# MERGA Conference Proceedings 2019

### Full Conference Proceedings

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**KEYNOTES**

Using Learning Trajectories to Personalise and Improve Math(s) Instruction at Scale

*Jere Confrey*

From Children’s Thinking to Curriculum to Professional Development to Scale: Research Impacting Early Maths Practice

*Julie Sarama, Douglas Clement*

Applying and building on what we know: Issues at the intersection of research and practice (The Clements-Foyster Lecture)

*Dianne Siemon*

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**SYMPOSIA**

STEM and Digital Technologies in Play Based Environments: A New Approach

*Douglas Clement (Chair), Tom Lowrie, Kevin Larkin, Tracy Logan*

A study of school mathematics curriculum enacted by teachers in Singapore secondary schools: Singapore enactment project

*Berinderjeet Kaur (Chair), Toh Tin Lam Toh, Leong Yew Hoong, Tong Cherng Luen, Tay Eng Guan, Lee Ngan Hoe, Ng Kit Ee Dawn, Yeo Boon Wooi Joseph, Yeo Kai Kow Joseph, Liyana Safii, Cheng Lu Pien, and Toh Wei Yeng Karen, Quek Khiok Seng*

Research Methods Involving Children’s Drawings in Mathematical Contexts

*Joanne Mulligan (Chair), Amy MacDonald, Steven Murphy, Jennifer Way, Jennifer Thom, Kate Quane, Mohan Chinnappan, Sven Trenholm, Jill Cheeseman, Andrea McDonough*

** **

**RESEARCH PAPERS**

Working Towards Equity in Mathematics Education: Is Differentiation the Answer?

*Glenda Anthony, Jodie Hunter, Roberta Hunter*

Numeracy Across the Curriculum in Initial Teacher Education

*Anne Bennison*

“The Task is Not the Challenge”: Changing Teachers’ Practices to Support Student Struggle in Mathematics

*Janette Bobis, Michelle Tregoning*

Does the NAPLAN match the Australian Mathematics Curriculum?

*Paul Brown, Kok-Sing Tang*

Factors that Influenced Year 11 Students’ Choices to Use CAS for Selected Algebra Problems

*Scott Cameron, Lynda Ball*

“Because 7 and 8 are always in all of them”: What do Students Write and Say to Demonstrate their Mathematical Fluency?

*Katherin Cartwright*

How Do Teachers Learn? Different Mechanisms of Teacher In-Class Learning

*Man Ching Esther Chan, Anne Roche, David J. Clarke, Doug M. Clarke*

Using video-based mathematics lesson analysis to develop pre-service teachers’ reflective practice

*Samukeliso Chikiwa, Mellony Graven*

Teachers’ Perspectives on the use of Interactive Whiteboards in Mathematics to Support Students’ Learning

*Fiona Collins*

Mathematics in Initial Teacher Education Programs in Sweden, Germany, and Australia

*Audrey Cooke, Lars Jenßen, Eva Norén*

Pāsifika Students’ Perspectives and Understandings of Mathematics Embedded Within Their Lives Beyond the Classroom

*Libby Cunningham*

Re-thinking fraction instruction in primary school: The case for an alternative approach in the early years

*Chelsea Cutting*

Conceptualising the critical factors that influence teachers’ mathematics planning decisions for student-centred learning

*Aylie Davidson*

Impact of spiral teaching on quadratics: Action research with Grade 11 students in Mauritius

*Ridhwaanah Hanna Dhunny, Khemduth Singh Angateeah*

The Impact of Whole School Professional Learning on Students’ Multiplicative Thinking

*Ann Downton, Kerry Giumelli, Barbara McHugh, Tammy Roosen, Nadine Meredith, Geraldine Caleta, Melissa King, Kathryn Salkeld, Paul Stenning*

The Case of Disappearing and Reappearing Zeros: A Disconnection Between Procedural Knowledge and Conceptual Understanding

*Ann Downton, James Russo, Sarah Hopkins*

Use it or Lose it: Mathematics for Language Maintenance

*Cris Edmonds-Wathen*

Multi-Dimensional Instructional Frameworks: A Promising Form of Domain-Specific Instructional Design

*David Ellemor-Collins, Bob Wright*

The affective impact of inclusive secondary mathematics for learners with Down syndrome: “I just love it!”

*Rhonda Faragher, Kim Beswick, Monica Cuskelly, Karen Nankervis*

Introducing Guided Mathematical Inquiry in the Classroom: Complexities of Developing Norms of Evidence

*Jill Fielding-Wells, Kym Fry*

Strategy Use in Mathematics Assessment: Does Spatial Reasoning Matter?

