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This paper reports on a section of a larger study, investigating the mathematics experiences of Down syndrome (DS) learners in Australian Primary Schools. Developing the numeracy skills to experience independence in post school settings is crucial for individuals with DS. The aim of this paper is to share the school mathematics experiences of six DS adults and their parents/carers to ascertain if their experiences (DS adults) with mathematics when they were at school have had consequences for how they engage and participate in society as adults. Initial findings suggest that DS adults' mathematics experiences have impacted on their quality of life in a post-school setting.

Mathematical self-concept refers to the perceived ability that one has in being able to do mathematics. While it has been shown to be a significant predictor for how students learn and apply mathematics, little research has been conducted into the relationship between the mathematical self-concept of teachers and their pedagogical practices in the mathematics classroom. This paper reports on a section of the findings from a small mixed methods study that sought to ascertain the nature of primary teachers' mathematical self-concept and how it is related to their teaching practices. Findings suggest that a teachers' mathematical self-concept does not necessarily reflect the mathematics practices evident in their classroom.

Student disengagement is influenced by the degree of success that is experienced in the mathematics classroom. In turn, success is often determined by the depth of understanding that students gain during predetermined time frames. This paper reports on the Five Question Approach to teaching mathematics which provides teachers with greater flexibility in content delivery, pacing and consolidation of content. This qualitative case study draws on data collected in three Australian secondary classrooms. Findings indicate that the Five Question Approach led to increased student engagement, academic improvement and a significant decrease in examination anxiety.

Teaching mathematics involves a lot of talking, and dialogic practices are central to most pedagogical practices in mathematics classrooms. Furthermore, for mathematical processes such as 'reasoning', 'explaining' and 'mathematical thinking' to be developed, there is a need for rich and robust dialogic interactions in the classroom. In this paper we investigate the dialogue in a "typical Year 5 mathematics lesson by analysing the transcript using two different analytical frameworks. While the analysis showed that there were many interactions with nearly half being student turns, it was also evident that almost all the exchanges followed an "Initiation-Response-Feedback" pattern, with a high degree of teacher control. Furthermore, there was little evidence that the dialogic pedagogies of the lesson promoted student development in the mathematical processes. Thus, we content that there is a need to understand the dialogue of mathematics pedagogy, and its impact on students' broader mathematical learning.

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.

Many primary schools in Australia are investing substantial funds introducing mobile technologies such as iPads to enhance teaching and learning. However, when new technologies are first introduced, teachers are often expected to integrate them into their practices without the support of appropriate professional development. This paper reports on a recent qualitative multiple case study that explored the pedagogical practices implemented by four primary teachers during the first six months of iPad use. Results of the study highlighted that although the iPads do have the potential to enhance teaching and learning of primary mathematics, appropriate professional development that addresses all aspects of technological and pedagogical content knowledge is required to ensure successful integration of new technologies into current teaching practices.

One of the most significant influences on student engagement is the teacher's pedagogical practices, including the incorporation of technology into the teaching and learning of mathematics. This paper reports on a qualitative study investigating how the incorporation of iPads into a Year 3 primary classroom during a six month trial influenced teaching and learning practices and student engagement with mathematics. All of the students appear to have had a positive experience during the trial and the classroom teacher believed their engagement with mathematics had improved as a result. Although there were challenges involved in integrating the iPads into mathematics lessons, some teaching practices were adapted to accommodate the technology. The integration of the iPads highlighted the need for teacher professional development and the importance of developing strong Technological Pedagogical Content Knowledge.

Engagement is a multifaceted concept that has attracted recent attention by researchers both in Australia and internationally (Attard, 2012; Chan, Baker, Slee, & Williamson, 2015). For many years mathematics education has been seen as boring and dull, and students have disengaged from a relatively early age in learning and participating in mathematics (Grootenboer & Marshman, 2016). Therefore, there seems to be an imperative for research and action into this issue, as low levels of engagement among school students can put them at risk of decreased participation and, ultimately, low levels of academic achievement (Fredrick et al, 2004). It is evident that there are three types of engagement consistent across the literature; emotional, behavioural, and cognitive. However, it appears that there are no existing data collection instruments that specifically focus on capturing student engagement in mathematics. Thus, some tools have been designed that derive specifically from the theoretical framework on engagement with the aim of being theoretically robust, conceptually relevant, and practically manageable.

