Research guided practice · 2019. 12. 23. · Curriculum in focus: Research guided practice The 37th Annual Conference of the Mathematics Education Research Group of Australasia University

Curriculum in focus:Research guided practice

The 37th Annual Conference of the Mathematics Education Research Group of Australasia

University of Technology, Sydney29 June – 3 July 2014

CONFERENCE PROGRAM

Conference sponsors: Australian Catholic University

Macquarie University University of Technology, Sydney

The University of Sydney

Welcome

It is a pleasure to welcome you to the MERGA 37 conference. The Venue is the Aerial

Function Centre at the University of Technology Sydney, from Sunday 29th June to Thursday

3rd July. All sessions are within the proximity of the Aerial Centre.

The conference consists of Keynote Presentations, a Panel Discussion, Research Papers (RP),

Symposia (SYM), Round Table Discussions (RT), Short Communications (SC), Poster Displays,

a Policy Meeting and the Annual General Meeting.

The Conference Dinner is at Dockside Darling Harbour which is located close to the Sydney

side of Pyrmont Bridge. It is within a reasonable walking distance of the Conference Centre

and nearby hotels. Details are given on the map in your conference satchel.

The conference is being jointly run and sponsored by Australian Catholic University, Sydney;

Macquarie University; University of Sydney; and University of Technology, Sydney.

This programme book contains the details of scheduling and provides information about the

day to day running of the conference.

INCLUSIONS:

• Conference Programme Overview

• Parallel Session Details, Times and Venues (19 Sessions)

• Keynote Abstracts in Alphabetical Order

• Research Paper Abstracts in Alphabetical Order

• Symposium Abstracts in Alphabetical Order

• Round Table Abstracts in Alphabetical Order

• Short Communication Abstracts in Alphabetical Order

• Poster Presentations in Alphabetical Order

• Executive Reports

Local Organising Committee

Judy Anderson Michael Cavanagh Mary Coupland Anne Prescott Paul White

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Session 1: Monday 30th June 11:00am to 11:40am Room Type Authors Title

Wattle RP Ove Gunnar Drageset How Students Explain and Teachers Respond

Thomas RP Gilah Leder & Helen Forgasz Learning from Assessment: NAPLAN and Indigenous Students

Broadway RP Catherine Attard & Joanne Orlando

Early Career Teachers, Mathematics and Technology: Device Conflict and Emerging Mathematical Knowledge

Jones RP Marlon Ebaeguin & Max Stephens

Why Lesson Study Works in Japan: A Cultural Perspective

Harris RP Omolola Ladele, Christine Ormond & Mark Hackling

The Effect of Professional Learning on Early Algebra Teachers’ Content Knowledge in Nigeria

Agincourt SC

Merrilyn Goos & Paul Hernandez-Martinez

Collegial Peer Observation as a Means of Influencing Change in University Mathematics Teaching

Greg Oates, John Hannah, David Holgate & Kevin McLeod

Towards an Investigation of the Pedagogical Content Knowledge of University Mathematics Teachers

Session 2: Monday 30th June 11:45am to 12:25pm Room Type Authors Title

Wattle RP Lisa Darragh Asking Questions and Performing Mathematics Identity

Thomas SC Ann Williams Dyscalculia, from a Teacher’s Perspective

Rose Golds What Does Ability Mean in Mathematics Learning?

Broadway RP Andrea McDonough & Sarah Ferguson

PPELEM: A “Creative” Interviewing Procedure for Gaining Insights into Teacher and Student Mathematics-related Beliefs

Jones RP Yvette Semler & Michael Cavanagh Newcomers’ Experiences at MERGA36

Harris RP Rose Knight & Vince Wright

Will this Net Work?: Development of a Diagnostic Interview

Agincourt RT Chris Hurst Numeracy ... Scientificity: Identifying, Linking and Using the ‘Big Ideas’ of Mathematics and Science for more Effective Teaching

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Session 3: Monday 30th June 12:30pm to 1:10pm Room Type Authors Title

Wattle RP Anne Bennison Teacher Identity and Numeracy: Evaluating a Conceptual Framework for Identity as a Teacher of Numeracy

Thomas RP Chan Chun Ming Eric Exploring Group Dynamics of Primary 6 Students Engaged in Mathematical Modelling Activities

Broadway RP Joanne Mulligan & Lyn English

Developing Young Students’ Meta-representational Competence through Integrated Mathematics and Science Investigations

Jones SC

Chrissy Monteleone, Roger Vallance & Paul White

The Performance Characteristics of Early Education Children in Mainstream Classrooms with Respect to Critical Mathematical Thinking

Susan McDonald & Louise Thomas

Early Childhood Educators as Teachers of Mathematics

Harris RP Janeen Lamb, Sarah Howard & Michael Easey

Pre-service Teachers’ use of Library Databases: Some Insights

Agincourt RT

Merrilyn Goos, Judy Anderson, Kim Beswick, Judy-Anne Osborn, Caz Sandison, James Dalitz, Kathryn Holmes & Elena Prieto-Rodriguez

Inspiring Mathematics and Science in Australian Teacher Education


Wattle RP Audrey Cooke Preliminary Investigations of Pre-service Teacher Numeracy

Thomas RP Ajay Ramful & Siew Yin Ho Quantitative Relationships Involving Additive Differences: Numerical Resilience

Broadway RP Kester Lee & Judy Anderson Who is Really Interested in Mathematics? An Investigation of Lower Secondary Students’ Mathematical Role Models

Jones RP Eugenie Kestel

Comparison of a Targeted Intervention Program Delivered Face-to-face and by Personal Video-conferencing for Primary and Middle School Students with Mathematical Learning Difficulties

Harris RP Sue Wilson & Monica Raven “Change my thinking patterns towards maths”: A Bibilotherapy Workshop for Pre-service Teachers’ Mathematics Anxiety

Agincourt SC Louise Hodgson Modelled Lessons Raise More Questions than

Answers

Seyum Getenet, Rosemary Callingham & Kim Beswick

Designing Professional Development: Beyond General Principles

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Wattle RP Patricia Morley A Reflective Approach to NAPLAN: Exploring the Implications of Students’ Responses to an “Adding Fractions” Item

Thomas RP Monica Wong, Jerry Lipka & Dora Andrew-Ihrke

Symmetrical Measuring: An Approach to Teaching Elementary School Mathematics Informed by Yup’ik Elders

Broadway SC

Geoff Woolcott, Daniel Chamberlain & Rassoul Sadeghi

Conceptual Development in Mathematics: Longitudinal Connections from Network Analysis of Multiple Choice Assessments

