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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.

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.

This document contains 95 papers and summaries of 5 poster sessions from an Australian conference on putting vocational education and training (VET) research to work. The following are among the areas covered in the papers: factors affecting VET graduates' employability over time; technical and further education (TAFE) institutes as models of learning organizations; school noncompleters' outcomes in VET; increasing disabled students' participation in VET; VET management; bringing research and policy development together; innovative and flexible approaches to training package implementation; online support for VET clients; work-based learning; self-determined learning in the workplace; quality control and employability; using statistical software to interpret educational research; moving from andragogy to heutagogy in VET; drivers of learning cultures within organizations; VET practices in foreign countries; action research as action learning; challenges facing TAFE teachers; urban disadvantage and provider equity strategies; factors preventing uptake of apprenticeships and traineeships among secondary school adolescents; literacy and first-line management; performance level assessment; linkages between adult continuing education and VET; using training indicators to improve VET planning; student experiences of generic competency learning; managing the transformation to an e-learning organization; learning from small enterprise structured work placements; and using research to inform business and strategic decisions. Many papers include substantial bibliographies. (MN)

This document contains a total of 57 welcoming speeches, theme addresses, seminar and workshop papers, and poster sessions that were presented at a conference on technological education and national development. The papers explore the ways technology and technological advances have both necessitated and enabled changes in the way education is designed and delivered. The following are among the themes addressed in the individual papers: rival views of technology and their impact on education; the learning needs of older adults using information technologies; entrepreneurship education; lifelong learning on the World Wide Web; issues faced by polytechnics and institutes of technology as they respond to the challenges of Internet technologies and new media; working knowledge; flexible delivery; strategies for teaching technical students to be critical; development of curricula incorporating "hands-on" experience and interaction with industry; a framework for open, flexible, and distributed learning; models of online teaching; the transition from secondary to university education; digital curriculum databases; use of technology to foster authentic communication for second language students; labor and education dilemmas facing the Arab Gulf States; the future of women's colleges; universal education; English for workplace purposes; empathy as a paradoxical key to successful human learning futures; economic education; and funding problems of technical education in developing countries. Many papers include substantial bibliographies. (MN)

