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Conference Proceedings 2015

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Mathematics education in the margins
MERGA 38 Table of contents
MERGA38 preface
List of Reviewers
MERGA38 list of Reviewers
Keynote Address
Exploring a Structure for Mathematics Lessons that Foster Problem Solving and Reasoning 39 downloads
Peter Sullivan, Nadia Walker, Chris Borcek, & Mick Rennie
Mathematics Education as a Field of Research: Have We Become Too Comfortable? 26 downloads
Tom Lowrie
Researching and Doing Professional Development Using a Shared Discursive Resource and an Analytic Tool 22 downloads
Jill Adler
Practical Implication Award
Teacher Actions to Facilitate Early Algebraic Reasoning 30 downloads
Jodie Hunter
Research Paper
The challenge of supporting a beginning teacher to plan in primary mathematics 28 downloads
Judy Bailey
Contemplating symbolic literacy of first year mathematics students 27 downloads
Caroline Bardini, Robyn Pierce, & Jill Vincent
Problematising Mathematics Education 27 downloads
Andy Begg
Identity as an Embedder-of-Numeracy: Identifying ways to support teachers to embed numeracy across the curriculum 25 downloads
Anne Bennison
Young Children’s Number Line Placements and Place-Value Understanding 31 downloads
Brenda Bicknell, & Jenny Young-Loveridge
The Role of Cultural Capital in Creating Equity for Pāsifika Learners in Mathematics 24 downloads
Trevor Bills, & Roberta Hunter
The importance of praxis in financial literacy education: An Indigenous perspective 25 downloads
Levon Blue, Peter Grootenboer, & Mark Brimble
Coming to do Mathematics in the Margins 24 downloads
Raymond Brown, & Trevor Redmond
“You play on them. They’re active.” Enhancing the mathematics learning of reluctant teenage students. 27 downloads
Nigel Calder, & Anthony Campbell
CAS or Pen-and-paper: Factors that Influence Students’ Choices 23 downloads
Scott Cameron, & Lynda Ball
The Language Used to Articulate Content as an Aspect of Pedagogical Content Knowledge 26 downloads
Helen Chick
Specialised Content Knowledge: Evidence of Pre-service teachers’ Appraisal of Student Errors in Proportional Reasoning 25 downloads
Mohan Chinnappan, & Bruce White
Learning from Lessons: Studying the Construction of Teacher Knowledge Catalysed by Purposefully-designed Experimental Mathematics Lessons 27 downloads
Doug Clarke, David Clarke, Anne Roche, & Man Ching Esther Chan
Inclusive Practices in the Teaching of Mathematics: Supporting the Work of effective primary teachers 28 downloads
Barbara Clarke, & Rhonda Faragher
Supporting Students to Reason About the Relative Size of Proper and Improper Fractions 23 downloads
Jose Luis Cortina, & Jana Visnovska
Proportional Reasoning as Essential Numeracy 29 downloads
Shelley Dole, Annette Hilton, & Geoff Hilton
A Case Study of the Pedagogical Tensions in Teacher’s Questioning Practices When Implementing Reform-Based Mathematics Curriculum in China 27 downloads
Lianchun Dong, Wee Tiong Seah, & David Clarke
Improving the Effectiveness of Mathematics Teaching through Active Reflection 28 downloads
Kerryn Driscoll
Promoting Teacher Growth through Lesson Study: A Culturally Embedded Approach 24 downloads
Marlon Ebaeguin
The Self-Efficacy of students with Borderline, Mild and Moderate Intellectual Disabilities and their Achievements in Mathematics 26 downloads
Agbon Enoma, & John Malone
Identifying Core Elements of Argument-Based Inquiry in Primary Mathematics Learning 27 downloads
Jill Fielding-Wells
STEM Education: What Does Mathematics Have To Offer? 28 downloads
Noleine Fitzallen
The Challenge for Non-first-language-English Academic Publishing in English Language Research Outlets 26 downloads
Vince Geiger, & Rudolf Straesser
The Impact of Let’s Count on Children’s Mathematics Learning 25 downloads
Ann Gervasoni, & Bob Perry, & Linda Parish
Comparing the Development of Australian and German 7-Year-Old and 8-Year-Old’s Counting and Whole Number Learning 25 downloads
Ann Gervasoni, & Andrea Peter-Koop
Learning at the Boundaries 23 downloads
Merrilyn Goos
The Practice of ‘Middle Leading’ in Mathematics Education 32 downloads
