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In Australia, all teachers are expected to explicitly attend to numeracy in the subjects they teach. Pre-service teachers, therefore, need to begin to develop effective numeracy teaching strategies but there is a limited research base to inform the design of courses that address this need. This paper reports on findings from a study investigating the impact of one such course. The paper draws on data from two pre-service teachers: two course tasks completed at the beginning of the course and interviews conducted at the end of the course. Data were analysed using the 21st Century Numeracy Model. Findings suggest there were changes to the pre-service teachers' understanding of numeracy and their capacity to embed numeracy in the subjects they will teach.

Engagement in mathematics education is an important factor in a successful student experience. This paper reports findings from a study of Year 5 student perceptions of engagement during a two-week, inquiry-based learning (IBL), problem-posing investigation. The study triangulated data from semistructured interviews, video observations and student work samples to understand the student's perspectives of IBL; however, this paper reports the interview data. The findings indicate that most of the students were behaviourally, emotionally, and cognitively engaged during the IBL investigation, and that the investigation provided an opportunity for students to experience levels of competence, relatedness, and autonomy need satisfaction.

Prospective secondary mathematics teachers in Australia are typically taught by mathematics educators and mathematicians who work in different faculties and seldom collaborate--a situation that can lead to conflicting views about how to teach mathematics. This paper reports on findings from semi-structured interviews with three mathematics teacher educators in a hybrid mathematics/mathematics education department. Valsiner's zone theory is used to analyse how their beliefs, institutional context and professional learning opportunities shape their identities as MTEs. Findings reveal that the MTEs had developed similar beliefs within supportive institutional context but drew on different sources of professional learning.

Mathematical reasoning is foundational to making sense of mathematics. Yet assessing mathematical reasoning can be challenging for teachers. This paper reports on a project where teachers taught two lessons with a specific focus on reasoning and came together with other teachers at their school to attempt to assess the reasoning of their students. Results, derived from an analysis of two post-lesson discussions about student work samples and associated completed assessment rubrics, provide insights into the challenges identified by 34 primary teachers at 4 Victorian government schools.

Secondary mathematics pre-service teachers often have different experiences of mathematics and its teaching and learning during their initial teacher education. This paper documents the beliefs about mathematics, its teaching, and its learning, of mathematicians and mathematics educators who teach secondary mathematics pre-service teachers. The beliefs of the surveyed sample of eighty-two academics and differences between groups were characterised using descriptive statistics and one-way comparisons between groups ANOVA. Generally, respondents had a Problem-solving view of mathematics and those with education backgrounds were more in agreement with that method of teaching.

In this paper, we provide an overview of the "Maths Inside" project, funded by the Australian Maths and Science Partnership Program (AMSPP). The overall aim of the AMSPP is to improve uptake and participation of students in mathematics and science at secondary and tertiary levels. In this research project, we aim to improve student interest in mathematics and support mathematics teachers in their professional learning, through provision of rich and investigative learning resources, including video case studies of CSIRO scientists and mathematicians. Data collection on the outcomes of the project is ongoing and will be reported in subsequent papers.

The purpose of this study was to explore the factorial structure of motivation and perception items from a student survey utilised as part of the Reframing Mathematical Futures II (RMFII) Project. Data was collected in 2017 from 442 students in Years 7 to 10 from various different States across Australia. An exploratory factor analysis identified four factors which were consistent with the studies the items were adapted from: Intrinsic and Cognitive Value of Mathematics, Instrumental Value of Mathematics, Mathematics Effort, and Social Impact of School Mathematics. An analysis of variance (ANOVA) also revealed that there were statistically significant differences between Year Level and State for some of these factors.