These proceedings consist of 66 conference papers on these themes: changing nature of work; emerging technologies; internationalization of vocational education and training (VET); enterprise and educational innovation; flexible delivery approaches; and research and technology and using technology in research. The papers are "Training Needs of Older Workers" (Ball et al.); "In Search of Evaluation Truths--Representation and Abstraction" (Barratt-Pugh); "Competency-Based Assessment--One-Minute Wonder or Here to Stay?" (Booth); "Technical and Further Education (TAFE) as a Pro-Active Partner in VET in Schools" (Bradbery, Murphy); "Work-Related Learning and Changing the Nature of Work" (Brown); "Improving the Incentives for Investment in Learning by Adults" (Burke); "Seductive Hope of Education Work" (Childs); "Managing a Case Study Approach in VET Research to Address the Funding Agency's Criteria" (Choy, Hill); "Constructing Work" (Crowley et al.); "Changing Nature of Work and the New Politics of Literacy" (Devereaux); "Key Competencies in Training Packages" (Down); "Facilitating Educational Growth" (Down); "Unintegrated Training? Exploring Links Between Off- and On-the-Job Learning" (Dymock, Gerber); "Leadership in VET" (Falk); "Outcomes for Apprentices and Trainees in Australian Small Enterprises" (Freeland); "National VET Research and Evaluation Program" (Gibb); "University-VET Transition" (Golding, Vallence); "Voices in VET" (Green); "Work as Paid Employment" (Hanrahan); "Trying to Hit a Moving Target" (Harris, Simons); "'There Are Workplace Trainers and Then There Are Workplace Trainers'" (Harris, Simons); "Measuring Organizational Capability" (Hase); "VET Research Information from Around the World" (Hayman); "Collaborative Insider Research in VET" (Herbert); "Researching VET and the Voluntary Sector" (Hopkins); "English Rules OK?" (Kell et al.); "VET in Rural Schools" (Kilpatrick et al.); "Contributions of VET to Regional Communities" (Kilpatrick et al.); "'I Am Still Studying, I Just Have Not Finished'" (Kirkby); "Lifelong Learning in the New Millennium" (Krogh); "Learning from History" (Kronemann); "Admin Training Company's Best Practice Models" (Lewanski); "RAVL Symposium" (McIntyre et al.); "Further Local Participation Study" (McIntyre); "Using Longitudinal Data for Research on VET" (McKenzie); "Value of Work-Based Learning" (McNickle);"Effectiveness of Workplace Training and Assessment Practices in On-the-Job Traineeships" (Misko et al.); "Impact of E-Commerce on Online Learning Systems in the VET Sector" (Mitchell); "Exploring Capacity-Building" (Modra, Seddon); "Relationship Between Course Design, Delivery, & Course Outcomes" (Moy et al.); "What Skill? Whose Knowing? Futures for Competency Based Training" (Mulcahy, James); "Management Education" (O'Keefe); "Strategic Alliances and the New World of Work" (Owen, Bound); "Outcomes from Enabling Courses" (Phan, Ball); "Selling TAFE Short" (Pitt); "Leadership of Change--TAFE Study" (Rice); "Learning and Assessment Issues in Apprenticeships and Traineeships" (Robertson et al.); "How Owner/Managers Decide to Participate with New Apprenticeships for the First Time" (Rowlands); "Impact of VET Research" (Smith); "Police Culture and the Learning Organization" (Shanahan); "Teenagers' Full-Time Work and Learning" (Smith); "Preparing Learners and Workplaces in the Effective Use of Flexible Delivery for Workforce Training" (Smith); "Research and Technology--Using Technology in Research--Implications for Researchers and the Researched" (Smyth et al.); "Implementing Training Packages" (Stewart); "Trainee and Apprentice Retention and Attrition in Australia" (Symons, Simons); "Measuring Performance" (Symons); "Workbased Learning as Critical Social Pedagogy" (Wagner, Childs); "Flexibility Through Technology--Lessons from the Field" (Walsh); "Equity in Australian Education and Training" (Watson, Pope); "Three Years Down the Track" (Webb, Gibson); "Best Practice in Managing Diversity in TAFE Distance Learning Centers" (Weeks); "Flexible Delivery Approaches--Evaluating Outcomes and Informing Learning" (Wemyss); "Introduction to the New Zealand Industry Training Sector and the Industry Training Federation" (Williams); "Current and New Research Tools and Techniques in Planning" (Young, Stockdale); "Measuring Long-Term Impacts of Short-Term Projects" (Young); and "In Their Own Words" (Zuvich). (YLB)