Peter Grootenboer, Christine Edwards-Groves, & Karin Rönnerman
Teaching Computation in Primary School without Traditional Written Algorithms 23 downloads
Judy Hartnett
Calculating fo r probability: “He koretake te rima” (Five is useless) 24 downloads
Ngārewa Hāwera, & Merilyn Taylor
Students’ Relationships with Mathematics: Affect and Identity 26 downloads
Naomi Ingram
Using Alternative Multiplication Algorithms to ‘Offload’ Cognition 30 downloads
Dan Jazby, & Cath Pearn
Successful Mathematics Lessons in Remote Communities: A Case Study of Balargo 23 downloads
Robyn Jorgensen
Differentiated Success: Combining Theories to Explain Learning 26 downloads
Robyn Jorgensen, & Kevin Larkin
The Mathematics Instructional Leader: What a Difference Crucial Conversations Make 24 downloads
Janeen Lamb, Carmel Diezmann, & Jillian Fox
The Search for Fidelity in Geometry Apps: An Exercise in Futility? 26 downloads
Kevin Larkin
Pre-service teachers and numeracy in and beyond the classroom 25 downloads
Gilah C Leder, Helen J Forgasz, Natalie Kalkhoven, & Vince Geiger
Gender Differences in Mathematics Attitudes in Coeducational and Single Sex Secondary Education 28 downloads
Kester Lee, & Judy Anderson
Developing a Theoretical Framework to Assess Taiwanese Primary Students’ Geometric Argumentation 29 downloads
Tsu-Nan Lee
Starting a Conversation about Open Data in Mathematics Education Research 29 downloads
Tracy Logan
A snapshot of young children’s mathematical competencies: Results from the Longitudinal Study of Australian Children 24 downloads
Amy MacDonald, & Colin Carmichael
Examining PCK in a Senior Secondary Mathematics Lesson 30 downloads
Nicole Maher, Tracey Muir, & Helen Chick
Teacher’s Scaffolding over the Year to Develop Norms of Mathematical Inquiry in a Primary Classroom 31 downloads
Katie Makar, Arthur Bakker, & Dani Ben-Zvi
Middle Years Students Influencing Local Policy 28 downloads
Margaret Marshman
Early Years Teachers’ Perspectives on Teaching through Multiple Metaphors and Multimodality 24 downloads
Paula Mildenhall
Young Indigenous Students’ Engagement with Growing Pattern Tasks: A Semiotic Perspective 26 downloads
Jodie Miller
Professional Knowledge Required when Teaching Mathematics for Numeracy in the Multiplicative Domain 25 downloads
Judith Mills
Determining a Student’s Optimal Learning Zone in Light of the Swiss Cheese Model 23 downloads
Patricia Morley, & Simone Zmood
Student and Parent Perspectives on Fipping the Mathematics Classroom 26 downloads
Tracey Muir
Authority and Agency in Young Children’s Early Number Work: A Functional Linguistic Perspective 26 downloads
Carol Murphy
Examples in the Teaching of Mathematics: Teachers’ Perceptions 28 downloads
Lay Keow Ng, & Jaguthsing Dindyal
How Inquiry Pedagogy Enables Teachers to Facilitate Growth Mindsets in Mathematics Classrooms 26 downloads
Mia O’Brien, Katie Makar, Jill Fielding-Wells, & Jude Hillman
Challenging the Mindset of Sammy: A Case Study of a Grade 3 Mathematically Highly Capable Student 23 downloads
Linda Parish
Facebook as a Learning Space: An Analysis from a Community of Practice Perspective 23 downloads
Sitti Maesuri Patahuddin, & Tracy Logan
Strategies for Solving Fraction Tasks and Their Link to Algebraic Thinking 35 downloads
Catherine Pearn, & Max Stephens
Mentoring to Alleviate Anxiety in Pre-Service primary mathematics Teachers: an orientation towards improvement rather than evaluation. 26 downloads
Timothy Perkins
Spatial Visualisation and Cognitive Style: How Do Gender Differences Play Out? 24 downloads
Ajay Ramful, & Tom Lowrie
The Practice of Teacher Aides in Tasmanian Primary Mathematics Classrooms 25 downloads
Robyn Reaburn
Qualitative Facets of Prospective Elementary Teachers’ Diagnostic Proceeding: Collecting and Interpreting in One-on-one Interviews 26 downloads
Simone Reinhold
Describing the nature and effect of teacher interactions with students during seat work on challenging tasks 27 downloads
Anne Roche, & Doug Clarke
Teachers’ talk about Robotics: Where is the Mathematics? 31 downloads
Annie Savard, & Kate Highfield
Teaching Statistics in Middle School Mathematics classrooms: Making Links with Mathematics but Avoiding Statistical Reasoning 28 downloads