Caroline Yoon SPOT Diagrams of a Partially Correct Construct

Jones SC

Geoff Woolcott, Adam Harris, Jackie Reid & Robert Whannell

Enhancing Mathematics and Science Teacher Education in Regional Australia: Modules for Primary Mathematics Pre-service Teachers

Annika Grothérus Scaffolding Formative Assessment Approach – Visualize Learning

Harris RP Nicole Maher & Tracey Muir

“I don’t really understand probability at all”: Final Year Pre-service Teachers’ Understanding of Probability

Agincourt SYM Colleen Vale, Leicha Bragg, Sandra Herbert, Esther Loong & Wanty Widjaja

Students’ Mathematical Reasoning and Teachers’ Developing Understanding of Mathematical Reasoning

Session 6: Monday 30th June 4:15pm to 4:55pm

Room Type Authors Title

Wattle RP Elizabeth Ferme A Working Understanding of Numeracy in the Secondary Setting

Thomas RP Elena Prieto & Kathryn Holmes

Online Students’ Perceptions of Interactive Tools to Support Postgraduate Learning of Mathematics

Broadway RP Wee Tiong Seah & Tasos Barkatsas

What Australian Primary School Students Value in Mathematics Learning: A WIFI Preliminary Study

Jones RP Colin Carmichael Gender, Parental Beliefs and Children’s Mathematics Performance: Insights from the Longitudinal Study of Australian Children

Harris SC Timothy Perkins

Mentoring to Alleviate Anxiety in Pre-service Primary Mathematics Teachers: Working at the Coal-face without having to Look over your Shoulder

Kathy Brady & Tiffany Winn Using Metaphors to Investigate Pre-service Primary Teachers’ Attitudes to Mathematics

Agincourt SYM Symposium continues

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Session 7: Tuesday 1st July 9:00am to 9:40am Room Type Authors Title

Wattle RP Tim Wilson & Tasos Barkatsas

The Effect of Language, Gender and Age in NAPLAN Numeracy Data

Thomas RP Lyn English & Jane Watson

Development of Fourth-grade Students’ Understanding of Experimental and Theoretical Probability

Broadway RP James Dalitz Undergraduate Mathematics Study Groups: What Mathematical Talk Actually Takes Place?

Jones RP Kevin Larkin & Robyn Jorgensen

Using Video Diaries to Record Student Attitudes and Emotions Towards Mathematics in Year Three and Year Six Students

Harris SC Gregor Lomas Like Topsy, ‘it just growed’? Or did it? The Ongoing

Development of a Strategy Teaching Model

Bill Barton Learning in Undergraduate Mathematics: The Trial of a Delivery Innovation

Agincourt RT

Halilah Bte Salim Alkhatib, Chen Ailing, Winnie Koh Mei Ling, Kang Hway Choon & Choy Ban Heng

Enhancing Productive Mathematical Noticing During Lesson Planning with Lesson Play

Session 8: Tuesday 1st July 9:45am to 10:25am Room Type Authors Title

Wattle RP Simone Zmood Fostering the Promise of High Achieving Mathematics Students through Curriculum Differentiation

Thomas RP Nathan Zoanetti, Magdalena Les & David Leigh-Lancaster

Comparing the Score Distribution of a Trial Computer-based Examination Cohort with that of the Standard Paper-based Examination Cohort

Broadway RP Janeen Lamb, Takashi Kawakami, Akihiko Saeki & Akio Matsuzaki

Leading a New Pedagogical Approach to Australian Curriculum Mathematics: Using the Dual Mathematical Modelling Cycle Framework

Harris SC Catherine Pearn Why Knowledge of Fractions is Important for Algebraic

Readiness in the Middle Years of Schooling

Duncan Symons & Cath Pearn The Flipped Classroom Model – A Literature Review

Agincourt RT Joanna Higgins & Raewyn Eden

Exploring Mindfulness within Mathematics Learning Environments

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Session 9: Tuesday 1st July 11:00pm to 11:40am Room Type Authors Title

Wattle RP Karen Skilling Teacher Practices: How they Promote or Hinder Student Engagement in Mathematics

Thomas RP Chris Hurst

Developing Pre-service Teacher Capacity to Make Appropriate Choices of Tasks and Resources through Diagnostic Assessment of Children’s Work

Broadway RP Caroline Bardini, Jill Vincent, Robyn Pierce & Deborah King

Undergraduate Mathematics Students’ Pronumeral Misconceptions

Jones RP Fabio D’Agostin The Value of Emoticons in Investigating Student Emotions Related to Mathematics Task Negotiation

Harris RP Dan Jazby Do Teachers Make Decisions Like Firefighters? Applying Naturalistic Decision-making Methods to Teachers’ In-class Decision Making in Mathematics

Agincourt RT Roberta Hunter, Jodie Hunter, Zain Thompson & Trevor Bills

Co-constructing Mathematical Inquiry Communities through Professional Development with Teachers

Session 10: Tuesday 1st July 11:45am to 12:25pm Room Type Authors Title

Wattle RP Rumi Rumiati

Arithmetical Strategies of a Student with Down Syndrome Mental Calculation Strategies of a Student Attending a Special School for the Intellectually Disabled

Thomas RP Cris Edmonds-Wathen, Priscilla Sakopa, Kay Owens & Vagi Bino

Indigenous Languages and Mathematics in Elementary Schools

Broadway RP Maria Mojica-Casey, John Dekkers & Rose-Marie Thrupp

Research Guided Practice: Student Online Experiences during Mathematics class in the Middle School

Jones RP Darren McGregor Does Inquiry Based Learning Affect Students’ Beliefs and Attitudes Towards Mathematics?

Harris SC

Sitti Maesuri Patahuddin & Barney Dalgarno

TPACK as an Analytical Tool to Understand Mathematics Teaching with Technology

Kim Beswick & Helen Chick

Responses to “the Scary Question”: How Teaching Challenges Impact the Use of Knowledge and its Development

Agincourt SYM

Chris Linsell, Megan Anakin, Naomi Ingram, Karen Major & Pamela Perger

Pre-service Teachers’ Mathematics Content Knowledge

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Session 11: Tuesday 1st July 12:30pm to 1:10pm Room Type Authors Title

Wattle RP Jodie Miller Young Australian Indigenous Students’ Growing Pattern Generalisations: The Role of Gesture When Generalising

Thomas RP Felipe Almuna Salgado & Kaye Stacey

Item Context Factors Affecting Students’ Performance on Mathematics Items

Broadway RP Peter Grootenboer & Christine Edwards-Groves

Mathematics Teaching as Praxis

Jones RP Thi L Tran & Robert J. Wright

Beliefs of Teachers who Teach Intensive One-to-one Intervention about Links to Classroom Teaching

