framework of productive noticing, we incorporated lesson play into our existing lesson study protocol to plan teachers’ responses to students’ reasoning. More specifically, we applied the ‘Three-point Framework’ to help us focus on key ideas, students’ cognitive difficulties, and how we might support students in their learning of Set Language and Notation (lower secondary) and Solving Trigonometric Equations (upper secondary). Initial findings suggest that teachers began noticing salient mathematical features of students’ thinking during the study. The study has heightened our sensitivity towards students’ thinking and provided opportunities to hone our questioning techniques. In this round table discussion, we hope to seek suggestions to enhance our noticing for future iterations.

The emotional climate of classrooms is important to the teaching and learning of mathematics. To date there have been few studies connecting emotions to learning environments. Starting from the premise that teaching is emotional work, we are interested in exploring physical, cognitive and psychological effects associated with a mindfulness intervention in Year 7-8 mathematics classrooms. The potential benefits of mindfulness – the cultivation of non-judgmental awareness and attention to the present moment – are an emerging field of inquiry for psychology and education researchers. For instance, findings from a growing body of studies suggest that a focus on breathing for a short time each day can mediate the impact of negative emotions in classroom events. The roundtable will begin by discussing emerging theoretical frameworks for understanding emotions with a focus on mindfulness practices in classrooms, and associated methodologies for studying mindfulness. The session will provide an opportunity to discuss: teachers’ and students’ increased awareness of their emotional reactions to classroom events; the connection between a breathing intervention and mathematics teaching and learning; and the potential of a mindfulness intervention to improve the emotional climate of learning environments.

There are substantial and ongoing concerns in the Australian and international secondary and tertiary education sectors about students’ transition from secondary to tertiary mathematics. Declining enrolments in university mathematics and increasing failure rates in first year are often attributed to falling participation in advanced mathematics in secondary school and less stringent university entry requirements, which have adversely affected students' mathematical preparedness for university study. In this round table I will present data collected on three topics: reasons for choosing/not choosing advanced mathematics in secondary school; attitudes towards learning mathematics at school; and attitudes towards learning mathematics at university. These data were collected from four separate groups of people: secondary school mathematics students; secondary school mathematics teachers; university mathematics academics; and university mathematics education academics. The results suggest that there are distinct differences in students’ thoughts depending on which mathematics they study in the last two years of secondary school. There are also differences between what students say are the reasons for their subject choice and what mathematics academics think are the reasons. The data also shed light on subject choice myths. This presentation is part of a two-year state-wide longitudinal project that is investigating the transition from secondary to tertiary mathematics.

In Australia, pre-service teacher education programs are structured so that future teachers of secondary school mathematics and science learn the content they will teach by taking courses in the university’s schools of mathematics and science, while they learn how to teach this content by taking content-specific pedagogy courses in the school of education. Such program structures provide few opportunities to interweave content and pedagogy in ways that help develop professional knowledge for teaching. This round table session will invite feedback on the early stages of a national project that is developing interdisciplinary approaches to mathematics and science pre-service teacher education. The project aims to foster collaborations between academics from different communities of practice – mathematics, science, education – in order to design and implement new teacher education approaches. It is hoped that these approaches will institutionalise new ways of integrating the content and pedagogical expertise of STEM academics and mathematics and science educators to enrich three key stages in teacher preparation– recruitment into teaching careers, participation in the pre-service program, and continuing professional learning following graduation. The goal of this Round Table session is to engage participants as critics, interpreters, and potential adopters of the products and processes of our project. Topics for discussion could include: the structures and cultures of STEM teacher education programs in different institutional, socio-economic and geographical contexts; examples of innovative teacher education approaches being implemented in other universities; barriers to and enablers of interdisciplinary collaboration.

The Mathematics Support Teacher (MST) intervention was designed for students who have been identified as having severe learning difficulties in mathematics. The MSTs provide intensive mathematics teaching support aiming to accelerate the students’ progress. The students were provided with four to five additional half hour lessons per week over a 15 to 20 week period. Initial involvement in the intervention has resulted in accelerated gains for the majority of these students. This study is aimed at tracking the progress of students who participated in the intervention in either 2011 or 2012. Longitudinal data were received from eight schools from different regions across New Zealand. Preliminary analysis of the results indicates that approximately half of the students maintained their progress and are on track to achieving at the expected level in relation to the mathematics standards. The remaining students have maintained their learning gains but have not continued to accelerate their mathematics progress. Approximately five percent of the students have made limited or no measurable progress. This round table forum presents longitudinal data after involvement in a mathematics intervention. It will provide an opportunity for participants to review the data, discuss findings and identify solutions for those students not sustaining progress after the MST intervention.

Recent curriculum documents such as the Common Core State Standards for Mathematics and the Australian Curriculum: Mathematics F to 10 continue the practice of presenting content in a linear and compartmentalized manner and appear not to accentuate the links and connections that are present in the ‘big ideas’ of mathematics. Both documents seem to pay lip service to the ‘big process ideas’ or proficiencies which should be the vehicles for developing and making explicit links between and within the ‘big content ideas’. To some extent, the same criticism could be levelled at the recently developed Australian Curriculum: Science F to 10 although that document at least embeds key process ideas as one of the three strands called Science Inquiry Skills. However, it is suggested that it may be beneficial to re-think the nature of key content and to organise it for teaching based on the ‘big ideas’ of mathematics and science, emphasizing the links and connections within and between them. In attempting to deal with the ‘crowded curriculum’, teachers would do well to consider similarities between ‘big mathematical ideas’ and ‘big scientific ideas’ and to make connections explicit for children. For many teachers, this would represent a change in the way in which they view content knowledge. Teachers should be encouraged to actively seek links and connections within and between concepts and bodies of knowledge and explicitly show children how those links exist and can be used. This round table will consider these and related issues such as the nature of ‘big ideas’, models for numeracy and what an equivalent model for its scientific equivalent might look like.