Full Conference Proceedings 

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The Practice of Mathematics Education

Peter Grootenboer



Appreciating the Intra-/Extra-mathematical Importance of Mathematics: AddedPedagogical Value Through Rapprochement and Synergy of Primary,Secondary and Tertiary Mathematics Teachers 

Elana Nardi

 Teaching to Learning and Research to Practice: Bridging the Fractal Divides

Peter Liljedahl 



Mathematical Sequences of Connected, Cumulative and Challenging Tasks inthe Early Years 

Janette Bobis, Ellen Corovic, Ann Downton, Maggie Feng, Jane Hubbard, Sharyn Livy, Melody McCormick, James Russo, Peter Sullivan

Supporting the Leadership of Mathematics in Schools

Jill Cheeseman, Ann Gervasoni, Aylie Davidson, Ann Downton, Sharyn Livy, James Russo Colleen Vale, Carmel Delahunty, Penelope Kalogeropoulos, Marj Horne, Michele Klooger

Key Shifts in Thinking in the Development of Mathematical Reasoning

Dianne Siemon, Max Stephens, Lorraine Day, Marj Horne, Rebecca Seah, Rosemary Callingham, Jane Watson, Greg Oates



Comparative Effectiveness of Example-based Instruction and van HieleTeaching Phases on Mathematics Learning

Saidat Morenike Adeniji, Penelope Baker

Senior High School Students’ Perceptions of Mathematics Teachers’Assessment Practices in Ghana

Fred Adusei Nsowah, Robyn Reaburn

Pre-service Teachers’ Re-constructed Geometry Disposition Scale: A Validityand Reliability Study in the Ghanaian Context

Stephen Rowland Baidoo, Robyn Reaburn, Greg Oates

Developing Pre-service Teachers’ Understanding of Numeracy

Anne Bennison

Exploring Visual Representations of Multiplication and Division in Early YearsSouth African Mathematics Textbooks

Tammy Booysen, Lise Westaway

Mathematics and Coding: How Did Coding Facilitate Thinking?

Nigel Calder

Understanding the Relationship Between Cognitive Activation and AcademicEmotions: A Comparison Between Students with Different MathematicsAchievements

Xin Chen

Reflection Model to Facilitate Teachers’ Adoption of the ConstructivistLearning Design

Lu Pien Cheng, Gayatri Balakrishnan, Zi Yang Wong, Ngan Hoe Lee

Considerations for Teaching with Multiple Methods: A Case Study of Missingvalue Problems in Proportionality

Sze Looi Chin, Ban Heng Choy, Yew Hoong Leong

Procedural Flowcharts Can Enhance Senior Secondary Mathematics

Musarurwa David Chinofunga, Philemon Chigeza, Subhashni Taylor

Making Visible a Teacher’s Pedagogical Reasoning and Actions Through theUse of Pedagogical Documentation

Ban Heng Choy, Jaguthsing Dindyal, Joseph B. W. Yeo

Perceptions of the Role of Primary Mathematics Leaders

Kate Copping

Resource Materials as Structured Guidance in Practice Change

Ellen Corovic, Ann Downton

Designing an Early Number Sequence for Teaching

José Luis Cortina, Jana Višňovská, Jesica Peña, Claudia Zúñiga

Teacher Agency and Professionalism in the Context of Online MathematicsInstructional Platforms

Lisa Darragh

Primary School Mathematics Leaders’ Actions that Facilitate EffectiveMathematics Planning and Support Teachers’ Professional Learning

Kerryn Driscoll

School Mathematics Leaders’ Support of Primary Teachers’ ProfessionalLearning in Meetings

Kerryn Driscoll, Jill Cheeseman

Methodological Choices Made When Using Design Based Research to ExploreMathematics Education: An Updated Analysis

Samuel Fowler, Chelsea Cutting, Deborah Devis, Simon Leonard

One Teacher’s Pedagogical Actions in Eliciting and Developing MathematicalReasoning Through a Contextually Relevant Task