Harris SC Angel Mok Cultural Identities and Mathematics Learning


Session 12: Tuesday 1st July 2:15pm to 2:55pm Room Type Authors Title

Wattle RP Matt Sexton & Ann Downton

School Mathematics Leaders’ Perceptions of Successes and Challenges of their Leadership Role within a Mathematics Improvement Project

Thomas RP Generosa Leach, Roberta Hunter & Jodie Hunter

Teachers’ Repositioning Culturally Diverse Students as Doers and Thinkers of Mathematics

Broadway RP Sharyn Livy & Sandra Herbert

Opportunities to Promote Mathematical Content Knowledge for Primary Teaching

Jones RP Kathy Brady Towards a Fresh Understanding of the Relationship Between Teacher Beliefs about Mathematics and their Classroom Practices

Harris SC

Siew Yee Lim & Hui Yi Ting

Development of a Set of Mathematical Modelling Rubrics

Maureen Siew Fang Chong & Masitah Shahrill

The Development in Integrating Mathematical Modelling into the Curriculum: Results of a Pilot Study

Agincourt

SC Lu Pien Cheng Developing Critical Reflection for Primary School

Mathematics Teachers through Laboratory Class Cycle

Malin Lindwall Ehrnlund The Meaning Making of Meaning Makers – Experienced Mathematics Teachers’ Interpretations of their Own Professional Practice

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Session 13: Wednesday 2ndJuly 11:00am to 11:40am Room Type Authors Title

Wattle RP Nicole Dimarakis, Janette Bobis, Jenni Way & Judy Anderson

“I just need to believe in myself more”: The Mathematical Self-belief of Year 7 Students

Thomas RP Linda Parish Defining Mathematical Giftedness

Broadway RP Tracey Muir & Helen Chick

Flipping the Classroom: A Case Study of a Mathematics Methods Class

Jones RP Christine Anestis Kargas & Max Stephens

Using Coaching to Improve the Teaching of Problem Solving to Year 8 Students in Mathematics

Harris RP Peter Sullivan & Aylie Davidson

The Role of Challenging Mathematical Tasks in Creating Opportunities for Student Reasoning

Agincourt SC

Naomi Ingram & Sandra Williamson-Leadley

Using iPads for Assessment in the Mathematics Classroom

Janelle Hill Mathematics and English Teachers’ Views and Expectations of iPads: A Pilot Study

Session 14: Wednesday 2ndJuly 11:45am to 12:25pm Room Type Authors Title

Wattle RP Kristy Goodwin & Peter Gould

Race in the Outback: Investigating Technology Designed to Support Number Development in a Preschool Serving an Under-resourced Community

Thomas RP Jill Cheeseman & Angela Mornane

Primary Students’ Perceptions of their Mathematics Learning

Broadway RP Chris Hurst Big Challenges and Big Opportunities: The Power of ‘Big Ideas’ to Change Curriculum and the Culture of Teacher Planning

Jones SC

Nor Azura Hj Abdullah, Masitah Shahrill & Maureen Siew Fang Chong

Investigating the Representations of Students’ Problem Solving Strategies

Margaret Marshman Middle Years Students Using Mathematics to Communicate a Local Issue

Harris RP Carly Sawatzki Connecting Social and Mathematical Thinking: The Use of “Real Life” Contexts

Agincourt RT Fiona McDiamid & Deborah Gibbs

Mathematics Support Teacher (MST): How Do We Help Students Maintain Mathematical Gains?

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Session 15: Wednesday 2ndJuly 12:30pm to 1:10pm Room Type Authors Title

Wattle RP Virginia Kinnear & Julie Clark

Probabilistic Reasoning and Prediction with Young Children

Thomas RP Jane Greenlees, Sitti Maesuri Patahuddin & Tom Lowrie

Different Versions of the Same Lesson Plan: Implications on the Lesson Design

Broadway SC

Janette Bobis, Jenni Way & Maryam Khosronejad

Exploring Mathematics Engagement in the Middle Years of School

Elizar & I Gusti Ngurah Darmawan

Self-efficacy and Attitude toward Mathematics: A Multigroup Invariance Analysis and Gender Difference

Jones Rp Rachel Lim, Glenda Anthony & Claire McLachlan

Learning Stories: Making Mathematics Learning Visible

Harris RP

Peter Sullivan, Doug Clarke, Jill Cheeseman, Angela Mornane, Anne Roche, Carly Sawatzki & Nadia Walker

Students’ Willingness to Engage with Mathematical Challenges: Implications for Classroom Pedagogies

Agincourt RT Michael Jennings, & PeteǊΦ!ŘŀƳǎ

Factors Influencing Student Decision on Senior Secondary School Subjects


Wattle RP Jenny Young-Loveridge & Brenda Bicknell

Supporting the Development of Number Fact Knowledge in Five- and Six-year-olds

Thomas RP Tom Lowrie, Ajay Ramful, Tracy Logan & Siew Yin Ho

Do Students Solve Graphic Tasks with Spatial Demands Differently in Digital Form?

Broadway RP Vince Geiger, Merrilyn Goos, Helen Forgasz & Anne Bennison

Devising Principles of Design for Numeracy Tasks

Jones RP Karina J Wilkie & Doug Clarke

Developing Students’ Functional Thinking in Algebra through different Visualisations of a Growing Pattern’s Structure

Harris RP Nadia Walker Improving the Effectiveness of the Whole Class Discussion in the Summary Phase of Mathematics Lessons

Agincourt SC Jennie Marston Using Picture Books to Implement the Mathematics

Curriculum: The Missed Opportunities

Jyoti Jhagroo Multiple Multiplication Models

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Wattle RP Peter Gould The Association between Students’ Number Knowledge and Social Disadvantage at School Entry

Thomas RP Belinda Aventi, Penelope Serrow & Steve Tobias

Linking Geogebra to Explorations of Linear Relationships

Broadway RP Jodie Hunter Developing a ‘Conjecturing Atmosphere’ in the Classroom through Task Design and Enactment

Jones RP Ban Heng Choy Noticing Critical Incidents in a Mathematics Classroom

Harris RP Vicki Steinle, Beth Price, Kaye Stacey & Eugene Gvozdenko

Using Percentages to Describe and Calculate Change

Agincourt SC

Khemduth Singh Angateeah, Preethee Gonpot & Kaviraj Sharma Sukon

An Investigation of Students’ Difficulties in Solving Non-routine Word Problems at Lower Secondary

Christina Lee, Omolola Ladele & Christine Ormond

Teachers’ Beliefs and Practice in Teaching Early Algebra

Panel Discussion: Wednesday 2ndJuly 4:15pm to 5:15pm Room Panelists Title

Jones/Harris

Glenda Anthony

Berinderjeet Kaur

Barbara Jaworski

Merrilyn Goos

Lessons learned from National Curriculum Development- what advice would you have for Australia?