This document contains the second volume of the proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education. Conference papers are centered around the theme of "Learners and Learning Environments." This volume features 43 research reports by presenters with last names beginning between Adl and Fre: (1) Working with Learners' Mathematics: Exploring a Key Element of Mathematical Knowledge for Teaching (Jill Adler, Zain Davis, Mercy Kazima, Diane Parker, and Lyn Webb); (2) A Comparison between Teachers' and Pupils' Tendency to Use a Representativeness Heuristic (Thekla Afantiti-Lamprianou, Julian S. Williams, and Iasonas Lamprianou); (3) Purposeful Task Design and the Emergence of Transparency (Janet G. Ainley, Liz Bills, and Kirsty Wilson); (4) A Developmental Model for Proportional Reasoning in Ratio Comparison Tasks (Silvia Alatorre and Olimpia Figueras); (5) Referential and Syntactic Approaches to Proof: Case Studies from a Transition Course (Lara Alcock and Keith Weber); (6) Teachers' Beliefs about Students' Development of the Pre-Algebraic Concept of Equation (Vassiliki Alexandrou-Leonidou and George N. Philippou); (7) Developing Students' Understanding of the Concept of Fractions as Numbers (Solange Amorim Amato); (8) Multiple Representations in 8th Grade Algebra Lessons: Are Learners Really Getting It? (Miriam Amit and Michael N. Fried); (9) Reform-Oriented Teaching Practices: A Survey of Primary School Teachers (Judy Anderson and Janette Bobis); (10) The Genesis of Signs by Gestures: The Case of Gustavo (Ferdinando Arzarello, Francesca Ferrara, Ornella Robutti, and Domingo Paola); (11) Students' Experience of Equivalence Relations: A Phenomenological Approach (Amir H. Asghari and David Tall); (12) How Series Problems Integrating Geometric and Arithmetic Schemes Influence Prospective Secondary Teachers' Pedagogical Understanding (Leslie Aspinwall, Kenneth L. Shaw, and Hasan Unal); (13) Dealing with Learning in Practice: Tools for Managing the Complexity of Teaching and Learning (Sikunder Ali Baber and Bettina Dahl); (14) Situations of Psychological Cognitive No-Growth (Roberto R. Baldino and Tania C. B. Cabral); (15) Good CAS Written Records: Insight from Teachers (Lynda Ball and Kaye Stacey); (16) Developing Procedure and Structure Sense of Arithmetic Expressions (Rakhi Banerjee and K. Subramaniam); (17) Struggling with Variables, Parameters, and Indeterminate Objects, or How to Go Insane in Mathematics (Caroline Bardini, Luis Radford, and Cristina Sabena); (18) Exploring How Power is Enacted in Small Groups (Mary Barnes); (19) A Framework for the Comparison of PME Research into Multilingual Mathematics Education in Different Sociolinguistic Settings (Richard Barwell); (20) Vygotsky's Theory of Concept Formation and Mathematics Education (Margot Berger); (21) Preservice Teachers' Understandings of Relational and Instrumental Understanding (Kim Beswick); (22) The Transformation of Mathematics in On-Line Courses (Marcelo C. Borba); (23) Using Cognitive and Situated Perspectives to Understand Teacher Interactions with Learner Errors (Karin Brodie); (24) Identification of Affordances of a Technology-Rich Teaching and Learning Environment (TRTLE) (Jill P. Brown); (25) The "A4-Project": Statistical World Views Expressed through Pictures (Michael Bulmer and Katrin Rolka); (26) A Whole-School Approach to Developing Mental Computation Strategies (Rosemary Callingham); (27) A Comparison of Perceived Parental Influence on Mathematics Learning among Students in China and Australia (Zhongjun Cao, Helen Forgasz, and Alan Bishop); (28) Using Word Problems in Malaysian Mathematics Education: Looking beneath the Surface (Kah Yein Chan and Judith Mousley); (29) Constructing Pedagogical Knowledge of Problem Solving: Preservice Mathematics Teachers (Olive Chapman); (30) Revisiting a Theoretical Model on Fractions: Implications for Teaching and Research (Charalambos Y. Charalambous and Demetra Pitta-Pantazi); (31) Students' Reflection on Their Sociomathematical Small-Group Interaction: A Case Study (Petros Chaviaris and Sonia Kafoussi); (32) Investigating Teachers' Responses to Student Misconceptions (Helen L. Chick and Monica K. Baker); (33) Studying the Distribution of Responsibility for the Generation of Knowledge in Mathematics Classrooms in Hong Kong, Melbourne, San Diego and Shanghai (David Clarke and Lay Hoon Seah); (34) Indigenous and Non-Indigenous Teaching Relationships in Three Mathematics Classrooms in Remote Queensland (Tom J. Cooper, Annette R. Baturo, and Elizabeth Warren); (35) Exploring the Strategies Used by Grade 1 to 3 Children through Visual Prompts, Symbols and Worded Problems: A Case for a Learning Pathway for Number (Ty Corvell Cranfield, Cally Kuhne, and Gary Powell); (36) Primary Students' Knowledge of the Properties of Spatially-Oriented Diagrams (Carmel Diezmann); (37) A Conceptual Framework for Studying Teacher Preparation: The Pirie-Kieren Model, Collective Understanding, and Metaphor (Maria A. Droujkova, Sarah B. Berenson, Kelli Slaten, and Sue Tombes); (38) Mathematical Modelling with 9-Year-Olds (Lyn English and James Watters); (39) Exploring "Lesson Study" in Teacher Preparation (Maria L. Fernandez); (40) Child-Initiated Mathematical Patterning in the Pre-Compulsory Years (Jillian Fox); (41) The Tacit-Explicit Nature of Students' Knowledge: A Case Study on Area Measurement (Cristina Frade); (42) Teachers as Interns in Informal Mathematics Research (John M. Francisco and Carolyn A. Maher); and (43) Exploring Excellence and Equity within Canadian Mathematics Classrooms (George Frempong). (Individual papers contain references.)