Lauren Frazerhurst, Generosa Leach

How Big is a Leaf? Using Cognitive Tuning to Explore a Teacher’sCommunication Processes to Elicit Children’s Emerging Ideas About Data

Kym Fry, Lyn English, Katie Makar

Designing Specific Tools to Enhance the Numeracy of Adults with IntellectualDisabilities

Lorraine Gaunt

A Typology for Instructional Enablers of Mathematical Modelling

Vince Geiger, Peter Galbraith, Mogens Niss, Ben Holland-Twining 

George Preferred Learning Fraction Concepts with Physical Rather than Virtual Manipulatives

Seyum Getenet

The Role of Technologies to Enhance Pre-service Teachers’ Engagement in an Online Mathematics Education Course

 Seyum Getenet, Sue Worsley, Eseta Tualaulelei, Yosheen Pillay

Developing Proficiency with Teaching Algebra in Teacher Working Groups: Understanding the Needs

Vesife Hatisaru, Helen Chick, Greg Oates

Regarding STEM: Perceptions of Academics Revealed in Their Drawings and Text

Vesife Hatisaru, Andrew Seen, Sharon Fraser

Development of the Self-Efficacy-Effort in Mathematics Scale and itsRelationship to Gender, Achievement, and Self-concept

Ian Hay, Yvonne Stevenson, Stephen Winn

 Teacher STEM Capability Sets that Support the Implementation of Mathematics Active STEM Tasks

Ben Holland-Twining, Vince Geiger, Kim Beswick, Sharon Fraser

Assessing Mathematical Competence Through Challenging Tasks

Jane Hubbard, James Russo, Sharyn Livy

Developing Equitable Participation Structures

Roberta Hunter, Jodie Hunter

“It has the same numbers, just in a different order”: Middle School StudentsNoticing Algebraic Structures Within Equivalent Equations

Jodie Hunter, Jodie Miller, Alexandra Bowmar, Ian Jones

Using Waiata in Mathematics Teaching: Te Whakamahia o te Waiata I roto I tePākarau

Naomi Ingram, Amie Curtis

Influence of the COVID-19 Lockdown on High School Mathematics Teachers’Beliefs About Using Digital Resources

Mairaj Jafri

Playing the “Research Game” in Marginalised Fields

Robyn Jorgensen, Mellony Graven

Are Learners Referring to the General or the Particular? Discursive Markers ofGeneric Versus Empirical Example-use

Jo Knox, Igor’ Kontorovich

Impact of Listening Pedagogy on Mathematics Teacher Thinking DuringLesson Study

Aneesah Latife

Preparing Job-embedded Primary Mathematics Specialists to Lead in AustralianSchools

Laurinda Lomas

Aligning Mathematical and Musical Linear Representations to SupportFractional Reasoning

Tarryn Lovemore, Sally-Anne Robertson, Mellony Graven

Linguistic Influences on Mathematics Learning: The Relations betweenSpacing/Spatial Relationship in Handwriting Legibility, Visual-MotorIntegration (VMI), and Number Line Estimation

Hong Lu, Xin Chen

The Role of Mathematics Anxiety and Attitudes in Adolescents’ Intentions toStudy Senior Science

Erin Mackenzie, Kathryn Holmes, Nathan Berger

Identities of Mathematics Teacher Educators in a “Hybrid” Mathematics andMathematics Education Department

Margaret Marshman, Anne Bennison, Merrilyn Goos

Diagrams in Mathematics: What Do They Represent and What Are They UsedFor?

Manju Manoharan, Berinderjeet Kaur

A Comparison of Classroom Pedagogical Practice Named by Middle SchoolMathematics Teachers in Australia and Chile

Carmel Mesiti, Valeska Grau, David D. Preiss, Amaya Lorca

Teacher Questioning to Support Young Students to Interpret and Explain TheirCritical Mathematical Thinking

Chrissy Monteleone

The Role of Mathematics Learning in the Interdisciplinary Mathematics andScience (IMS) Project

Joanne Mulligan, Russell Tytler, Vaughan Prain, Peta White, Lihua Xu, Melinda Kirk

Exploring the Alignment Between Pre-service Mathematics Teachers’ Beliefsand Espoused Practice