*Alex Forndran, Tom Lowrie, Danielle Harris*

Undergraduates’ Uses of Examples in Introductory Topology: The Structural Example

*Keith Gallagher, Nicole Infante*

Designing Individual Goals to Enhance the Numeracy of Adults with Intellectual Disabilities

*Lorraine Gaunt, Jana Visnovska, Karen Moni*

Insights About the Progress of Grade 1 Children Who Are Mathematically Vulnerable and Participate in a Mathematics Intervention Program

*Ann Gervasoni, Anne Roche, Kerry Giumelli, Barbara McHugh*

What gendered constructs about mathematics do parents have as their children begin school in Australia?

*Rachelle Glynn*

Impact of a National Professional Development Program on the Beliefs and Practices of Out-of-Field Teachers of Mathematics

*Merrilyn Goos, Máire Ní Ríordáin, Ciara Lane, Fiona Faulkner*

Primary Pre-service Teachers’ Noticing of Structural Thinking in Mathematics

*Mark Gronow, Michael Cavanagh, Joanne Mulligan*

What Australian Students Say They Value Most in Their Mathematics Learning

*Cindy Di Han, Wee Tiong Seah*

STEM Learning Environments: Perceptions of STEM Education Researchers

*Vesife Hatisaru, Kim Beswick, Sharon Fraser*

Challenges in assessing mathematical reasoning

*Sandra Herbert*

Is ‘Capacity’ Volume? Understandings of 11 - 12 year old Children

*Angeline Ho, Heather McMaster*

Exploring the dynamics of changing teaching

*Sally Hughes*

Individualism and Collectivism: Examining Student Mathematical Identity in Hierarchal Grouping Arrangements

*Jennifer James*

Teacher Noticing of Primary Students’ Mathematical Reasoning in a Problem-solving Task

*Dan Jazby, Wanty Widjaja*

Student re-engagement and valuing of mathematics learning through an intervention program

*Penelope Kalogeropoulos, Michele Klooger, James Russo, Peter Sullivan*

Exploring 10th Grade Students’ Self-directed Learning in a Mathematics Problem-based Learning Classroom

*Napason Kampinkaew, Duanghathai Katwibun*

Maths anxiety and poor performance: Targeted tuition to break the vicious cycle

*Eugenie Kestel*

What can be more challenging than square-rooting from squared things?

*Igor’ Kontorovich*

Queensland Pre-service Teachers’ Beliefs on the Integration of Children’s Literature in Mathematics Teaching: A Pilot Case Study

*Kevin Larkin, Natthapoj Vincent Trakulphadetkrai*

Strength Based Grouping: A Call for Change

*Generosa Leach*

The Mathematics Enrolment Choice Motivation Instrument

*Ning Li*

The variability effect in high and low guidance instruction: A cognitive load perspective

*Vicki Likourezos, Slava Kalyuga*

Connecting Mathematics with Science to Enhance Student Achievement- A Position Paper

*Jake Little*

Enhancing a mathematics leader’s knowledge for teaching through a co-teaching situation

*Sharyn Livy, Marie Yanni, Ann Downton, Tracey Muir*

What is Mathematics Education for Children under Three? A Snapshot of Findings from a National Survey

*Amy MacDonald*

Subject Matter Knowledge: It Matters!

*Christine Mae*

Young children’s movement in outside spaces: could this reveal mathematical awareness?

*Catherine McCluskey, Joanne Mulligan, Penny Van Bergen*

Describing and Prescribing Classroom Practice: Do We Have a Common Language?

*Carmel Mesiti, David Clarke, Jan van Driel*

Developing Mathematical Resilience Among Diverse Learners: Preliminary Progress and Problematics

*John Griffith Moala, Roberta Hunter*

Exploring the role of visual imagery in learning mathematics

*Carol Murphy*

Practices contributing to Mathematics success in a low socioeconomic rural Victorian school

*Steve Murphy*

Investigation of 10th Grade Students’ Agency and Authority in a Mathematics Problem-Based Learning Classroom

*Phongwasu Naimsamphao, Duanghathai Katwibun*

Technology and the Knowledge Quartet

*Greg Oates, Rosemary Callingham, Seyum Getenet, Ian Hay, Kim Beswick, Damon Thomas*

An Analysis of Teacher Language in Primary Mathematics: A Comparison of Two Differing Approaches