This document presents the proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia (MERGA). The theme of this conference is "Navigating Currents and Charting Directions." The theme reminds us that, although we are constantly pushed to account for the quality and impact of our research, we need to assert some control over our work by making our own research futures. The conference was sponsored by the University of Queensland, Teaching and Educational Development Institute. Volume 1 includes the following: (1) Stars, Compass, and GPS: Navigating Currents and Charting Directions for Mathematics Education Research on Gender Issues (Helen Forgasz); (2) Praxis and Practice Architectures in Mathematics Education (Stephen Kemmis); (3) Facilitating Communities of Mathematical Inquiry (Roberta Hunter); (4) Assessing Primary Preservice Teachers' Mathematical Competence (Karoline Afamasaga-Fuata'i, Paul Meyer, and Naomi Falo); (5) Teachers' Motivation to Attend Voluntary Professional Development in K-10 Mathematics (Judy Anderson); (6) Using National Numeracy Testing to Benefit Indigenous Students: Case Studies of Teachers Taking Back Control of Outcomes (Annette R. Baturo, Tom J. Cooper, Matthew T. Michaelson, and Jessica Stevenson); (7) Recollections of Mathematics Education: Approaching Graduation and 5 Years Later (Kim Beswick and Shelley Dole); (8) Using Paper-Folding in the Primary Years to Promote Student Engagement in Mathematical Learning (Kathy Brady); (9) The Case of Mathematical Proof in Lower Secondary School: Knowledge and Competencies of Pre-service Teachers (Jill Brown, Gloria Stillman, Bjorn Schwarz, and Gabriele Kaiser); (10) Employing Mathematical Modelling to Respond to Indigenous Students' Needs for Contextualised Mathematics Experiences (Kelli Brown); (11) Reconceptualising Agency through Teachers Talking About a Sociocultural Approach to Teaching Mathematics in the Classroom (Raymond Brown and Trevor Redmond); (12) Middle School Students' Interest in Statistical Literacy (Colin Carmichael and Ian Hay); (13) One Secondary Teacher's Use of Problem-Solving Teaching Approaches (Michael Cavanagh); (13) Does Student Success Motivate Teachers to Sustain Reform-Oriented Pedagogy? (Linda Cheeseman); (15) Year Five Students Solving Mental and Written Problems: What Are They Thinking? (Julie Clark); (14) Mathematics for Engineering Education: What Students Say (Mary Coupland, Anne Gardner, and Georgina Carmody); (15) Advancing Research Into Affective Factors in Mathematics Learning: Clarifying Key Factors, Terminology and Measurement (Patricia C. Cretchley); (16) Explorations of Early Childhood: New Entrant Transition in Mathematics (Ngaire M. Davies and Karen Walker); (17) Eliciting Growth in Teachers' Proportional Reasoning: Measuring the Impact of a Professional Development Program (Shelley Dole, Doug Clark, Tony Wright, Geoff Hilton, and Anne Roche); (18) Links between Children's Understanding of Multiplication and Solution Strategies For Division (Ann Downton); (19) Intervention Instruction in Structuring Numbers 1 to 20: The Case of Nate (David Ellemor-Collins and Robert Wright); (20) Interdisciplinary Problem Solving: A Focus on Engineering Experiences (Lyn D. English); (21) Addressing Verbal Memory Weaknesses to Assist Students with Mathematical Learning Difficulties (Maureen Finnane); (22) Validation of an Assessment Instrument Developed for Eliciting Student Prior Learning in Graphing and Data Analysis (Noleine Fitzallen); (24) Using Valsiner (Linda Galligan); (25) CAS Enabled Devices as Provocative Agents in the Process of Mathematical Modelling (Vince Geiger, Rhonda Faragher, Trevor Redmond, and Jim Lowe); (26) Researcher-Teacher Relationships in Mathematics Education (Merrilyn Goos); (27) Towards a Sociocultural Framework for Understanding the Work of Mathematics Teacher-Educator-Researchers (Merrilyn Goos); (28) Identity as a Lens to Understand Learning Mathematics: Developing a Model (Peter Grootenboer and Robyn Zevenbergen); (29) Capturing Students' Thinking about Strategies used to Solve Mental Computations by Giving Students Access to a Pedagogical Framework (Judy Hartnett); (30) A Review of Recent Research in Early Mathematics