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This publication contains two papers on the implications of school decentralization for teacher education, student achievement, and democracy. The first paper, "Devolution in Education Systems: Implications for Teacher Professional Development and Pupil Performance" (Geoff Whitty), explores the way education reform movements for decentralization have developed generally by looking at how reforms have worked in England with some cross references to experiences in New Zealand and the United States. In doing so it reviews several studies and discusses the context in which reforms were installed. The conclusion notes that the overall benefits are not yet apparent and that reforms seem to intensify the links between educational and social inequality. The paper also notes that these reforms were part of a larger Thatcherite political project that must have influenced their effects. The second paper, "Decentralisation and Democracy" (Terri Seddon), argues that current educational reform is limited by its neglect of the interdependencies of development, democracy, and education; and that the character of decentralization is the key issue for debate. In three sections the paper comments on contemporary educational reform in Australia, discusses the consequences of decentralization for democracy, and suggests a way to reframe the problem of education reform to recognize the interdependency of development and democracy. (Contains 53 references.) (JB)

For learners to be individuals equipped with the 21st-century skills when they start business life after graduation, they must be able to gain these skills during their education. However, due to their nature, it's not possible for students to acquire these skills under a specific course. For these skills to be achieved, they must be integrated across all curricula. In this study, an evaluation was conducted to see whether various countries incorporate the 21st-century skills in their curricula, how these skills are applied, and how these skills should be handled in their curricula. Within the scope of this research, the curricula applied in Australia, New Zealand, Canada, England, Ireland, and Turkey were examined. When the 12 skills defined by the P21 platform are considered, it can be seen that all skills are interconnected and that one cannot fully exist without the other. It can be said that starting to gain these skills, which are required by the 21st-century professions and which employers expect from graduates, from an early age it is important for individuals to be properly and fully prepared for the future. In accordance with the 21st-century expectations, evaluations, educational materials, teaching methods, professional growth opportunities, and learning environments should all be synchronized to create a supportive framework that generates the 21st-century results for contemporary students. [This paper was published in: "EJER Congress 2023 International Eurasian Educational Research Congress Conference Proceedings," Ani Publishing, 2023, pp. 97-126.]

With smartphone saturation at 100% among Japanese university students, educators are developing new and innovative ways to bring them to the forefront of learning, ensuring students are as engaged with their technology in their formal learning as they are with their informal learning. Smartphones of today are small, portable, have high spec cameras, microphones, and a large storage capacity. These devices also allow for videos to be edited within applications on the smartphone itself, without the need for a separate and expensive computer and editing software. Aspects such as these make using smartphones to make Digital Stories (DS) one possible way to effectively use this technology for formal learning purposes. This paper shows the results of a paper-based survey and discusses preliminary observations conducted with 38 Japanese university students undertaking a short-term study abroad experience in Australia and New Zealand. [For the complete proceedings, see ED600837.]

Rural social work education and practice in North America underwent a revival in recent decades and remains a valid praxis and pedagogic model for the 21st Century. The paper posits through rigorous literature review and analysis there are numerous elements central to North American (U.S. and Canadian) and Commonwealth of Nations (U.K., Australia, etc.) rural social work that make this framework significantly germane to Filipinos. These include the necessity to function in an environment of marginal or stressed community, personnel resources and educational opportunities. Significantly, the generalist practice model comprises the core of North American rural social work; it also predominates in Philippine methodology. Both frameworks require robust client and social justice advocacy roles encouraging awareness of needs and aspirations of at risk populations. Indeed, social work researcher Thelma Lee-Mendoza reports that historically modern Philippine practice originated and is primarily organized from North American models. Rural social workers in the West, like their Philippine counterparts, are more typically generalists and innovative environmental operators. Daily they rely on profound survey and calculation of services and innovative ways to make them meaningful. The paper concludes by urging creative international and transnational research with a view towards optimizing service delivery.