*Lisa O’Keeffe*

Recognising Mathematical Giftedness

*Linda Parish*

A Large-scale PD Intervention for Improvement of Teachers’ Mathematical Knowledge in Disadvantaged Communities

*Sitti Patahuddin, Ajay Ramful, Siti Rokhmah*

Monitoring and Prompting Emergent Algebraic Reasoning in the Middle Years: Using Reverse Fraction Tasks

*Catherine Pearn, Max Stephens, Robyn Pierce*

Students’ understanding of randomness after an introductory tertiary statistics course

*Robyn Reaburn*

Lesson Study: Investigating How Facilitators Support Teacher Noticing

*Rachel Restani, Jodie Hunter, Roberta Hunter*

Place-based mathematics and Projection Augmented Landscape Models (PALM) on the Tiwi Islands: Building Powerful Aboriginal Hypothetical Learning Trajectory

*Joël Rioux, Michael Michie, Michelle Hogue, Rohan Fisher*

Learning Progressions for Students working within Level 1 of the New Zealand Mathematics Curriculum

*Julie Roberts, Vince Wright*

Yes, it is “immersion” of a sort, but not one that conduces to mathematical sense-making

*Sally-Ann Robertson, Mellony Graven*

The Impact of Teacher Interest-Led Inquiry on the Student Learning Experience

*Toby Russo, James Russo*

11th Grade Students’ Self-Beliefs in a Mathematics Problem-Based Learning (PBL) Classroom

*Supatchana Sangkaew, Duanghathai Katwibun*

An exploratory study on students’ reasoning about symmetry

*Rebecca Seah, Marj Horne*

The Heaviness of Objects and Heaviness of a Material Kind: Some 11 to 12-year-old Children’s Understandings of Mass and Density

*Leane Senzamici, Heather McMaster*

Assessment for Learning Techniques in the Pacific Island Context: What are Teachers’ Views?

*Penelope Serow, Julie Clark*

Impact of Teachers’ Participation in Networked Learning Community on Classroom Practices

*Cynthia Seto*

Addressing Language Barriers in Multilingual Statistics Classrooms: A Collaborative Study

*Sashi Sharma*

A Teacher’s Approach to Creating Learning Opportunities and Supporting Students to Make Contributions: A Case Study in Iran

*Sara Haghighi Siahgorabi, Jana Visnovska*

Primary School Teachers’ Experience of Mathematics Education

*Sarah Tamburri, Paula Mildenhall, Fiona Budgen*

Passing a Proof Message: Student-Teacher Communication Through A Commognitive Lens

*Eng Guan Tay, Weng Kin Ho, Lim Seo Hong, Yew Hoong Leong, Teo Kok Ming*

Learning from Their Mistakes - An Online Approach to Evaluate Teacher Education Students’ Numeracy Capability

*Thuan Thai, Kate Hartup, Adelle Colbourn, Amanda Yeung*

Teaching number fact and computational fluency: teachers’ perceptions and impact upon practice

*Catherine Thiele, Shelley Dole, Peter Carmichael, Jenny Simpson, Christine O’Toole*

Operationalize Mathematical Sophistication in a Collaborative Problem-solving: A Conceptual Paper

*Dung Tran, John Munro*

Tensions in mathematics home-school partnerships

*Bridget Wadham, Lisa Darragh, Fiona Ell*

Practicing Statistics in Year 4

*Jane Watson, Noleine Fitzallen, Suzie Wright*

Preschool Children’s Drawings of ‘Tall and Short’

*Jennifer Way*

Striking a Balance between Children’s Need of Support and Parental Roles in Mathematics Homework

*Daya Weerasinghe*

Learning through critiquing: Investigating students’ responses to others’ graphs of a real-life functional situation

*Karina Wilkie, Michal Ayalon*

Students’ Ability to Solve Mental Rotation Items: Gender Perspective Within a Disadvantaged Community

*Destina Wahyu Winarti, Sitti Maesuri Patahuddin*

Academic numeracy and first year undergraduate studies across six regional universities

*Geoff Woolcott, Linda Galligan, Robert Whannell, Margaret Marshman, Taryn Axelsen*

Studying Student Interactive Positioning in Collaborative Mathematics Problem Solving: The Case of Four Chinese Students

*Shu Zhang, Man Ching Esther Chan, Yiming Cao*

**SHORT COMMUNICATIONS**

Learning from Lessons: A Study on Structure and Construction of Mathematics Teacher Knowledge - First Results of German Case Studies

*Daniel Barton, Judith Huget*

A Comparative Analysis of the Pedagogical Content Knowledge for Teaching Secondary School Mathematics

*Brantina Chirinda, Kim Beswick*

Teacher and Students’ Experiences in the Oral Assessment

*Cho, Hyungmi, Ko, Eun-Sung*

Teaching as Professional Learning: towards a more sustainable model for mathematics teacher professional development

*Ban Heng Choy, Jaguthsing Dindyal*

On-line mathematics instruction: Augmenting or replacing the role of the teacher?