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Session 18: Thursday 3rd July 9:00am to 9:40am

Room Type Authors Title Computer

Labs RP Bing Ngu The Complexity of One-Step Equations

Thomas RP Steve Thornton The Technological Enframing of Mathematics Education

Broadway RP Raman Ganesan & Jaguthsing Dindyal

An Investigation of Students’ Errors in Logarithms

Jones RP Bernadette Long The Impact of an Intervention Program on Student Approaches to Learning: A Case Study

Harris SC

Hiro Ozasa, Takeshi Okawa & Akio Matsuzaki

Understanding Media in Mathematics Education: Media and Extensions of the Students

John Kusznirczuk The Contribution of a Poetics of Mathematics Classroom Interaction to Curriculum Design

Agincourt SYM

Kay Owens, Vagi Bino, Geori Kravia, Cris Edmonds-Wathen, Priscilla Sakopa, Kila Tau & Martha Kull

Elementary Teachers in Papua New Guinea’s Professional Learning for Cultural Mathematics

Session 19: Thursday 3rd July 9:45am to 10:25am Room Type Authors Title

Thomas RP Robyn Jorgensen Social Theories of Learning: A Need for a New Paradigm in Mathematics Education

Broadway RP Jill P. Brown & Gloria Stillman Affordances: Ten Years On

Jones RP

Diana Grace Aniban, Von Christopher Chua, Jellen Garcia & Levi Esteban Elipane

From Arithmetic to Algebra: Sequences and Patterns as an Introductory Lesson in Seventh Grade Mathematics

Harris SC Sven Trenholm Evidence of Evolutionary Changes in the Nature of Interactions in Fully Asynchronous Online Mathematics Courses


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Keynotes

Barbara Jaworski Mathematics Education Development Research in Teaching Learning in Practice

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.

Berinderjeet Kaur Evolution of Singapore’s School Mathematics Curriculum

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.

Peter Galbraith Custodians of Quality: Mathematics Education in Australasia Where from? Where at? Where to?

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.

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Research Reports Felipe Almuna Salgado & Kaye Stacey

Item Context Factors Affecting Students’ Performance on Mathematics Items

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.

Diana Grace Aniban, Von Christopher Chua, Jellen Garcia & Levi Esteban Elipane

From Arithmetic to Algebra: Sequences and Patterns as an Introductory Lesson in Seventh Grade Mathematics

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.

Catherine Attard & Joanne Orlando

Early Career Teachers, Mathematics and Technology: Device Conflict and Emerging Mathematical Knowledge

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.

Belinda Aventi, Penelope Serrow & Steve Tobias Linking Geogebra to Explorations of Linear Relationships

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.

Caroline Bardini, Jill Vincent, Robyn Pierce & Deborah King

Undergraduate Mathematics Students’ Pronumeral Misconceptions

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

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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.

Anne Bennison Teacher Identity and Numeracy: Evaluating a Conceptual Framework for Identity as a Teacher of Numeracy

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.

Kathy Brady Towards a Fresh Understanding of the Relationship Between Teacher Beliefs about Mathematics and their Classroom Practices

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.

Jill Brown & Gloria Stillman Affordances: Ten Years On

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.

Colin Carmichael Gender, Parental Beliefs and Children’s Mathematics Performance: Insights from the Longitudinal Study of Australian Children

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.

Jill Cheeseman & Angela Mornane Primary Students’ Perceptions of their Mathematics Learning

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

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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.

Chan Chun Ming Eric Exploring Group Dynamics of Primary 6 Students Engaged in Mathematical Modelling Activities

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.

Ban Heng Choy Noticing Critical Incidents in a Mathematics Classroom 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.

Audrey Cooke Preliminary Investigations of Pre-service Teacher Numeracy 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.

Fabio D’Agostin The Value of Emoticons in Investigating Student Emotions Related to Mathematics Task Negotiation

‘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.

James Dalitz Undergraduate Mathematics Study Groups: What Mathematical Talk Actually Takes Place?

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

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are the lack of prior preparation, avoidance of high level cognitive questions and the inability to recognise and then develop opportunities.

Lisa Darragh Asking Questions and Performing Mathematics Identity 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.

Nicole Dimarakis, Janette Bobis, Jenni Way & Judy Anderson

“I just need to believe in myself more”: The Mathematical Self-belief of Year 7 Students

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.

Ove Gunnar Drageset How Teachers Explain and Students Respond 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.

Marlon Ebaeguin & Max Stephens Why Lesson Study Works in Japan: A Cultural Perspective

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.

Cris Edmonds-Wathen, Priscilla Sakopa, Kay Owens & Vagi Bino

Indigenous Languages and Mathematics in Elementary Schools

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.

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Lyn English & Jane Watson

Development of Fourth-grade Students’ Understanding of Experimental and Theoretical Probability

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.

Elizabeth Ferme A Working Understanding of Numeracy in the Secondary Setting 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.

Raman Ganesan & Jaguthsing Dindyal An Investigation of Students’ Errors in Logarithms

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.

Vince Geiger, Merrilyn Goos, Helen Forgasz & Anne Bennison

Devising Principles of Design for Numeracy Tasks

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.

Kristy Goodwin & Peter Gould

Race in the Outback: Investigating Technology Designed to Support Number Development in a Preschool Serving an Under-resourced Community

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.

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Peter Gould The Association between Students’ Number Knowledge and Social Disadvantage at School Entry

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.

Jane Greenlees, Sitti Maesuri Patahuddin & Tom Lowrie

Different Versions of the Same Lesson Plan: Implications on the Lesson Design

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.

Peter Grootenboer & Christine Edwards-Groves

Mathematics Teaching as Praxis

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.

Jodie Hunter Developing a ‘Conjecturing Atmosphere’ in the Classroom through Task Design and Enactment

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.

Chris Hurst Big Challenges and Big Opportunities: The Power of ‘Big Ideas’ to Change Curriculum and the Culture of Teacher Planning

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-

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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.

Chris Hurst Developing Pre-service Teacher Capacity to Make Appropriate Choices of Tasks and Resources through Diagnostic Assessment of Children’s Work

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.

Dan Jazby Do Teachers Make Decisions Like Firefighters? Applying Naturalistic Decision-making Methods to Teachers’ In-class Decision Making in Mathematics

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.

Robyn Jorgensen Social Theories of Learning: A Need for a New Paradigm in Mathematics Education

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.

Christine Anestis Kargas & Max Stephens

Using Coaching to Improve the Teaching of Problem Solving to Year 8 Students in Mathematics

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.

Eugenie Kestel

Comparison of a Targeted Intervention Program Delivered Face-to-face and by Personal Video-conferencing for Primary and Middle School Students with Mathematical Learning Difficulties

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

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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.