Annie Savard, & Dominic Manuel
Context counts: The potential of realistic problems to expose and extend social and mathematical understandings 33 downloads
Carly Sawatzki
Theorising about Mathematics Teachers’ Professional Knowledge: The Content, Form, Nature, and Course of Teachers’ Knowledge 25 downloads
Thorsten Scheiner
Understanding Geometric Ideas: Pre-service Primary Teachers’ Knowledge as a Basis for Teaching 31 downloads
Rebecca Seah
Mathematical Language Development and Talk Types in Computer Supported Collaborative Learning Environments 23 downloads
Duncan Symons, & Robyn Pierce
The Individual Basic Facts Assessment Tool 22 downloads
Sandi Tait-McCutcheon, & Michael Drake
Affording and Constraining Local Moral Orders in Teacher-Led Ability-Based Mathematics Groups 26 downloads
Sandi Tait-McCutcheon, Joanna Higgins, Mary Jane Shuker, & Judith Loveridge
Exploring relationship between scientific reasoning skills and mathematics problem solving 27 downloads
Nor’ain Mohd Tajudin, & Mohan Chinnappan
Developing Adaptive Expertise with Pasifika Learners in an Inquiry Classroom 27 downloads
Zain Thompson, & Jodie Hunter
Getting out of Bed: Students’ Beliefs 27 downloads
Jane Watson, & Rosemary Callingham
Improving Student Motivation and Engagement in Mathematics Through One-to-one Interactions 31 downloads
Jennifer Way, Amelia Reece, Janette Bobis, Judy Anderson, & Andrew Martin
A Cross-cultural Comparison of Parental Expectations for the Mathematics Achievement of their Secondary School Students 29 downloads
Daya Weerasinghe, & Debra Panizzon
“I was in year 5 and I failed maths”: Identifying the Range and Causes of Maths Anxiety in first year Pre-service Teachers. 28 downloads
Sue Wilson
Enhancing Mathematics (STEM) Teacher Education in Regional Australia: Pedagogical Interactions and Affect 26 downloads
Geoff Woolcott, & Tony Yeigh
Mathematics, Programming, and STEM 31 downloads
Andy Yeh, & Vinesh Chandra
Laying the Foundation for Proportional Reasoning 31 downloads
Ann Downton
The Development and Evaluation of an Individualised Learning Tool for Mathematics students with Intellectual Disability: IMPELS 24 downloads
Agbon Enoma, & John Malone
Capturing Mathematical Learning in an Inquiry Context: There are Some Things Not Easily Measured 22 downloads
Kym Fry
Teacher Professional Growth through using a Critical Mass Mentoring System: Effective Whole School Teacher Professional Development 26 downloads
Judy Hartnett, & Jim Midgley
Anatomy of a Mathscast 27 downloads
Carola Hobohm, & Linda Galligan
An Exploration of Strategies That Teachers Use When Teaching Beginning Algebra 27 downloads
Christina Lee, & Christine Ormond
Factors Influencing Social Process of Statistics Learning within an IT Environment 24 downloads
Ken W. Li, & Merrilyn Goos
Identifying categories of Pre-service Teachers’ Mathematical Content Knowledge 24 downloads
Sharyn Livy
Using Drawings and Discussion to Prompt Young Learners to Reflect Upon and Describe Their Mathematical Understandings 29 downloads
Andrea McDonough, & Jill Cheeseman
Language and Mathematics: Exploring a New Model to Teach in Bi/Multilingual Mathematics Classroom 24 downloads
Charly Muke
Exploring the Influence of Early Numeracy Understanding Prior to School on Mathematics Achievement at the End of Grade 2 21 downloads
Andrea Peter-Koop, & Sebastian Kollhoff
An Irish Response to an International Concern:Challenges to Mathematics Teaching 23 downloads
Lisa O’Keeffe, Olivia Fitzmaurice, & Patrick Johnson
An Analysis of Modelling Process based on McLuhan’s Media Theory: Focus on Constructions by Media in Cases of Using Geoboard 23 downloads
Hiro Ozasa
The Knowledge Dimension of Revised Bloom’s Taxonomy for Integration 23 downloads
Farzad Radmehr, Robin Averill, & Michael Drake
Developing an analysing tool for dynamic mathematics-related student interaction regarding affect, cognition and participation 29 downloads
Laura Tuohilampi
Thinking Strategies Used by 7th-Grade Students in Solving Number Sense Problems 27 downloads
Palanisamy Veloo, & Parmjit Singh
Short Communication (abstract only)
A Focus Question Approach to the Teaching of Mathematics
John Ley