Although gender differences in mathematics are smaller than they have been in the past, prominent voices still attribute these differences to a variety of fixed individual factors, such as genetic characteristics of men and women. We hold the alternative view that these differences can be ultimately attributed to malleable factors. From this vantage, societies could influence gender differences in mathematics by changing students' experiences in school. In this study, we built on prior work suggesting that mathematics anxiety causes lower mathematics scores. In particular, we found that mathematics anxiety entirely explains the gender differences evident in mathematics scores from the 2012 US Programme for International Student Assessment (PISA). Furthermore, we found that gender moderates the mediating role of mathematics anxiety: math anxiety is more detrimental for male than for female students. Because math anxiety is a malleable individual characteristic, we conclude that gender differences reveal more about gendered societal experiences than they do about innate characteristics of men and women. [For the complete proceedings, see ED629884.]

Research across five countries has identified inability to pay attention to mathematical detail -- the discipline of noticing -- is an issue in senior secondary school mathematics teachers. The test and questionnaire completed by an Australian cohort further identifies a reluctance to employ non-routine questions in assessments, with teachers concerned about damaging the trust relationship they enjoy with their students. As teachers fail to demonstrate strong ability in non-routine written test questions themselves, this paper questions whether there exists a 'conspiracy' between teachers and their students to avoid scrutiny of conceptual understanding.

Government regulations require businesses to improve their processes and products/services in a green and sustainable manner. For being environmentally friendly, businesses should invest more on eco-innovation practices. Firms eco-innovate to promote eco-efficiency and sustainability. This paper evaluates the eco-innovation performance of Organisation for Economic Co-operation and Development (OECD) countries with data envelopment analysis (DEA). Data were gathered from the world bank database and global innovation index report. Findings show that for most OECD countries, energy use and ecological sustainability are more important than other inputs and outputs for enhancing eco-innovation. [For full proceedings, see ED571459.]

As a contribution to honour the foresight of Ken Clements and John Foyster in founding MERGA [Mathematics Education Research Group of Australasia] 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.

Drawing on survey data from over 2000 parents, this paper explores the possibility of early-years swimming to add mathematical capital to young children. Using developmental milestones as the basis, it was found that parents reported significantly earlier achievement on many of these milestones. Such data suggest that the early years swim environment may offer enhanced opportunities for learning skills that help transition young children into formal schooling. This paper explores those milestones that are related to early mathematics.

This paper presents a critical analysis of literature relating to why males choose to become primary school teachers. Discussion within the paper concentrates on identifying and exploring connections between what is currently known about being a male primary school teacher and what motivates these men as they both pursue and practice within the profession. This paper reflects the preliminary investigations of a broader doctoral project that will examine the recruitment and retention of male primary teachers within Tasmania. Countries such as Australia, New Zealand and the United Kingdom have experienced calls for increased male recruitment to and retention in the primary teaching profession. Current research into the male primary school teacher experience offers strong arguments for the need to recruit and retain more men into primary teaching as well as many attempting to explain the reasons for low numbers of male classroom primary teachers. Interestingly, studies investigating the motivations of those men who choose to teach young children are far less common. The critical review of relevant literature allows for deeper understanding of present perceptions of the male primary school teacher and teaching experience to be established. In doing so, the paper emphasises exploration of the motivations of men who choose to be male primary school teachers, and proposes that it is within the exploration of male's attitudes towards and motivations to being a male primary school teacher that will elicit rich insight into how strategies currently utilised for the recruitment and retention of male primary teachers can be improved.

Mathematics education is highly regarded as a research field within our region, especially when compared to other fields within the broader education discipline. The field has been relatively cohesive, well organised and internationally influential in a universally strong field. Mathematics education research has developed and evolved in challenging times-- when other fields have become fragmented and lost vision--have we more to offer? This keynote paper considers the challenges we face as a field of research as we navigate our theoretical underpinnings and pedagogical practices, within both the mathematical sciences and broader education disciplines.

Mathematical knowledge in classrooms is mediated through the use of both technical and informal language. This paper is a report of a study of the language use of teachers as they examine students' work and discuss teaching for the topic of fraction operations. This provides a window on their pedagogical content knowledge and also on the way in which language is used to make sense of mathematical knowledge, either personally or for students. It was found that some mathematical knowledge appeared to be "taken as understood," perhaps because the expected words were used.

Mathematics in Australia specifies spatial reasoning as a general capability within the curriculum. However, psychological research to date limits spatial assessment to psychometric tests leaving little room for a well-defined spatial curriculum. Although there are clear relationships between mathematics and spatial thinking, the independence in the measurement of the two constructs in research literature is rarely explored. In the present study, professionals in the fields of STEM Education and Cognitive Psychology evaluated mathematics and spatial assessment items. The results show evidence for a distinction between the two constructs in the content of the items, however with a caveat that thoughtful selection of assessment items is crucial to ensure independence in the measures.