Virginia Kinnear & Julie Clark Probabilistic Reasoning and Prediction with Young Children

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.

Rose Knight & Vince Wright

Will this Net Work?: Development of a Diagnostic Interview

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.

Omolola Ladele, Christine Ormond & Mark Hackling

The Effect of Professional Learning on Early Algebra Teachers’ Content Knowledge in Nigeria

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.

Janeen Lamb, Takashi Kawakami, Akihiko Saeki & Akio Matsuzaki

Leading a New Pedagogical Approach to Australian Curriculum Mathematics: Using the Dual Mathematical Modelling Cycle Framework

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.

Janeen Lamb, Sarah Howard & Michael Easey Pre-service Teachers’ use of Library Databases: Some Insights

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

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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.

Kevin Larkin & Robyn Jorgensen

Using Video Diaries to Record Student Attitudes and Emotions Towards Mathematics in Year Three and Year Six Students

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.

Generosa Leach, Roberta Hunter & Jodie Hunter

Teachers’ Repositioning Culturally Diverse Students as Doers and Thinkers of Mathematics

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.

Gilah Leder & Helen Forgasz Learning from Assessment: NAPLAN and Indigenous Students

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.

Kester Lee & Judy Anderson

Who is Really Interested in Mathematics? An Investigation of Lower Secondary Students’ Mathematical Role Models

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.

Rachel Lim, Glenda Anthony & Claire McLachlan

Learning Stories: Making Mathematics Learning Visible

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

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and analyse mathematics learning that occurs within explicit mathematics activities rather than within play that involves mathematics.

Sharyn Livy & Sandra Herbert

Opportunities to Promote Mathematical Content Knowledge for Primary Teaching

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.

Bernadette Long The Impact of an Intervention Program on Student Approaches to Learning: A Case Study

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.

Tom Lowrie, Ajay Ramful, Tracy Logan & Siew Yin Ho

Do Students Solve Graphic Tasks with Spatial Demands Differently in Digital Form?

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.

Nicole Maher & Tracey Muir

“I don’t really understand probability at all”: Final Year Pre-service Teachers’ Understanding of Probability

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.

Andrea McDonough & Sarah Ferguson

PPELEM: A “Creative” Interviewing Procedure for Gaining Insights into Teacher and Student Mathematics-related Beliefs

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.

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Darren McGregor Does Inquiry Based Learning Affect Students’ Beliefs and Attitudes Towards Mathematics?

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.

Jodie Miller Young Australian Indigenous Students’ Growing Pattern Generalisations: The Role of Gesture When Generalising

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.

Maria Mojica-Casey, John Dekkers & Rose-Marie Thrupp

Research Guided Practice: Student Online Experiences during Mathematics class in the Middle School

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.

Patricia Morley A Reflective Approach to NAPLAN: Exploring the Implications of Students’ Responses to an “Adding Fractions” Item

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.

Tracey Muir & Helen Chick

Flipping the Classroom: A Case Study of a Mathematics Methods Class

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.

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Joanne Mulligan & Lyn English

Developing Young Students’ Meta-representational Competence through Integrated Mathematics and Science Investigations

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.

Bing Ngu The Complexity of One-Step Equations 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.

Linda Parish Defining Mathematical Giftedness 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.

Elena Prieto & Kathryn Holmes

Online Students’ Perceptions of Interactive Tools to Support Postgraduate Learning of 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.

Ajay Ramful & Siew Yin Ho

Quantitative Relationships Involving Additive Differences: Numerical Resilience

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.

Rumi Rumiati Arithmetical Strategies of a Student with Down Syndrome 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

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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.

Rumi Rumiati & Bob Wright

Mental Calculation Strategies of a Student Attending a Special School for the Intellectually Disabled.

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

Carly Sawatzki Connecting Social and Mathematical Thinking: The Use of “Real Life” Contexts

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.

Wee Tiong Seah & Tasos Barkatsas

What Australian Primary School Students Value in Mathematics Learning: A WIFI Preliminary Study

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. Yvette Semler & Michael Cavanagh Newcomers’ Experiences at MERGA36

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.

Matt Sexton & Ann Downton

School Mathematics Leaders’ Perceptions of Successes and Challenges of their Leadership Role within a Mathematics Improvement Project

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

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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.

Karen Skilling Teacher Practices: How they Promote or Hinder Student Engagement in Mathematics

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.

Vicki Steinle, Beth Price, Kaye Stacey & Eugene Gvozdenko

Using Percentages to Describe and Calculate Change

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.

Peter Sullivan, Doug Clarke, Jill Cheeseman, Angela Mornane, Anne Roche, Carly Sawatzki & Nadia Walker

Students’ Willingness to Engage with Mathematical Challenges: Implications for Classroom Pedagogies

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.

Peter Sullivan & Aylie Davidson

The Role of Challenging Mathematical Tasks in Creating Opportunities for Student Reasoning

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.

Steve Thornton The Technological Enframing of Mathematics Education 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

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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.

Thi L Tran & Bob Wright Beliefs of Teachers who Teach Intensive One-to-one Intervention about Links to Classroom Teaching

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.

Nadia Walker Improving the Effectiveness of the Whole Class Discussion in the Summary Phase of Mathematics Lessons

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.

Karina J Wilkie & Doug Clarke

Developing Students’ Functional Thinking in Algebra through different Visualisations of a Growing Pattern’s Structure

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.

Sue Wilson & Monica Raven

“Change my thinking patterns towards maths”: A Bibilotherapy Workshop for Pre-service Teachers’ Mathematics Anxiety

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.

Tim Wilson & Tasos Barkatsas

The Effect of Language, Gender and Age in NAPLAN Numeracy Data

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.

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Monica Wong, Jerry Lipka & Dora Andrew-Ihrke

Symmetrical Measuring: An Approach to Teaching Elementary School Mathematics Informed by Yup’ik Elders

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.

Jenny Young-Loveridge & Brenda Bicknell

Supporting the Development of Number Fact Knowledge in Five- and Six-year-olds

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.

Simone Zmood Fostering the Promise of High Achieving Mathematics Students through Curriculum Differentiation

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.

Nathan Zoanetti, Magdalena Les & David Leigh-Lancaster

Comparing the Score Distribution of a Trial Computer-based Examination Cohort with that of the Standard Paper-based Examination Cohort

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.

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Symposia Symposium 1

Colleen Vale, Leicha Bragg, Sandra Herbert, Esther Loong & Wanty Widjaja

Students’ Mathematical Reasoning and Teachers’ Developing Understanding of Mathematical Reasoning

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. Symposium 2 Chris Linsell, Megan Anakin, Naomi Ingram, Karen Major & Pamela Perger

Pre-service Teachers’ Mathematics Content Knowledge

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. Symposium 3 Kay Owens, Vagi Bino, Geori Kravia, Cris Edmonds-Wathen, Priscilla Sakopa, Kila Tau & Martha Kull

Elementary Teachers in Papua New Guinea’s Professional Learning for Cultural Mathematics

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.