This is a presentation on a focus question approach to teaching mathematics (FFQA) which is the title of my thesis. It is proposed to investigate the impact of the FFQA at the commencement of each mathematics lesson on the learning and motivation of students. The style of five questions that I propose to investigate has the first four questions as instrumental style questions that focus on procedural knowledge, with the final question using a relational understanding approach with some of the questions being open ended investigational style questions focusing on conceptual knowledge. The research is ongoing.

A Problem Solving Lesson: Pre-service Teachers Initiation to Lesson Study
Jaguthsing Dindyal

Three pre-service teachers (PST) who had no prior experience with lesson study had to use a lesson study approach to plan and teach a problem solving lesson. This paper documents how the three PSTs were initiated into the Japanese style of lesson study and then how as a team they went about planning their research lesson on problem solving for a primary three class and then teaching it. The focus is on some of the issues that surfaced when preparing this problem solving lesson on magic squares and how they addressed them.

Breaking down Barriers
Peter Howley

Engaging cohorts including less quantitatively-adept students and educating them about the value of Statistics has its challenges. This talk will outline two successes: the first resulted in a first-year Statistics for Business course increasing student satisfaction scores from under 3.5 out of 5 to 4.72 whilst maintaining ‘challenge’ scores and reducing Failure rates previously exceeding 25% to 7-12%; the second is a national project-based learning activity (piloted in the Hunter Region in 2014) which facilitates boundary encounters (between secondary, tertiary, and industry sectors and students having varied backgrounds and areas of interest) and develops key communication, research and quantitative skills.