This is a record of the proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia (MERGA). The theme of the conference is "Mathematics: Essential research, essential practice." The theme draws attention to the importance of developing and maintaining links between research and practice and ties in with the joint day of presentations with the 21st biennial conference of the Australian Association of Mathematics Teachers (AAMT). This special feature highlights the benefits of collaboration between researchers, practicing classroom teachers, and curriculum developers. Volume 1 contains the following papers: (1) The Beginnings of MERGA (Ken Clements); (2) Teaching and Learning by Example: The Annual Clements/Foyster Lecture (Helen L. Chick); (3) Introducing Students to Data Representation and Statistics (Richard Lehrer); (4) Studies in the Zone of Proximal Awareness (John Mason, Helen Drury and Liz Bills); (5) Empowered to Teach: A Practice-based Model of Teacher Education (Janette Bobi); (6) Communicating Students' Understanding of Undergraduate Mathematics using Concept Maps (Karoline Afamasaga-Fuata'i); (7) Primary Student Teachers' Diagnosed Mathematical Competence in Semester One of their Studies (Karoline Afamasaga-Fuata'i, Paul Meyer and Naomi Falo); (8) An Online Survey to Assess Student Anxiety and Attitude Response to Six Different Mathematical Problems (Vincent Anderson); (9) Mathematical Investigations: A Primary Teacher Educator's Narrative Journey of Professional Awareness (Judy Bailey); (10) Describing Mathematics Departments: The Strengths and Limitations of Complexity Theory and Activity Theory (Kim Beswick, Anne Watson and Els De Geest); (11) Three Student Tasks in a Study of Distribution in a "Best Practice" Statistics Classroom (Anthony Bill and Jane Watson); (12) Teacher Researchers Questioning their Practice (Linda Bonne & Ruth Pritchard); (13) Imagined Classrooms: Prospective Primary Teachers Visualise their Ideal Mathematics Classroom (Kathy Brady); (14) Early Notions of Functions in a Technology-Rich Teaching and Learning Environment (TRTLE) (Jill Brown); (15) Collective Argumentation and Modelling Mathematics Practices Outside the Classroom (Raymond Brown and Trevor Redmond); (16) Visual Perturbances in Digital Pedagogical Media (Nigel Calder); (17) Professional Experience in Learning to Teach Secondary Mathematics: Incorporating Pre-service Teachers into a Community of Practice (Michael Cavanagh and Anne Prescott); (18) Young Children's Accounts of their Mathematical Thinking (Jill Cheeseman and Barbara Clarke); (19) Mathematical Reform: What Does the Journey Entail for Teachers? (Linda Cheeseman); (20) Year Six Fraction Understanding: A Part of the Whole Story (Doug M. Clarke, Anne Roche and Annie Mitchell); (21) Teaching as Listening: Another Aspect of Teachers' Content Knowledge in the Numeracy Classroom (Ngaire Davies and Karen Walker); (22) Essential Differences between High and Low Performers' Thinking about Graphically-Oriented Numeracy Items (Carmel M. Diezmann, Tom J. Lowrie and Nahum Kozak); (23) High School Students' Use of Patterns and Generalizations (Jaguthsing Dindyal); (24) The Teacher, The Tasks: Their Role in Students' Mathematical Literacy (Katherine Doyle); (25) Informal Knowledge and Prior Learning: Student Strategies for Identifying and Locating Numbers on Scales (Michael Drake); (26) Documenting the Knowledge of Low-Attaining Third- and Fourth-Graders: Robyn's and Bel's Sequential Structure and Multidigit Addition and Subtraction (David Ellemor-Collins, Robert Wright and Gerard Lewis); (27) Interdisciplinary Modelling in the Primary Mathematics Curriculum (Lyn English); (28) Students' Tendency to Conjoin Terms: An Inhibition to Their Development of Algebra (Judith Falle); (29) Towards "Breaking the Cycle of Tradition" in Primary Mathematics (Sandra Frid and Len Sparrow); (30) Exploring the Number Knowledge of Children to Inform the