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Round Table Discussions

Halilah Bte Salim Alkhatib, Chen Ailing, Winnie Koh Mei Ling, Kang Hway Choon & Choy Ban Heng

Enhancing Productive Mathematical Noticing During Lesson Planning with Lesson Play

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. Merrilyn Goos, Judy Anderson, Kim Beswick, Judy-Anne Osborn, Caz Sandison, James Dalitz, Kathryn Holmes & Elena Prieto-Rodriguez

Inspiring Mathematics and Science in Australian Teacher Education

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.

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Joanna Higgins & Raewyn Eden

Exploring Mindfulness within Mathematics Learning Environments

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. Roberta Hunter, Jodie Hunter, Zain Thompson & Trevor Bills

Co-constructing Mathematical Inquiry Communities through Professional Development with Teachers

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.

Chris Hurst Numeracy ... Scientificity: Identifying, Linking and Using the ‘Big Ideas’ of Mathematics and Science for more Effective Teaching

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

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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.

Michael Jennings & PeterΦ!ŘŀƳǎ

Factors Influencing Student Decision on Senior Secondary School Subjects

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. Fiona McDiamid & Deborah Gibbs

Mathematics Support Teacher (MST): How Do We Help Students Maintain Mathematical Gains?

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.

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Short Communications

Nor Azura Hj Abdullah, Masitah Shahrill & Maureen Siew Fang Chong

Investigating the Representations of Students’ Problem Solving Strategies

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.

Bill Barton Learning in Undergraduate Mathematics: The Trial of a Delivery Innovation

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. Kim Beswick & Helen Chick

Responses to “the Scary Question”: How Teaching Challenges Impact the Use of Knowledge and its Development

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. Janette Bobis, Jenni Way & Maryam Khosronejad

Exploring Mathematics Engagement in the Middle Years of School

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. Kathy Brady & Tiffany Winn

Using Metaphors to Investigate Pre-service Primary Teachers’ Attitudes to Mathematics

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

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had negative attitudes to mathematics there existed a preparedness to approach mathematics in a reasonably positive manner.

Lu Pien Cheng Developing Critical Reflection for Primary School Mathematics Teachers through Laboratory Class Cycle

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. Maureen Siew Fang Chong & Masitah Shahrill

The Development in Integrating Mathematical Modelling into the Curriculum: Results of a Pilot Study

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. Elizar & I Gusti Ngurah Darmawan

Self-efficacy and Attitude toward Mathematics: A Multigroup Invariance Analysis and Gender Difference

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. Seyum Getenet, Rosemary Callingham & Kim Beswick

Designing Professional Development: Beyond General Principles

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.

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Rose Golds What Does Ability Mean in Mathematics Learning? 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. Merrilyn Goos & Paul Hernandez-Martinez

Collegial Peer Observation as a Means of Influencing Change in University Mathematics Teaching

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. Annika Grothérus Scaffolding Formative Assessment Approach – Visualize 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.

Janelle Hill Mathematics and English Teachers’ Views and Expectations of iPads: A Pilot Study

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. Louise Hodgson Modelled Lessons Raise More Questions than Answers 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.

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Naomi Ingram & Sandra Williamson-Leadley Using iPads for Assessment in the Mathematics Classroom

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. Jyoti Jhagroo Multiple Multiplication Models 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.

John Kusznirczuk The Contribution of a Poetics of Mathematics Classroom Interaction to Curriculum Design

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. Christina Lee, Omolola Ladele & Christine Ormond

Teachers’ Beliefs and Practice in Teaching Early Algebra

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. Siew Yee Lim & Hui Yi Ting Development of a Set of Mathematical Modelling Rubrics

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

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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.

Malin Lindwall Ehrnlund The Meaning Making of Meaning Makers – Experienced Mathematics Teachers’ Interpretations of their Own Professional Practice

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.

Gregor Lomas Like Topsy, ‘it just growed’? Or did it? The Ongoing Development of a Strategy Teaching Model

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.

Margaret Marshman Middle Years Students Using Mathematics to Communicate a Local Issue

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.

Jennie Marston Using Picture Books to Implement the Mathematics Curriculum: The Missed Opportunities

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. Susan McDonald & Louise Thomas Early Childhood Educators as Teachers of Mathematics

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

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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. Angel Mok Cultural Identities and Mathematics Learning 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. Chrissy Monteleone, Roger Vallance & Paul White

The Performance Characteristics of Early Education Children in Mainstream Classrooms with Respect to Critical Mathematical Thinking

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

Greg Oates, John Hannah, David Holgate & Kevin.McLeod

Towards an Investigation of the Pedagogical Content Knowledge of University Mathematics Teachers

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. Hiro Ozasa, Takeshi Okawa & Akio Matsuzaki

Understanding Media in Mathematics Education: Media and Extensions of the Students

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.

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Sitti Maesuri Patahuddin & Barney Dalgarno

TPACK as an Analytical Tool to Understand Mathematics Teaching with Technology

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.

Catherine Pearn Why Knowledge of Fractions is Important for Algebraic Readiness in the Middle Years of Schooling

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.

Timothy Perkins Mentoring to Alleviate Anxiety in Pre-service Primary Mathematics Teachers: Working at the Coal-face without having to Look over your Shoulder

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. Duncan Symons & Cath Pearn The Flipped Classroom Model – A Literature Review

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.

Sven Trenholm Evidence of Evolutionary Changes in the Nature of Interactions in Fully Asynchronous Online Mathematics Courses

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.

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Ann Williams Dyscalculia, from a Teacher’s Perspective 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. Geoff Woolcott, Daniel Chamberlain & Rassoul Sadeghi

Conceptual Development in Mathematics: Longitudinal Connections from Network Analysis of Multiple Choice Assessments

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. Geoff Woolcott, Adam Harris, Jackie Reid & Robert Whannell

Enhancing Mathematics and Science Teacher Education in Regional Australia: Modules for Primary Mathematics Pre-service Teachers

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.

Caroline Yoon SPOT Diagrams of a Partially Correct Construct

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.

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Poster Presentations

Harry Kanasa The Ebb and Flow of Themes in 37 years of Mathematics Education Research by MERGA.

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.

Malin Lindwall Ehrnlund Using the Interconnected Model of Professional Growth as a Dynamic Tool for School Improvement

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.

Rumi Rumiati & Geoff Woolcott

Mathematics Learning and Exceptionality through a Complexity Lens

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.