Building upon the Language Model of Mathematics
Harry Kanasa, & Kevin Larkin

The language model of mathematics is a useful framework to conceptualise the teaching and learning of mathematics from a constructivist perspective. The model currently proposes that students move along two dimensions (visual and verbal) towards increasing levels of mathematical abstraction. We present the case for theorising the existence of a third dimension, the gestural, by drawing upon established theories of learning within mathematics and also from brain based learning. Examples will be provided on how the addition of the gestural dimension can enhance mathematics education at all levels.

Conceptual Connectivity in Mathematics
Joanne Mulligan, & Geoff Woolcott

Human environmental interactions involve general conceptual connectivity processes such as categorisation, abstraction and generalisation. These are linked to the development of mathematics concepts, but research in this area is relatively new in mathematics education. A conceptual connectivity lens, however, has been used in cases where there are difficulties in mathematics learning, such as developmental dyscalculia, as well as in studies of mathematical pattern and structure with young gifted children. This presentation suggests that such studies support the determination that individual differences in processing of environmental information are an important way forward in understanding what underpins mathematics conceptual development.

Examining a Students’ Resource for Reconstructing the Limit Concept at Need: A Structural Abstraction Perspective
Thorsten Scheiner, & Márcia M. F. Pinto

This presentation examines a student’s learning of the limit concept of a sequence compatible with his strategy of making sense, through which the structural abstraction framework evolves and is further refined. The attention is focused on a student’s generic representation of the limit concept that allows him to generate meaningful components specific to particular contexts. Further, a sketch of the basic ideas of structural abstraction is given, and the use of the generic representation as a resource to reconstruct the meaning of the concept at need is discussed. Additionally, the importance of structural abstraction for learning mathematics is elaborated.

Exploring Students’ Views on using iPads in Mathematics
Janelle Hill

The use of iPads in education is increasing, with increasing numbers of studies focussing on teacher use of this tool in mathematics teaching and learning. As a stakeholder group, the views of students must also be investigated. As part of a larger case study, the views of Year 5 to Year 12 students from one Victorian school were sought about the use of iPads in mathematics. A number of concerns related to the perceived negative impact of iPad use in mathematics learning arose and will be further explored in the presentation.

Mapping school students’ aspirations for STEM careers
Kathryn Holmes, Adam Lloyd, Jenny Gore, & Max Smith

Declining enrolments in STEM disciplines and a lack of interest in STEM careers is concerning at a time when society is becoming more reliant on complex technologies. We examine student aspirations for STEM careers by drawing on survey data from 8235 school students in Years 3 to 11 who were asked to indicate their occupational choices and give reasons for those choices. These data are also examined in relation to student SES, gender, prior achievement and educational aspirations. The analysis provides a strong empirical basis for understanding current student interest in STEM and exploring implications for educational policy and practice.

Mathematical Thinking in a Context of ‘General Thinking’: Implications for Mathematics Education
Corinne Miller, Geoff Woolcott, & Christos Markopoulos

This new project explores the similarities and differences of mathematical thinking and ‘general thinking’, as well as related motivational and emotional aspects, focusing on how these differ in educational contexts. It will examine assumptions of the underlying feature of mathematics curriculum design and pedagogy, for example, that linear structure is the most efficient means of building mathematical knowledge or that number-based knowledge is a reliable indicator of mathematical skill. Insights gained will be used to improve the current paradigms in course structure and pedagogy for classroom mathematics in order to develop a structure better aligned to student capabilities and potentials.

Paternal influence on school students’ aspirations for STEM careers
Adam Lloyd, Jenny Gore, & Max Smith

There is a growing awareness of the important and differential influence fathers have on child lifestyle behaviours compared to mothers. This ‘paternal’ influence could potentially carry across to children’s early career aspirations. A sample of n = 8235 school students in Years 3 to 11 were asked to indicate their occupational choices, give reasons for those choices and also provide information about their parents education and occupation. Using regression analysis, associations between paternal and maternal education levels and occupations with children’s STEM career aspirations were modelled. The findings provide further evidence of the potential differential influence parents have on their child’s aspirations.