Monica Mwakifuna, Carol Murphy

A Snapshot of Gender and Mathematics Anxiety in Years 5 to 8

Lisa O’Keeffe, Bruce White, Amie Albrecht, Melanie O’Leary

Numeracy Across the Curriculum in Initial Teacher Education

Kathy O’Sullivan, Merrilyn Goos

Teacher Actions to Progress Mathematical Reasoning of Five-year-old Students

Emily Pearce, Roberta Hunter

Wicked Problems as a Context for Probability Education

Theodosia Prodromou, Chronis Kynigos

Embodied Task to Promote Spatial Reasoning and Early Understanding ofMultiplication

Susilahuddin Putrawangsa, Sitti Patahuddin

Evaluating Factors that Influence Young Children’s Attitudes TowardsMathematics: The Use of Mathematical Manipulatives

Kate Quane

Problem-solving Proficiency: Prioritising the Development of StrategicCompetence

Bronwyn Reid O’Connor

Using Enabling and Extending Prompts in the Early Primary Years WhenTeaching with Sequences of Challenging Mathematical Tasks

James Russo, Janette Bobis, Anne Downton, Sharyn Livy, Peter Sullivan

Solving Multistep Problems: What Will It Take?

Rebecca Seah, Marj Horne

Building Understanding of Algebraic Symbols with an Online Card Game

Jiqing Sun

Primary Teachers’ Mathematical Self-concept and its Relationship withClassroom Practice

Matt Thompson, Catherine Attard, Kathryn Holmes

Teacher Views of Parent Roles in Continued Mathematics Home Learning

Pamela Vale, Mellony Graven

Supporting Pāsifika Students in Mathematics Learning

Mepa Vuni, Generosa Leach

Exploring the Potential for Student Development of the Big Ideas of Statisticswith Random Trials: The Case of the Mystery Spinner

Jane Watson, Noleine Fitzallen

A Call for Translational Research in Embodied Learning in Early Mathematicsand Science Education: The ELEMS Project

Jennifer Way, Paul Ginns

The Nature of Research on Pre-service Teachers’ Mental Mathematics: A BriefSystematic Review

Lise Westaway, Pam Vale

The Role of Mathematics Education in Developing Students’ 21st CenturySkills, Competencies and STEM Capabilities

Racheal Whitney-Smith, Derek Hurrell

Using Mathematics Curriculum Materials When Planning on Practicum: A CaseStudy of One Primary Year Three Pre-service Teacher

Susanna Wilson

Student Perspectives of Engagement in Mathematics

Kristin Zorn, Kevin Larkin, Peter Grootenboer



A Multifaceted Project Design to Understand and Build the Strengths of Out-offield Secondary Mathematics Teachers

Judy Anderson, Jannette Bobis, Kathryn Holmes, Helen Watts

Numeracy ≠ Mathematics: Numeracy and the General Public

Helen Forgasz

Intended Versus Enacted Curriculum: Teacher Knowledge and CurriculumChange at the Senior Secondary Level

Michael Jennings, Merrilyn Goos

What Makes Effective Leadership When Implementing Research-based, Equity driven Professional Learning and Development?

Jodie Hunter, Roberta Hunter, Viliami Latu, Robin Staples, Bridget Wadham 



Teacher Practices in the Mathematics Classroom Following ProfessionalLearning and Development: Association with Student Outcomes

Alexandra Bowmar, Roberta Hunter

Raising Teacher Expectations of Students’ Capabilities by Examining StudentWork Samples

Geraldine Caleta, Tammy Roosen

Concept Maps as a Resource for Teaching and Learning of Mathematics

David Chinofunga, Philemon Chigeza, Subhashni Taylor

Use and Development of Mathematical Processes During an Online EscapeGame

Megan Clune

Repurposing Bronfenbrenner’s Ecological Theory to Focus on Very YoungPreverbal Children’s Mathematical Engagement

Audrey Cooke

Challenges to Inclusive Teaching of Mathematicsin Aotearoa New Zealand

Lisa Darragh, Fiona Ell, Missy Morton, Jude MacArthur

Investigating High School Students’ Understanding of DecompositionTechniques in Mathematics

Michael Dennis

Co-teaching Mathematics in Flexible Learning Spaces: What is the Effect onPedagogy and Achievement?