Development of a Professional Learning Plan for Teachers in the Ballarat Diocese as a Means of Building Community Capacity (Ann Gervasoni, Teresa Hadden and Kathie Turkenburg); (31) Technology-Enriched Teaching of Secondary Mathematics: Factors Influencing Innovative Practice (Merrilyn Goos and Anne Bennison); (32) Supporting an Investigative Approach to Teaching Secondary School Mathematics: A Professional Development Model (Merrilyn Goos, Shelley Dole, and Katie Makar); (33) Identity and Mathematics: Towards a Theory of Agency in Coming to Learn Mathematics (Peter Grootenboer and Robyn Zevenbergen); (34) Categorisation of Mental Computation Strategies to Support Teaching and to Encourage Classroom Dialogue (Judy Hartnett); (35) Student Experiences of VCE Further Mathematics (Sue Helme and Stephen Lamb); (36) Video Evidence: What Gestures Tell Us About Students' Understanding of Rate of Change (Sandra Herbert and Robyn Pierce); (37) The Role of Dynamic Interactive Technological Tools in Preschoolers' Mathematical Patterning (Kate Highfield and Joanne Mulligan); (38) Students Representing Mathematical Knowledge through Digital Filmmaking (Geoff Hilton); (39) What Does it Mean for an Instructional Task to be Effective? (Lynn Hodge, Jana Visnovska, Qing Zhao and Paul Cobb); (40) A School-Community Model for Enhancing Aboriginal Students' Mathematical Learning (Peter Howard and Bob Perry); (41) Benchmarking Preservice Teachers' Perceptions of their Mentoring for Developing Mathematics Teaching Practices (Peter Hudson); (42) Relational or Calculational Thinking: Students Solving Open Number Equivalence Problems (Jodie Hunter); (43) Scaffolding Small Group Interactions (Roberta Hunter); (44) Numeracy in Action: Students Connecting Mathematical Knowledge to a Range of Contexts (Chris Hurst); and (45) A Story of a Student Fulfilling a Role in the Mathematics Classroom (Naomi Ingram). Volume 2 contains the following papers: (1) Secondary-Tertiary Transition: What Mathematics Skills Can and Should We Expect This Decade? (Nicolas Jourdan, Patricia Cretchley and Tim Passmore); (2) The Power of Writing for all Pre-service Mathematics Teachers (Keith McNaught); (3) "Connection Levers:" Developing Teachers' Expertise with Mathematical Inquiry (Katie Makar); (4) Acquiring the Mathematics Register in te reo Maori (Tamsin Meaney, Uenuku Fairhall and Tony Trinick); (5) Teaching Ratio and Rates for Abstraction (Mike Mitchelmore, Paul White and Heather McMaster); (6) Setting a Good Example: Teachers' Choice of Examples and their Contribution to Effective Teaching of Numeracy (Tracey Muir); (7) Developing the Concept of Place Value (Mala Saraswathy Nataraj and Michael O. J. Thomas); (8) Interdisciplinary Learning: Development of Mathematical Confidence, Value, and the Interconnectedness of Mathematics Scales (Dawn Kit Ee Ng and Gloria Stillman); (9) Mathematical Methods and Mathematical Methods Computer Algebra System (CAS) 2006--Concurrent Implementation with a Common Technology Free Examination (Pam Norton, David Leigh-Lancaster, Peter Jones and Michael Evans); (10) A Concrete Approach to Teaching Symbolic Algebra (Stephen Norton and Jane Irvin); (11) Developing Positive Attitudes towards Algebra (Stephen Norton and Jane Irvin); (12) Changing Our Perspective on Measurement: A Cultural Case Study (Kay Owens and Wilfred Kaleva); (13) Enhancing Student Achievement in Mathematics: Identifying the Needs of Rural and Regional Teachers in Australia (Debra Panizzon and John Pegg); (14) The Growth of Early Mathematical Patterning: An Intervention Study (Marina Papic and Joanne Mulligan); (15) Whole Number Knowledge and Number Lines Help to Develop Fraction Concepts (Catherine Pearn and Max Stephens); (16) Identifying and Analysing Processes in NSW Public Schooling Producing Outstanding Educational Outcomes in Mathematics (John Pegg, Debra Panizzon and Trevor Lynch); (17) Teachers Research their Practice: Developing Methodologies that Reflect Teachers' Perspectives (Ruth Pritchard and Linda Bonne); (18) Teacher Professional Learning in Mathematics: An Example of a Change Process (Pauline Rogers); (19) Seeking Evidence of Thinking and Mathematical Understandings in Students' Writing (Anne Scott); (20) Utilising the Rasch Model to Gain Insight into Students' Understandings of Class Inclusion Concepts in Geometry (Penelope Serow); (21) Exploring Teachers' Numeracy Pedagogies and Subsequent Student Learning across Five Dimensions of Numeracy (Jane Skalicky); (22) The Complexities for New Graduates Planning Mathematics Based on Student Need (Carole Steketee and Keith McNaught); (23) Students' Emerging Algebraic Thinking in the Middle School Years (Max Stephens); (24) A Framework for Success in Implementing Mathematical Modelling in the Secondary Classroom (Gloria Stillman, Peter Galbraith, Jill Brown and Ian Edwards); (25) Eliciting Positive Student Motivation for Learning Mathematics (Peter Sullivan and Andrea McDonough); (26) Learning from Children about their Learning with and without ICT using Video-Stimulated Reflective Dialogue (Howard Tanner and Sonia Jones); (27) Dependency and Objectification in a Year 7 Mathematics Classroom: Insights from Sociolinguistics (Steve Thornton); (28) Pedagogical Practices with Digital Technologies: Pre-service and Practicing Teachers (Colleen Vale); (29) Procedural Complexity and Mathematical Solving Processes in Year 8 Mathematics Textbook Questions (Jill Vincent and Kaye Stacey); (30) Designing Effective Professional Development: How do we Understand Teachers' Current Instructional Practices? (Jana Visnovska); (31) "Doing Maths:" Children Talk About Their Classroom Experiences (Fiona Walls); (32) The Role of Pedagogy in Classroom Discourse (Margaret Walshaw and Glenda Anthony); (33) Australian Indigenous Students: The Role of Oral Language and Representations in the Negotiation of Mathematical Understanding (Elizabeth Warren, Janelle Young and Eva deVries); (34) Student Change Associated with Teachers' Professional Learning (Jane Watson, Kim Beswick, Natalie Brown and Rosemary Callingham); (35) Choosing to Teach in the "STEM" Disciplines: Characteristics and Motivations of Science, ICT, and Mathematics Teachers (Helen M. G. Watt, Paul W. Richardson and James Pietsch); (36) Percentages as Part Whole Relationships (Paul White, Sue Wilson, Rhonda Faragher and Mike Mitchelmore); (37) My Struggle with Maths May Not Have Been a Lonely One: Bibliotherapy in a Teacher Education Number Theory Unit (Sue Wilson); (38) Students' Conceptual Understanding of Equivalent Fractions (Monica Wong and David Evans); (39) Statistics Teachers as Scientific Lawyers (Joanne Woodward and Maxine Pfannkuch); (40) Developing Pedagogical Tools for Intervention: Approach, Methodology, and an Experimental Framework (Robert Wright, David Ellemor-Collins and Gerard Lewis); (41) Pedagogy and Interactive Whiteboards: Using an Activity Theory Approach to Understand Tensions in Practice (Robyn Zevenbergen and Steve Lerman); (42) International Perspectives on Early Years Mathematics (Jillian Fox); (43) Early Childhood Mathematics Education Research: What is Needed Now? (Bob Perry and Sue Dockett); (44) Trimangles and Kittens: Mathematics Within Socio-dramatic Play in a New Zealand Early Childhood Setting (Shiree Lee); (45) Children's Number Knowledge in the Early Years of Schooling (Ann Gervasoni); (46) Listening to Students' Voices in Mathematics Education (Brian Doig, Susie Groves, Coral Campbell, Judith Mousley, and Gaye Williams); (47) Students' Pedagogical Knowledge: A Source of Pedagogical Content Knowledge (Brian Doig and Susie Groves); (48) Research Enriched by the Student Voice (Gaye Williams); (49) Listening to Student Opinions about Group Assessment (Judith Mousley and Coral Campbell); (50) Profiles of Thinking Skills and Levels of Motivation in a Problem-Solving Task (Sarah