Pre-service Teachers’ Views on Mathematics Homework Practices
Sven Trenholm, & Mohan Chinnappan

Literature suggests that homework plays an important role in mathematics learning yet, in the Australian context, there is limited related research on this issue. This exploratory study sets out to better understand pre-service teachers’ intentions and practices concerning mathematics homework. Using a survey design, we analysed data collected from a questionnaire administered to 98 (71% response rate) pre-service teachers (PSTs), all in the third year of their BEd program and completing a third course in mathematical methods as well as professional experience. Contrary to our expectation, the difference in perceptions among PSTs teaching upper and lower primary grades were not statistically significant.

Primary-Middle Pre-Service Teachers reported use of the Mathematics Textbook
Lisa O’Keeffe

The 1999 TIMSS video study highlighted a heavy reliance on the mathematics textbook in Australian classrooms (Hiebert et al., 2003). This promoted further investigation by Vincent & Stacey (2008) who have documented the differences between mathematical textbooks and concerns with regard to problem solving. However, there is much anecdotal evidence to suggest that the role of the textbook may be changing and that the emergence of digital technologies may in fact replace the mathematics textbook (Hu, 2011). Hence, this exploratory study intends to a brief insight into the current status of the mathematics textbook and its use within Australian classrooms.

Promoting Financial Literacy in Pre-service Teacher Education through On-line Modules
Leigh Wood, Carmel Coady, Joanne Mulligan, Michael Cavanagh, & Damian Bridge

Opening Real Science (ORS) is 3-year Australian Government project led by Macquarie University supported by the Office for Learning and Teaching under the Enhancing the Training of Mathematics and Science Teachers Scheme (ETMST). ORS is developing a series of modules for implementation in teacher education programs, some of which focus on financial literacy: budgeting, investing and protecting, and modelling. The modules will be designed for active learning incorporating digital literacy themes to showcase implementation of technology integration into curriculum. Currently there are several trials in progress at three partner Australian universities. Evaluation data will inform the design-based approach to program re-development aimed at building the mathematical competence, and confidence of teachers.

Promoting the Development of Foundation Content Knowledge in all Primary Pre-service Teachers
Chris Linsell, Naomi Ingram, & Megan Anakin

A feature of Linsell and Anakin’s (2013) concept of foundation content knowledge is that all pre-service teachers should have a growth oriented disposition and extend their knowledge, whether or not it is initially strong. This study reports on the use in mathematics pedagogy classes of introductory problems designed to encourage all first year primary pre-service teachers to become aware of the features of foundation content knowledge and to extend their own knowledge. Eighty-one percent of those pre-service teachers whose foundation content knowledge was not initially strong considered the introductory problems helpful, compared to 61% of those whose knowledge was strong.

Teachers’ Beliefs about Knowledge of Content and Students and its Effect on their Practice
Vesife Hatısaru

This study investigated mathematics teachers’ beliefs about teachers’ knowledge of content and students (Ball, Thames, & Phelps, 2008) about particular mathematical content and its effect on teaching practice. Two teachers participated in the study. Data were collected through classroom observations and an interview. The interview was based on An, Kulm, Wu, Ma, and Wang (2002) and focused mainly on teachers’ beliefs about knowledge of students’ thinking, approach to planning the mathematics instruction, students’ homework, and importance and approach to grading homework. The study indicated both teachers believed the importance of teachers’ understanding the way students think about a certain mathematics subject or the difficulties they experience with it. Nevertheless, it is seemed the teachers’ beliefs had no effect on their teaching practice. Moreover, they had limited awareness of how to identify students’ difficulties.