Learning and Technology (Kate Highfield and Kristy Goodwin); (31) The Development of Students' Use of Justification Strategies (Jodie Hunter and Glenda Anthony); (32) Using Task-Based Interviews to Assess Mathematical Thinking of Primary School Students (Chris Hurst); (33) Who a Student Sits Near to in Maths: Tension between Social and Mathematical Identities (Naomi Ingram); (34) Social Constructivism in the Classroom: From a Community of Learners to a Community of Teachers (Jane Irvin); (35) Primary Teachers' Beliefs about the Use of Mathematics Textbooks (Romina Jamieson-Proctor and Carmen Byrne); (36) Abstraction in Context, Combining Constructions, Justification and Enlightenment (Ivy Kidron and Tommy Dreyfus); (37) How Humanism Can Foster Mediocrity in Early Years Mathematics Education: A Poststructuralist Comparison (Mary Klein); (38) Preservice Teachers and Numeracy Education: Can Poststructuralism Contribute? (Mary Klein); and (39) High Achievers in Mathematics: What Can We Learn from and about Them? (Gilah Leder). Volume 2 contains: (1) The 2007 Common Technology Free Examination for Victorian Certificate of Education (VCE) Mathematical Methods and Mathematical Methods Computer Algebra System (CAS) (David Leigh-Lancaster, Pam Norton, Peter Jones, Magdalena Les, Michael Evans, and Margaret Wu); (2) Focusing Year 8 Students on Self-Regulating their Learning of Mathematics (Andrea McDonough and Peter Sullivan); (3) Feedback about Professional Growth for Teachers of Mathematics: A Developmental Perspective (Greg McPhan, John Pegg, and Stefan Horarik); (4) Fraction Number Line Tasks and the Additivity Concept of Length Measurement (Annie Mitchell and Marj Horne); (5) "Zero Is Not a Number": Teachable Moments and Their Role in Effective Teaching of Numeracy (Tracey Muir); (6) Students' Attitude Towards Using Materials to Learn Algebra: A Year 7 Case Study (Stephen Norton and Will Windsor); (7) Teaching Mathematics and Technology through Design Practice (Stephen Norton and Tom J. Cooper); (8) Engaging Mathematics Teachers in Professional Learning by Reflecting on Their Pedagogical Practice (Richard O'Donovan); (9) Primary Teachers' Perceptions of Their Knowledge and Understanding of Measurement (Michelle O'Keefe and Janette Bobis); (10) Use of the Internet for Teacher Professional Development and for Teaching Mathematics: Supports and Inhibitors (Sitti Maesuri Patahuddin); (11) A Situated Perspective on Learning to Teach Secondary Mathematics (Anne Prescott and Michael Cavanagh); (12) The Hospital Problem Revisited. Tertiary Students' Perceptions of a Problem Involving the Binomial Distribution (Robyn Reaburn); (13) The Identification of Partially Correct Constructs (Gila Ron, Rina Hershkowitz, and Tommy Dreyfus); (14) Making Connections: Promoting Connectedness in Early Mathematics Education (Abigail Sawyer); (15) Engagement versus Deep Mathematical Understanding: An Early Career Teacher's Use of ICT in a Lesson (Anne Scott, Ann Downton, Donna Gronn, and Adam Staples); (16) Investigating a Phase Approach to Using Technology as a Teaching Tool (Penelope Serow); (17) The Introduction of Interactive Whiteboard Technology in the Primary Mathematics Classroom: Three Case Studies (Penelope Serow and Rosemary Callingham); (18) School Readiness: What Do Teachers Expect of Children in Mathematics on School Entry? (Brenda Sherley, Megan Clark, and Joanna Higgins); (19) Gaining Insight into Alice's Pedagogy with Respect to Five Dimensions of Numeracy (Jane Skalicky); (20) Modes of Reasoning in Explanations in Year 8 Textbooks (Kaye Stacey and Jill Vincent); (21) What Does Three-Quarters Look Like? Students' Representations of Three-Quarters (Vicki Steinle and Beth Price); (22) Some Key Junctures in Relational Thinking (Max Stephens); (23) Chinese Young Children's Strategies on Basic Addition Facts (Huayu Sun); (24) Self-Efficacy in Mathematics: Affective, Cognitive, and Conative Domains of Functioning (S. L. Tait-McCutcheon); (25) Neuropsychological Evidence for the Role of Graphical and Algebraic Representations in Understanding Function (Michael O. J. Thomas, Anna J. Wilson, Michael C. Corballis, and Vanessa K. Lim); (26) Speaking with Different Voices: Knowledge