Mathematical reasoning features in curriculum documents around the world, but is understood and enacted poorly by teachers in classrooms. We explore teachers' noticing of reasoning during observed lessons. Two teams of primary teachers in Canada and Australia worked to plan, deliver, and observe lessons intended to include reasoning. They observed each other teaching a lesson that was planned with the assistance of a researcher, and later, a researcher observed each post-lesson discussion. Given the reported benefits of teachers' noticing of reasoning during peer-observed lessons, targeted professional learning support is required to further enact teachers' peer discourse to facilitate mathematical reasoning.

This paper reports from a broad investigation of mathematics knowledge as dependent on interconnected concepts. The paper focuses specifically on illustrating how network analysis may be used in examining spatiotemporal relationships between learned mathematics concepts, or curriculum outcomes, and concepts inherent in assessment items. Connections both within and between year levels are shown, based on primary years' multiple-choice assessment items related to measurement. Network analysis provides a potentially powerful tool that may offer educators greater specificity in approaches to the design of revision and intervention through a view of complex rather than linear conceptual connectivity in mathematics learning. [For the complete proceedings, see ED597799.]

As a contribution to honour the foresight of Ken Clements and John Foyster in founding MERGA [Mathematics Education Research Group of Australasia] 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.

This paper reports on a project that aims to foster interdisciplinary collaboration between mathematicians and mathematics educators in pre-service teacher education. The project involves 23 investigators from six universities. Interviews were conducted with selected project participants to identify conditions that enable or hinder collaboration, and to identify learning mechanisms at the boundaries between disciplinary communities. A hybrid narrative constructed from the interviews is used to illustrate "transformation" as a learning mechanism that leads to new practices. [This project is funded by the Australian Government Office for Learning and Teaching (grant #MS13-3174).]

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.

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.

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. [The research reported in this paper was part of a larger project supported by an Australian Research Council Linkage grant.]

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. An appendix presents the assessment task used at the beginning of the lesson sequence.

Why have an organisation like MERGA? This question will be addressed from past, present and future perspectives (1976, 2012, and 2025). One focus of the paper will be the need to improve mathematics curricula, and to improve the teaching and learning of mathematics, at all levels. I shall argue that we have not done enough to make sure that MERGA has delivered, is still delivering, and will continue to deliver the goods on such basic curriculum/teaching/learning issues. Part of the difficulty is that we researchers have not reached agreement on what we mean by "improvement". That is as much a political issue as anything else, of course, but the MERGA community needs to do more to make sure that the responsibility for defining what improvement means, and how it is assessed, is not in the wrong hands. A second focus of the paper will be some reflections on what the "A" in MERGA might represent. This Conference is being held in Singapore, and the challenge is for a wider vision of MERGA's role in Asia to be formulated and implemented.

In this study we examine the use of cumulative and exploratory talk types in a year 5 computer supported collaborative learning environment. The focus for students in this environment was to participate in mathematical problem solving, with the intention of developing the proficiencies of problem solving and reasoning. Findings suggest that students engaged in exploratory talk may more regularly attempt the use of technical (tier 3) mathematical vocabulary.

Mathematics anxiety affects primary pre-service teachers' engagement with and future teaching of mathematics. The study aimed to assess the level and range of mathematics anxiety in first year pre-service teachers entering their teacher education course, and to investigate the sources of this anxiety as perceived and identified by them. Data collection methods included the RMARS survey, and Critical Incident Technique. The results indicate that the most common negative impacts on pre-service teacher mathematical self-concept involved experiences with teachers. However, their current mathematics anxiety is most commonly aroused under testing or evaluation situations.

The aim of this study was to determine the role of semiotics in assisting young Indigenous students to engage with and identify the general structure of growing patterns. The theoretical perspective of semiotics underpinned the study. Data are drawn from two Year 3 students, including analysis of pretest questions and two conjecture-driven lessons. Results indicate that particular semiotic signs (iconic signs) contribute to how young Indigenous students attend to, and identify the structure of growing patterns.

This paper identifies the strategies Singaporean and Australian students (n = 1,187) employed to solve a 24-item mathematics test. A mathematics-processing framework is proposed, which describes the way primary-aged students successfully process graphic and non-graphic mathematics tasks. There were distinct differences in the way in which the students from the respective countries approached the tasks with the Singaporean students more likely to employ strategies that were explicitly taught and practiced in the classroom, whereas the Australian students tended to employ a more diverse range of approaches.