Teaching out-of-field: Meanings, representations and silences
Colleen Vale, Linda Hobbs, Christopher Speldewinde, & Zahra Parvanehnezhadshirazian

Teaching out-of-field is a concern internationally, and in Australia, and is linked to social, economic and educational costs for students and teachers along with an ethical and social justice issue for the community. At the national level, out-of-field teaching is most often represented as a problem of teacher quality involving less qualified teachers. Using a critical lens, meanings and representations of government policy and stakeholder perspectives and practices are analysed. The findings show how teaching out-of-field occurs and is legitimated and reveal the opportunities for contesting these positions to improve the outcomes for students and out-of-field teachers.

The Australian Mathematics Competition: What’s the Score?
Andrew Kepert, & Mike Clapper

The Australian Mathematics Competition (AMC) is a problem-solving competition for Primary and Secondary students. Each paper has 30 problems graded from routine to baffling, challenging and rewarding students of all abilities. The competition’s quality depends on the collective effort of dozens of Mathematics Educators (Primary to University) who write and scrutinise the papers in several stages. Our current work is to ensure the AMC provides a reliable challenge for students. Tools for calibrating the performance of questions and papers across a range of question types are improving the competition, measured by the relative performance of each question, and by each paper’s aggregate score.

The Pattern and Structure of the Australian Curriculum-Mathematics
Catherine McCluskey, Joanne Mulligan, & Michael Mitchelmore

The mathematical proficiencies in the Australian Curriculum—Mathematics describe the processes students are engaged in while developing mathematical concepts (ACARA, 2014). This presentation focuses on how the proficiencies: understanding, problem solving, reasoning and fluency, may work together to build patterns of thinking which can lead to generalised understandings of mathematical concepts. The authors connect the combined role of these proficiencies with a proposed Generalised Model of Patterning (McCluskey, Mitchelmore, & Mulligan, 2013), highlighting the role of patterning in the development of conceptual understandings within and beyond mathematics.

Understanding Mathematics: Teacher Knowledge, Task Design and Evaluating Students’ Mathematical Reasoning
Christine Mae, Janette Bobis, & Jenni Way

This presentation describes a research project designed to understand the relationship between teachers’ conceptual understandings of mathematics, the tasks they design for their students and their evaluation of students’ responses to tasks. Using Timperley’s (2008) Teacher Knowledge Building and Inquiry Cycle, Year 5 and 6 primary teachers and leaders at a range of career stages engaged in tasks to highlight the connection between what students need to know, what teachers need to know and what teachers need to learn. The implications for developing teachers’ understandings of mathematics will be discussed in terms of system-level professional learning.

Poster (abstract only)
Round Table (abstract only)
Investigating Mathematical Inquiry
Katie Makar, Jill Fielding-Wells, Kym Fry, Sue Allmond, & Jude Hillman

The aim of this Round Table is to bring together a community of researchers who focus on the teaching, learning, assessment, and research of a mathematical inquiry approach. We invite those interested in the study of mathematical inquiry to discuss their work or aspects of inquiry that are in need of research. A few questions are listed below to provoke conversation. Bring your own! 1. What shared and unshared perspectives do we have of mathematical inquiry? 2. What are purposes of mathematical inquiry? 3. How can mathematical inquiry be used to assess learning? 4. What signature practices characterise inquiry pedagogy in mathematics education? 5. How is mathematical inquiry similar to or different from inquiry in other content areas, such as science? 6. How does the teaching of mathematical inquiry fit into the broader repertoire of pedagogies used by teachers in the course of a year? 7. What challenges do teachers and students face in adopting mathematical inquiry? 8. Does an inquiry approach benefit children with different backgrounds differently? 9. What are key benefits and drawbacks of learning mathematics through inquiry? 10. Do particular strands of mathematics fit better with inquiry? 11. Does mathematical inquiry improve learning in mathematics? 12. Is mathematical inquiry scalable? 13. How can different paradigms contribute to a diversity of insights into mathematical inquiry? 14. What key research areas are strongly tied to mathematical inquiry (e.g., argumentation, socio-mathematical norms, collaboration)? 15. What are possible programs of research for mathematical inquiry?