Buckley, Mary Ainley and Pip Pattison); (51) An Investigation of Mathematics Strategies in Traditional School Contexts and Real-World Contexts (Julie Clark and Kathy Brady); (52) Maori Student's Perspective on Their Mathematical Journey Through Maori Medium (Leeana Herewini); (53) Some Methodological Considerations in the Estonian Study about Students' Beliefs in Mathematics: Is Triangulation Necessary? (Kirsti Kislenko); (54) Progress in Mathematics--Learning through Home School Partnership (Denise Smith and Gaynor Terrill); (55) Exploring Data Representation and Statistical Reasoning through Integrated Investigations in a Grade 2 Classroom (Karen Ahearn); (56) Reform and Assessment Practice: The Need for an Investigation (Julie Anderson); (57) Autobiographical Research and Mathematics Curriculum (Andy Begg); (58) Mathematically Gifted Students Managing School Transfer (Brenda Bicknell); (59) Improving Procedures for Effective Teaching (Murray Black, Farida Kachapova and Ilias Kachapov); (60) Using Counter-Examples and Paradoxes in Teaching Probability: Students' Attitudes (Murray Black, Farida Kachapova, Sergiy Klymchuk and Ilias Kachapov); (61) Using Cabri Geometry to Explore the Geometric Properties of Parallelograms in Year 7 Mathematics Classrooms (Sahar Bokosmaty); (62) Defining Teacher Knowledge Needed in the Teaching of Statistics at Primary School Level (Tim Burgess); (63) Year 12 Students' Participation in Higher Mathematics Courses (Mohan Chinnappan, Stephen Dinham, Tony Herrington and Dale Scott); (64) Pre-service Primary Teachers Developing Positive Attitudes towards Teaching Mathematics (Julie Clark); (65) Measuring the Effectiveness and Efficiency of Language-In-Use for Algebra Learning: A Multi-Level Nested Modelling and DEA Approach (Robert de la Serna); (66) Te Poutama Tau (TPT): An Indigenous Response to the Numeracy Development Project 2002-2006 (Wini Emery and Leeana Herewini); (67) "I Have a Fear of Maths and it Does Worry Me a Bit as a Future Teacher:" The Cycle of Maths Anxiety (Gillian Frankcom); (68) Using Electronic Handwriting and Tablet PCs to Enhance Distance Students' Understanding of First Year Mathematics at University (Linda Galligan, Birgit Loch, Janet Taylor and Christine McDonald); (69) Mathematical Modelling in CAS Clothing (Vince Geiger, Rhonda Faragher and Trevor Redmond); (70) The Cognitive and Pedagogical Affordances of Digital Learning Tools on Early Mathematical Development (Kristy Goodwin, Joanne Mulligan and John Hedberg); (71) Revisions and Extensions of a Pirie-Kieren-Based Teaching Model (Peter Hughes); (72) An Insight into Norwegian Students' Thoughts about Mathematics (Kirsti Kislenko); (73) The Impact of Didactical Contract on Students' Perceptions of their Intentional Learning Acts (Troels Lange and Tamsin Meaney); (74) The Impact of an Intervention on the Development of Mathematical Pattern and Structure in the First Year of Schooling (Joanne Mulligan, Mike Mitchelmore, Coral Kemp, Jennie Marston and Kate Highfield); (75) Activity Theory as a Framework to Analyse the Positive Influence of Formative Assessment on Student Learning (Trish O'Toole); (76) Teaching Geometry with CAS in the Junior Secondary Classroom: A Case Study (Warren Palmer); (77) Wanted: One Great Maths Teacher! (Pamela Perger); (78) Building Early Childhood Educators' Knowledge, Skills and Confidence in the Facilitation and Assessment of Young Children's Mathematical Learning (Bob Perry, Elspeth Harley and Sue Dockett); (79) CAS in the Middle Secondary Years: Strengths, Weaknesses, Opportunities and Threats (Robyn Pierce); (80) Myths and Positioning: Insights from Hermeneutics (Steve Thornton); (81) Misconceptions in Locating Negative Decimals on the Number Line (Wanty Widjaja, Kaye Stacey and Vicki Steinle); and (82) Proportional Reasoning: A Global or Localised Development? (Vince Wright). [Individual papers contain references, figures, tables, and appendices.