Peter Dennis

A Comparison of Rational Number Word Problem Types Across Three Grade 4to 6 South African Textbook Series

Demi Edwards

Senior Secondary Probability Assessment Task Support for Development ofThinking Skills

Heather Ernst Finding

Effective Methods for Mathematics Learning: Concept Mapping as anAssessment Task

Tanya Evans, Inae Jeong

Pedagogical Factors Predicting Mathematics Achievement: Analysis of theTIMSS 2019 Large-scale Data

Tanya Evans, Timothy Bickers, Josephine Greenwood

Investigating Students’ Engagement with Teach-first and Task-first LessonStructures Incorporating Challenging Mathematical Tasks

Maggie Feng, Jannette Bobis, Jennifer Way

Making the Invisible, Visible: Supporting Numeracy in the Arts

Elizabeth Ferme

Enabling Students’ Critical Mathematical Thinking

Vince Geiger, Kim Beswick, Jill Fielding, Thorsten Scheiner, Gabriele Kaiser, Merrilyn Goos

Difficult Progressions in Multiplicative Thinking forPrimary Students

Ann Gervasoni, Kerry Giumelli, Barbara McHugh, Paul Stenning

Mathematics Teacher Noticing: Adapting Practices in the Online Environment

Anita Green

Application of the Legitimation Code Theory to the Draw a Mathematician andDraw a Mathematics Classroom Research

Vesife Hatisaru

Exploring the Incentive to Study a Higher-level Mathematics Course atSecondary School: A Western Australian Perspective

Gregory Hine

Understanding Mathematical Identities of Learners Who Chose MathematicalLiteracy in High School After Participating in After-school Mathematics Clubsin Primary School Wellington

Munetsi Hokonya

Teaching Demands for Mathematical Explorations

S. Jaysaree

Enhancing Mathematics Teachers’ Pedagogical Content Knowledge inCommunities of Practice

Osman Kasimu, Carol Murphy, Vesife Hatisaru, Robyn Reaburn

Spatialising the Pedagogy: Directions for Future Research

Tracy Logan, Tom Lowrie, Ilyse Resnick, Danielle Harris 

Towards Increasing Interest in Teaching School Mathematics as a Career

Houry Melkonian, Katie Makar

Addressing the Learning Gap Through Talk in Mathematics Classrooms

Carol Murphy, Tracey Muir, Damon Thomas

Mathematics Homework and Intergenerational Reproduction of Confidence

Lisa O’Keeffe, Carolyn Clarke, Sarah McDonald, Barbara Comber

Learners’ Affective Field During the COVID-19 Pandemic: PredictingPerceptions of Impact on Learning

Kaitlin Riegel

Working On and With Verbal, Visual and Gestured Confluences inMathematical Meaning-making

Sally-Ann Robertson, Mellony Graven

The Use of iPads in the Early Years: Investigating the Effectiveness of Apps in Mathematics Learning

Rebekah Strang

Beyond the Arithmetic Operation: How an Equal Sign is Introduced in the Chinese Classroom

Jiqing Sun

Is it “off-task”? Non-game Interaction During Game-based Mathematics Learning

Jiqing Sun

Action Learning as a Tool for Teachers: A Case of Promoting Self-regulated Learning Pedagogy to Secondary Mathematics and Science Teachers

Tamsyn Terry, Sitti Patahuddin

Designing Inquiry Tasks in Primary Mathematics

Kristen Tripet, Ruqiyah Patel, Olive Chapman

Developing Primary Teachers’ Teaching Practices Through Communities of Inquiry

Kristen Tripet, Jannette Bobis, Olive Chapman

Learning Mathematics as a Child of a So-called “Tiger Mother”

Daya Weerasinghe

The Influence of Traditional Mathematics Teaching and Assessment on the Pedagogical Use of Technology

Benjamin Zunica