Promoting Positive Emotional Engagement in Mathematics of Prospective Primary Teachers
Joanna Higgins, & Janette Bobis

Good teaching is described as that which is “charged with positive emotion” (Hargreaves, 1998, p.835). Yet, primary pre-service teacher education programs predominantly focus on the development of knowledge and pedagogy while affective aspects, including emotions, are only implicitly treated (Gootenboer, 2008). To date, research exploring the role emotions play in the process of learning to teach mathematics has received little attention (Hogden & Askew, 2007). The round table will begin by outlining the rationale and theoretical underpinnings of a trans-Tasman research project that aims to deepen primary pre-service teachers’ [PST] emotional and intellectual engagement in learning to teach mathematics. The Mathematics Emotional Engagement [MEE] project aims to develop and assess the effectiveness of an innovative teaching approach designed to promote positive emotional engagement in learning and teaching mathematics. The study explores the impact of a three-step interventional framework, referred to as ‘AIR’, that utilises a series of research-based instructional activities involving preservice primary teachers in: (1) Attending to their existing emotional responses towards the learning and teaching of mathematics; (2) Interpreting the causes and potential impact of existing emotional responses; and (3) Responding to their emotions with strategies to ameliorate negative affects on their learning and teaching of mathematics. Data from the first stage of the project—developing and refining AIR instructional strategies—will provide the stimulus for discussion amongst participants.

Senior Secondary Students’ Pre-calculus and Calculus Understanding
Michael Jennings, & Peter Adams

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 advanced mathematics in secondary schools and less stringent university entry requirements are seen as a major concern for the future of STEM education in Australia. In this round table, I will present data collected from secondary school students on precalculus and calculus topics. These data were collected from two groups of students: those studying intermediate mathematics in the last two years of secondary school; and those studying both intermediate and advanced mathematics. The results suggest that there are distinct differences in students’ procedural and conceptual understanding depending on which mathematics they studied in the last two years of secondary school. Students who studied both intermediate and advanced mathematics performed considerably better in all questions, not only on the calculus questions but also on junior mathematics pre-calculus topics such as gradient of a straight line. The data also showed that both groups of students had difficulty identifying lines parallel to axes, as well as explaining the meaning of the definition of the derivative. This presentation is part of a two-year state-wide longitudinal project that is investigating the transition from secondary to tertiary mathematics.

Working Across Disciplinary Boundaries in Pre-service Teacher Education
Merrilyn Goos, Judy Anderson, Jo Balatti, Kim Beswick, Tricia Forrester, & Jenni Way

In Australia, a suite of national projects has been funded by the Australian government to promote strategic change in mathematics and science pre-service teacher education. This round table session will share some of the interdisciplinary strategies being trialled in one project, Inspiring Mathematics and Science in Teacher Education (IMSITE), and invite feedback from participants on the transferability of strategies to other institutional contexts and the sustainability of these strategies over time. The specific objectives of the IMSITE project are: • to develop and validate a repertoire of strategies for combining knowledge of content and pedagogy in mathematics and science; and • to connect academics from different communities of practice – mathematics, science, education – in order to collaboratively design and implement these new teacher education approaches. Six universities and 23 investigators – mathematicians, scientists, and mathematics and science teacher educators – are the core participants in the project, with more universities to be added in 2015. The first half of the round table session will showcase interdisciplinary strategies such as: • Collaborative development and delivery of new content and pedagogy courses by mathematicians and mathematics educators; • Reciprocal tutoring by mathematicians and mathematics educators into each other’s courses; • Peer observation by mathematicians and mathematics educators of each other’s teaching; • Development of a mathematics specialisation in primary pre-service programs. The remainder of the session will invite discussion of challenges to interdisciplinary collaboration (“siloing” of disciplines, inflexible workload and course funding models, cultural differences between the disciplines) and ways to overcome these.