Hazel TAN, NG Kit Ee Dawn & CHENG Lu Pien

Assessment Literacy among Primary School Mathematics Teachers

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.

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MERGA Executive Reports

President’s Report 2014 After last year’s successful conference in Melbourne it’s a pleasure to return to Sydney for our annual conference for the first time since 2001.

The individual Executive portfolio reports provide updates on a range of MERGA activities for the past year, so in this report I’ll highlight activities that relate specifically to the President’s portfolio and MERGA’s international presence.

One of the President’s responsibilities is to maintain liaison with other organisations with interests in mathematics education or educational research. From September 2013 to February 2014 I was fortunate to have a 6-month appointment at Loughborough University in the UK, working in the Mathematics Education Centre with Director Barbara Jaworski – recently elected as President of PME. This appointment afforded many informal opportunities for collaboration with UK colleagues and affirmed MERGA’s standing as an international mathematics education research organisation. Further support for this comes from PME’s decision to award the 2015 conference to an Australian team based at the University of Tasmania (led by Kim Beswick), with the conference to be hosted in Hobart. Plans are under way for the MERGA 2015 conference (to be held at the University of the Sunshine Coast) to link with the PME conference so that both events attract a substantial group of international delegates.

Within this same portfolio responsibility, MERGA continues to be represented through the President on the National Committee for the Mathematical Sciences (a discipline committee of the Australian Academy of Science). Over the past 12 months, the work of this committee has focused on creating a Decadal Plan for the mathematical sciences. Kim Beswick is chairing the sub-committee on mathematics and statistics education in schools and colleges. Tracey Muir oversaw preparation of MERGA’s submission to the decadal plan, and I am a member of the overall Steering Committee guiding development of the plan.

MERGA is also a member of Science and Technology Australia (STA, formerly FASTS), and my 2-year term as the representative of the Mathematical Sciences cluster of societies on the STA Board has now ended. John Henstridge, representing the Statistical Society of Australia, has assumed this role, and MERGA remains a member society of STA.

Another responsibility of the President’s portfolio is to ensure that MERGA is represented at meetings of international societies with which we are affiliated or of which we are members. There are many ways in which this goal can be fulfilled. For example, at the next ICME in Hamburg in 2016, many MERGA members have been invited to serve as Chairs or organising committee members of Topic Study Groups, Discussion Groups, and Survey Teams, or to give invited lectures. MERGA’s international presence is also strengthened through the service of members as editors of journals (in addition to our own MERJ and MTED) such as ZDM, the Journal of Mathematics Teacher Education, and Educational Studies in Mathematics.

Finally, as always, I want to thank all members of the MERGA Executive for their unflagging support and their dedication to serving MERGA.

Merrilyn Goos

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Treasurer’s Report 2014

Annual Statement

Following the 2012 vote at the AGM, the financial year has now shifted to align with the calendar and membership year (Jan – Dec). This report covers the audited 2013 accounts, which is the first year where the accounts for the calendar year have been presented. An update of the first half of 2014 will be given at the AGM in Sydney. Income for 2013 is $38550.00 while expenditure was $49530.00. At the AGM in 2013 the membership voted for MTED to be offered only online. This will mean that without the publishing and distribution costs a closer alignment of income and expenditure is expected in 2014. Full details of income and expenditure will be discussed at the Annual General Meeting to be held during the conference in July.

Annual Conference Accounts

Congratulations to the MERGA team for organising the Melbourne conference of 2013, which returned a close to budget conference with a small surplus.

Copyright and Royalties

The Copyright Agency Limited (CAL) distributes money collected as licence fees to MERGA for copyright charges it collects on our publications. The amount available for distribution each year depends on how much of the printed work copied is captured in CAL’s random audits of licence holders. During 2013 we received $2350.77 for copyright. In contrast, royalties from Springer are a more dependable source of income with $5086.30 received in 2013.

Term Deposits

Rates have stabilised this year in the term deposits. A number of years of surpluses have provided a solid foundation to MERGA’s financial health in recent years.

Janeen Lamb

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Vice President (Conferences) Report 2014

To begin this report I would like to give thanks on behalf of the MERGA executive and community to the 2013 MERGA 36 Melbourne team led by Vicki Steinle. The team hosted an extremely enjoyable conference for participants held at the Melbourne Graduate School of Education, Melbourne University. The final day overlapped with the biennial conference of the Australian Association of Mathematics Teachers. This offered MERGA participants an opportunity to engage in further discussions about mathematics education research and practice.

This year MERGA 37 is being held in another central Australian city, Sydney. A collaborative team of organisers from a range of Universities in Sydney have been working together to organise the conference. This includes Judy Anderson, Michael Cavanagh, Mary Coupland, Anne Prescott and Paul White. Thank you for your hard work in organising this conference.

Thanks also to all those who agreed to convene review panels this year and also to those who were panel members. This is an extremely important role which contributes to the success of the MERGA conference. In total nine panels comprising of mathematics education researchers with appropriate expertise were convened across Australasia. As in previous years each paper was independently reviewed by two panel members, and then the panels met as part of the process and discussed assessments and produced a single consensus report that provided the author(s) with detailed feedback. Panels used a flexible approach to the meeting process with some teams utilising conference calls, Skype meetings or video conferencing. Overall 105 papers were sent out for review this year including 40 papers which were included in the early bird submission process. This illustrates the popularity of this option for both new writers and those with more experience who wish to take advantage of the earlier submission time. The acceptance rate for papers to be both published and presented remained consistent with previous years with the final acceptance rate at 76%.

MERGA 38, 2015 moves away from the capital cities of Australia to the Sunshine coast. The organising team will be led by Margaret Marshman and the theme of the conference will be ‘Mathematics Education in the Margins’. The dates are set for Sunday 28th of June till Thursday 2nd of July. I am sure that this will be an enjoyable conference and those attending will appreciate the warm location.

We are currently in discussion about the venue for 2016 and this will be announced in due course.

To finish the report I would like to express my thanks to those who have supported me as I have undertaken my new role as VP conferences. To begin with thanks to Bobbie Hunter for the support she has provided in mentoring me into this role. I would also like to thank the MERGA president, Merrilyn Goos for both her leadership and the support she has given me and quick responses to any questions I have had. Finally I would also like to give my thanks to other members of the MERGA executive who have also been helpful.