The use of high-stakes assessment to measure students' mathematical performance has become commonplace in schools all over the world. Such assessment instruments provide national or international comparisons of student (and potentially teacher performance). Each form of assessment is specialised in nature and is characteristic of the culture and intent of the governing bodies. The purpose of this paper is to highlight differences and similarities between two national high-stakes assessments and the possible implications to students' sense making.

Rhetoric about the importance of students being equipped to apply mathematics to relevant problems arising in their lives, individually, as citizens, and in the workplace has never been matched by serious policy or curricular support. This paper identifies and elaborates authenticity implications for addressing this issue, and describes aspects of a modelling challenge in which students were mentored to engage in problem solving located in real world settings. Characteristics of the approach and selected student responses to the challenge are provided.

"Make It Count" was a large scale, government-funded, project aimed at improving the mathematics learning of Indigenous students. NAPLAN Numeracy test results were used as one measure of the effect of the program. In this paper we report on the performance on these tests of Indigenous students in schools involved in the project. Group data and, where available, longitudinal data for individual students are reported.

Students develop understanding of mathematics when they translate between and within different mathematical representations. This paper explores a student-generated story and content descriptors from the Australian Curriculum: Mathematics to highlight how primary school students can represent mathematical concepts through exploring the links between everyday physical objects, pictures, oral/written language, models and mathematical symbols. This active experience enhances the students' capacity to represent mathematical concepts and ideas, symbolise these, and eventually learn to abstract and generalise.

A current concern is student learning outcomes and these are largely a function of teachers' knowledge and their practice. This position paper is premised on the notion that certain knowledge is required for the teaching of mathematics. An exploration of literature demonstrates that such professional knowledge development can be supported by Learning Trajectories (LT). We propose to use LT as theoretical lens to examine pre-service teachers' Content and Pedagogical Content knowledge and advance a research design.

This paper presents the results from an initial lesson in a series of design experiments focusing on young Indigenous students' understandings of growing patterns. Indigenous students in Year 2 and 3 (n = 16) participated in pre lesson activities and a 45 minute lesson on growing patterns. Tentative findings from this study suggest that; (a) Year 2 and 3 Indigenous students are capable of working with growing patterns; (b) contextual artefacts assisted with communication; and (c) gesture played an important two-fold role in the lessons and communication of the mathematics experienced.

Using an innovative recruitment tool, the social network site Facebook, survey data were gathered from samples of the Australian general public and from around the world. Views on the gendering of mathematics, science, and ICT were gathered. In this paper we report the findings from six of the 15 questions on the survey, and only from respondents in predominantly English-speaking countries. The findings reveal that the majority was not gender-stereotyped about mathematics and related careers. However, if a gendered view was held, it was overwhelming to endorse the male stereotype. Male respondents' views were more strongly gendered than were females'. [For the complete proceedings, see ED585874.]

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.

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.

A 3-year longitudinal study "Transforming Children's Mathematical and Scientific Development" integrates, through data modelling, a pedagogical approach focused on mathematical patterns and structural relationships with learning in science. As part of this study, a purposive sample of 21 highly able Grade 1 students was engaged in an innovative data modelling program. In the majority of students, representational development was observed. Their complex graphs depicting categorical and continuous data revealed a high level of structure and enabled identification of structural features critical to this development.

The IADIS CELDA 2012 Conference intention was to address the main issues concerned with evolving learning processes and supporting pedagogies and applications in the digital age. There had been advances in both cognitive psychology and computing that have affected the educational arena. The convergence of these two disciplines is increasing at a fast pace and affecting academia and professional practice in many ways. Paradigms such as just-in-time learning, constructivism, student-centered learning and collaborative approaches have emerged and are being supported by technological advancements such as simulations, virtual reality and multi-agents systems. These developments have created both opportunities and areas of serious concerns. This conference aimed to cover both technological as well as pedagogical issues related to these developments. The IADIS CELDA 2012 Conference received 98 submissions from more than 24 countries. Out of the papers submitted, 29 were accepted as full papers. In addition to the presentation of full papers, short papers and reflection papers, the conference also includes a keynote presentation from internationally distinguished researchers. Individual papers contain figures, tables, and references.

The processes of mathematisation, the use of mathematical models and representations of real world contexts, and contextualisation, the embedding of mathematical ideas into a meaningful context, are key aspects of students' mathematical learning. We present a conceptual framework for thinking about mathematising and contextualising developed as part of the "Make it Count," a national project that seeks to develop an evidence base of practices that improve Indigenous students' learning in mathematics. We suggest that an intentional focus on mathematisation and contextualisation helps to make mathematics meaningful, particularly for Indigenous students. In particular we suggest that such a focus has the potential to enhance the mathematical resilience of Aboriginal students.