*Lisa Darragh*

Preservice Teachers’ Beliefs about Numeracy

*Diana Doust*

Can teachers adopting a more connectionist approach achieve better student performance in mathematics?

*Shyam Drury*

Mathematics Identity research: where have we got to and where to from here

*Mellony Graven, Einat Heyd-Metzuyanim*

Lower Secondary Students’ Perceptions of Mathematics Classroom Environment

*Vesife Hatısaru*

Narrative mathematical learner identities of high school learners

*Wellington Hokonya, Pamela Vale, Mellony Graven*

The perspectives of researchers when undertaking work involving cultural contexts in mathematics education

*Jodie Hunter, Jodie Miller*

Teacher self-efficacy: Impact on pedagogy

*Naomi Ingram, David Berg, Mustafa Asil, Jeff Smith*

Assessing Conditional Reasoning

*Christina W. Lommatsch, Warren W. Esty*

Analysing institutional identities authorised for South African foundation year teachers

*Roxanne Long*

Paradigm Shifts in Mathematics

*Terence Mills, Aimé Sacrez*

*From Arithmetic to Emergent Algebraic Thinking: Case Studies in Three Australian Schools
Joshua Moore, Greg Oates, Bruce White, Rosemary Callingham*

Interdisciplinary Mathematics and Science (IMS) Learning in the Primary School

*Joanne Mulligan, Russell Tytler*

The development of a spatial reasoning assessment interview in the primary grades

*Joanne Mulligan, Geoff Woolcott, Michael Mitchelmore, Brent Davis*

*Changing students' attitudes to mathematics through WebQuests: Evidence from Qatar
Carol Murphy, Nigel Calder, Abdullah Abu-Tineh, Nasser Mansour*

Transformation of comprehended ideas: A teacher’s choice of examples

*Lay Keow Ng, Jaguthsing Dindyal*

Effective Professional Learning: Improving Impact

*Michael O’Connor*

Teaching for the Conceptual Understanding of Fractions: The Role of the Official Curriculum

*Maria Quigley*

Relation between Mathematics Achievement, Fraction Magnitude Estimation, and Proportional Reasoning: A Cross-Cultural Study

*Ilyse Resnick, Micah B. Goldwater, Nora S. Newcombe*

The Mathematical Discourse in Instruction Framework as Knowledge Resource for Teachers

*Erlina Ronda*

From teacher churn to adaptive practice: Supporting out-of-field mathematics teachers’ transdisciplinary practice

*Colleen Vale*

Communicating mathematical concepts in diverse languages: Lessons from a cross-continental collaboration

*Pamela Vale, Mellony Graven, Jana Visnovska, Jose Luis Cortina*

An investigation of the effectiveness of screencast technology as an assessment tool in mathematics learning

*Tracey Walls*

A Conceptual Framework for Designing Pedagogical Problems to Investigate Mathematics Teachers’ Pedagogical Reasoning

*Kai-Lin Yang*

Teacher-student relationship and mathematical problem solving ability: Mediating roles of self-efficacy and math anxiety

*Da Zhou, Xiaofeng Du*

**POSTER**

Intermediate Frameworks and Design Tools Emerging from Iterative Process of Designing Data Modelling Activities

*Kai-Lin Yang*

**ROUND TABLES**

NAPLAN numeracy, single-sex schools, and SES

*Gilah Leder, Helen Forgasz*

Barely functional: students’ misconceptions of functions and related notation

*Michael Jennings, Merrilyn Goos, Peter Adams*

Developing an equitable opportunity to learn: Does withdrawing students do harm?

*Fiona McDiarmid, Heather Lewis*

Defining and Measuring Pre-service Teacher Satisfaction with Professional Teaching Experiences

*Joanne Goodell*

What does pedagogical reasoning imply for teachers of mathematics?

*Jaguthsing Dindyal, Ban Heng Choy*

Factors that influence teachers of Years 7-10 Mathematics adopting pedagogies that support students' development of STEM capabilities and 21st century skills

*
Rachael Whitney-Smith, Lorraine Day, Derek Hurrell*