Thanks for your support

Jodie Hunter

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Vice President (Development) Report 2014 Awards and Bursaries The Beth Southwell Practical Implications Award for 2013 was presented to Peter Gould at the 36th MERGA conference in Melbourne. In 2014, we received a small number of entries and unfortunately the judges felt that the papers were not of the high calibre required for the award. All entries received written feedback on their papers and encouragement to enter again in the future. There were no teacher bursaries applied for (or awarded) in 2014. Newcomers’ Function A Newcomers’ Function was held on the first day of the conference in July 2013. Approximately 35 attendees had the opportunity to meet other MERGA members, with approximately 20 also attending an additional workshop, ‘How to Manage your Supervisor’, which was aimed at Research Higher Degree students. In 2013, we continued with the MERGA buddy initiative and will do so again in 2014. Feedback from new MERGA members was sought through a survey with all 18 respondents reporting positive experiences. As a result of feedback received, the 2014 Newcomers’ Function will have more of a focus on interacting between members. Two MERGA members will be presenting the findings from a wider survey at this year’s conference (Newcomers’ Experiences at MERGA36 – Yvonne Semler/Michael Cavanagh). Projects with AAMT In my role as VP (Development), I am currently representing MERGA in the AAMT coordinated Connect with Maths Project. This project aims to build a dynamic education community to support Australian teachers of mathematics in intuitive, personalised and flexible ways. Teachers will access a range of networks and activities that support quality contemporary learning in the context of implementation of mathematics in the Australian Curriculum. More information is available at http://www.aamt.edu.au/Activities-and-projects/Connect-with-Maths. There are plans to launch two more communities: Maths in Action and Engaging Students, with both projects involving MERGA members. A feature of the Early Years Learning in Mathematics community was the hosting of a series of webinars which were well attended and available for downloading. The Make it Count resources are also available and there were a number of MERGA members who acted as evaluators and critical friends in the project. Unfortunately I could not attend the Reach for the Stars workshop this year. The theme for 2014 is ‘All about Water’. Once again, students, teachers and parents are invited to collect information and data related to the theme and submit it to AAMT as part of Literacy and Numeracy Week: https://literacyandnumeracy.gov.au/reach-stars In January I attended a AAMT workshop and worked with teachers and other MERGA members to devise materials for ESA around statistics and food. AAMT was commissioned to produce four mathematics units focussing on primary industry: dairy, cotton, fruit and wheat. The theme of food and fibre was used to inform students of some of the processes of production, marketing, consumption, and sustainable use of resources within a mathematics context. The resources will be published by ESA shortly and will be available through Scootle. A number of MERGA members have contributed to AAMT’s Top Drawer resources. There are currently 6 drawers: Fractions, mental computation, patterns, reasoning, statistics and geometric reasoning with plans to include more (http://topdrawer.aamt.edu.au/).

Tracey Muir

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http://www.aamt.edu.au/Activities-and-projects/Connect-with-Maths

Vice President (Communications) Report 2014

MERGA Newsletter

The format for the regular newsletter has been well received. MERGA members have continued to forward items of interest for publication in the newsletter and everyone is encouraged to continue to do so. News of conferences, seminars, webinars, forums etc. is most welcome, as is news of new publications that members might have written or know about. As well, we welcome information about new theses.

Membership

Currently MERGA individual membership stands at 220. This compares to a total of 144 individual members at this time in 2013. This is a healthy situation and indicative of the strength of the MERGA community.

Everyone is urged to be on the lookout for potential new members. MERGA is not a large community and its members, whilst they do improve with age, are not ageless! It is heartening to see a healthy number of new members attending the pre-conference seminar as we need a continued ‘supply of new blood’ to ensure a strong membership and of course, new ideas and ways of doing things are always needed and welcome. So if you know of anyone who might be interested in joining MERGA, ask them to sign up. We all know what a great organisation MERGA is and what we all gain from it.

AARE Special Interest Group (SIG)

Members will be aware of the idea of approaching the Australian Association for Research in Education (AARE) to establish a SIG for Mathematics and Science Education Research. This was put to the AARE membership in 2013 but insufficient interest was shown for the SIG to be established. Following discussions with some AARE members it was decided to try again this year with the proposed SIG to be titled STEM Education. Unfortunately, a similar response rate was received. Hence, plans to establish a SIG at AARE for either Mathematics and Science Education or STEM Education have been abandoned for the time being.

MERGA Membership Directory

Work continues on the MERGA Directory of Members and it is anticipated that this will be completed by the conference or shortly afterwards.

MERGA Website

All newsletters and attachments sent as part of newsletters are now stored on the website under the Communications menu. These newsletters are accessible to members and potential members.

Chris Hurst

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Conference Programme Overview Registration, Tea breaks and lunch are all in the Aerial Centre

Sunday 29 Monday 30 Tuesday 1 Wednesday 2 Teacher’s Day

Thursday 3

8.00 Registration 8.30 Registration 8.30 Registration 8.30 Registration

Clements -Foyster Keynote

Peter Galbraith 9.00 – 10.30 Jones/Harris

Session 7 9.00 – 9.40

Keynote

Barbara Jaworski 9.00 – 10.30 Jones/Harris

Session 18 9.00 – 9.40

Session 8 9.45 – 10.25

Session 19 9.45 – 10.25

Tea Break 10.30-11.00

Tea Break 10.30 – 11.00

Tea Break 10.30 – 11.00

Tea Break 10.30 – 11.00

Session 1 11.00 – 11.40

Session 9 11.00 – 11.40

Session 13 11.00 – 11.40

11.00am Closing Jones/Harris

Session 2 11.45 – 12.25

Session 10 11.45 – 12.25

Session 14 11.45 – 12.25

Registration Opens 12.30

Session 3 12.30 – 1.10

Session 11 12.30 – 1.10

Session 15 12.30 – 1.10

Newcomers Welcome

1.00 – 2.00 Agincourt

Lunch 1.15-2.15

Lunch 1:15-2:15

Posters on Display

Lunch 1.15-2.15

Posters on Display

Session 4 2.15 – 2.55

Session 12 2.15 – 2.55

Session 16 2.15 – 2.55

Workshop Reviewing Journal

Articles 2.30 – 4.30 Agincourt

Session 5 3.00 – 3.40

3.00 – 3.40 Poster

Presentations

Session 17 3.00 – 3.40

Conference Opening

5.00 pm and Keynote

Berinderjeet Kaur 5.30 – 6.45

Jones/Harris

Tea Break 3.40 – 4.15

Tea Break 3.40 – 4.15

Tea Break 3.40 – 4.15

Session 6 4.15 – 4.55

AGM 4.15 – 5.30

Jones Panel Discussion

4.15 – 5.15 Jones/Harris Policy Meeting

5.00 – 6.00 Jones

Welcome Reception

Aerial Centre 6.45 – 7.45

Conference Dinner Dockside Darling

Harbour 7.00 – 12.00

Happy Hour 5.30 – 6.30

Aerial Centre

Documents

Research guided practice · 2019. 12. 23. · Curriculum in focus: Research guided practice The 37th Annual Conference of the Mathematics Education Research Group of Australasia University