Legitimation Codes of Mathematicians and Mathematics Educators (Steve Thornton); (27) Recognising Different Starting Points in Aboriginal Students' Learning of Number (Kaye Treacy and Sandra Frid); (28) Deepening the Mathematical Knowledge of Secondary Mathematics Teachers Who Lack Tertiary Mathematics Qualifications (Colleen Vale and Alasdair McAndrew); (29) Indigenous Students' Early Engagement with Numeracy: The Case of Widgy and Caddy (Elizabeth Warren, Janelle Young, and Eva De Vries); (30) Building Informal Inference in Grade 7 (Jane Watson and Julie Donne); (31) Proportional Reasoning: Student Knowledge and Teachers' Pedagogical Content Knowledge (Jane Watson, Rosemary Callingham, and Julie Donne); (32) Counting on 2007: A Program for Middle Years Students Who Have Experienced Difficulty with Mathematics (Allan White); (33) How Group Composition Can Influence Opportunities for Spontaneous Learning (Gaye Williams); (34) Success and Consistency in the Use of Heuristics to Solve Mathematics Problems (Khoon Yoong Wong); (35) Fractions as a Measure (Monica Wong and David Evans); (36) Mixing Colours: An ICT Tool Based on a Semiotic Framework for Mathematical Meaning-Making about Ratio and Fractions (Andy Yeh and Rod Nason); (37) Secondary School Students Investigating Mathematics (Joseph Yeo); (38) Teaching Area and Perimeter: Mathematics-Pedagogical-Content Knowledge-in-Action (Kai Kow and Joseph Yeo); (39) Problem Solving Activities in a Constructivist Framework: Exploring How Students Approach Difficult Problems (Oleksiy Yevdokimov and Tim Passmore); (40) Creating Equitable Practice in Diverse Classrooms: Developing a Tool to Evaluate Pedagogy (Robyn Zevenbergen, Richard Niesche, Peter Grootenboer, and Jo Boaler); (41) The Role of Information Graphics in Mathematical Proficiency (Carmel Diezmann and Tom Lowrie); (42) A Longitudinal Study of Student Performance on Items Rich in Graphics (Tom Lowrie); (43) Standardised Assessment in Mathematics: The Tale of Two Items (Tracy Logan and Jane Greenless); (44) Graphics and the National Numeracy Tests (Carmel Diezmann); (45) The Construction of Knowledge: Theoretical Approaches (Tommy Dreyfus, Michael O. J. Thomas, Jill P. Brown, and Gaye Williams); (46) Motivation and Engagement in School Mathematics During the Middle Years (Catherine Attard); (47) Moving beyond the Script: Addressing Numeracy Needs of Low Achieving Students through Quality Professional Development (Moira Blair and Anuja Singh); (48) MERGA: Including the X and Y in Mathematics Education Research (Peter Grootenboer and Naomi Ingram); (49) Issues in Bridging between Senior Secondary and First Year University Mathematics (Michael Jennings); (50) Student Achievement in Mathematics: Learning through Home School Partnership (Honor Ronowicz and Gaynor Terrill); (51) The Role of Mathematics Competitions (Brenda Bicknell); (52) Scaffolding Students' Understanding of Geometric Properties Using Dynamic Geometry Software (Sahar Bokosmaty); (53) The Next Big Teaching Resource: Interactive White Boards But Where is the Research? (Philip C. Clarkson); (54) Errors Made by Student Teachers When Writing Test Items (Jaguthsing Dindyal); (55) Insights from Pre-Service Secondary Mathematics Teachers on their Practicum Experience (Jaguthsing Dindyal); (56) Improving Language for Problem Solving (Benedicte Esterman); (57) Reflections on Exponential Functions (Sandra Herbert and Farhang Afshar); (58) Coaching and Mentoring Numeracy Lead Teachers to Improve Student Learning: The Journey of Two Year Seven and Eight Teachers (Judith Mills); (59) Connecting the Points: Students Learning Decimal Place Value (Bruce Moody and Jenny Young-Loveridge); (60) The Role of Pattern and Structure in Early Mathematics Learning: An Evaluation Study in the First Year of Formal Schooling (Joanne Mulligan, Lyn English, and Mike Mitchelmore); (61) Motivation and Engagement in Mathematics: The Transition from Primary to Secondary School (Karen Skilling); (62) Achieving Computational Fluency in Multi-Digit Multiplication and Division (Kristen Tripet); and (63) Financial Modelling with Matlab (Peter Watson and Jiling Cao). (Individual papers contain references.) [Cover title varies.]