This volume comprises the refereed proceedings of the 2007 ATLAANZ (Association of Tertiary Learning Advisors of Aotearoa/New Zealand) conference. The first three chapters set the scene well for the breadth and depth of issues addressed by the authors. In Chapter 1, Andy Begg refers to his own educational journey in discussing the inseparability of educational experiences and outcomes from day-to-day life. In Chapter 2, Owen Ormsby stresses the importance of integrating the cultural attributes of indigenous people within education to achieve meaningful forms of success. Justin Heke, in Chapter 3, addresses the question of how to incorporate Maori (the indigenous people of New Zealand) perspectives and experiences into the content of national curricula. Chapters 4 to 6 address issues about the broader sense of identity of tertiary learning advisors. Susan Carter and Julie Trafford report in Chapter 4 on learning advisors' views about themselves and their work. Susan Carter in Chapter 5 then discuss how tertiary learning advisors consider it best to define their identity, practice, and profession. Barbara Morris in Chapter 6 examines the critical question of how the instruction and support provided by learning centres produce tangible benefits for institutes of technology and their students. The next three chapters describe initiatives in response to the ever-changing needs of students. In Chapter 7, Jude Robinson and Liz Kerry discuss methods for overcoming some of the social problems that online delivery of student support presents. In Chapter 8, Nishani Singh examines the appropriateness and practical implications of developing reflective skills in a postgraduate preparatory programme delivered offshore. And in Chapter 9, Caroline Malthus discusses issues arising from workshops to promote the development of students' spoken "literacy". In Chapters 10 to 12, the core tertiary learning advisor work of providing one-to-one support for students is examined. Margaret Wilson, in Chapter 10, investigates her own practice when working one-to-one with students on their writing. In Chapter 11, Catherine Mitchell looks into the facilitative role of emotions in one-to-one consultations. Then Lois Wilkinson, Natilene Bowker, Judith Deane-Freeman, and Sam Rullan discuss in Chapter 12 useful lessons learnt from an online pre-reading service they provide to distance students. The final two chapters in this volume deal with research. In Chapter 13, Emmanuel Manalo examines the role of research in the work of tertiary learning advisors. Then, in Chapter 14, Barry White describes an approach to teaching research methodology and interdisciplinarity workshops for postgraduate students. (Individual papers contain references.) [This report was produced by the Association of Tertiary Learning Advisors of Aotearoa New Zealand (ATLAANZ).]

This document contains the fifth volume of the proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 59 research reports by presenters with last names beginning between Sac and Zaz: (1) Bryan's Story: Classroom Miscommunication about General Symbolic Notation and the Emergence of a Conjecture during a CAS-Based Algebra Activity (Ana Isabel Sacristan and Carolyn Kieran); (2) A Teacher's Method to Introduce Story-Problems: Student-Generated Problems (Adalira Saenz-Ludlow); (3) "There's More than Meets the Eye": Analysing Verbal Protocols, Gazes and Sketches on External Mathematical Representations (Jonathan P. San Diego, James Aczel, Barbara Hodgson, and Eileen Scanlon); (4) Notions of Variability in Chance Settings (Ernesto Sanchez and Miguel Mercado Martinez); (5) Elementary Preservice Teacher Learning Levels (Victoria Sanchez and Miguel Mercado Martinez); (6) Mathematics Achievement: Sex Differences vs. Gender Differences (Dora Santos, Sonia Ursini, Martha Patricia Ramirez, and Gabriel Sanchez); (7) Self Assessment and Appropriation of Assessment Criteria (Leonor Santos and Anabela Gomes); (8) Drawing as Problem-Solving: Young Children's Mathematical Reasoning through Pictures (Carole Saundry and Cynthia Nicol); (9) The Role of the Teacher in Turning Claims to Arguments (Baruch Schwarz, Rina Hershkowitz, and Shirly Azmon); (10) Learning Mathematics for Teaching (Nanette Seago and Lynn Goldsmith); (11) Coherence of Mathematics Lessons in Japanese Eighth-Grade Classrooms (Yasuhiro Sekiguchi); (12) Triangle Property Relationships: Making the Connections (Penelope Serow); (13) Access to Mathematics versus Access to the Language of Power (Mamokgethi Setati); (14) Compartmentalization of Representation in Tasks Related to Addition and Subtraction Using the Number Line (Myria Shiakalli and Athanasios Gagatsis); (15)The Derivation of a Learning Assessment Framework for Multiplicative Thinking (Dianne Siemon, John Izard, Margarita Breed, and Jo Virgona); (16) Sources of Students' Frustration in Bridging Mathematics Courses (Anna Sierpinska); (17) What Makes a Good Problem? An Aesthetic Lens (Nathalie Sinclair and Sandra Crespo); (18) Discovering a Rule and Its Mathematical Justification in Modeling Activities Using Spreadsheet (Hong-chan Son and Hee-chan Lew); (19) Investigating Preservice Teachers' Understanding and Strategies on a Student's Errors of Reflective Symmetry (Ji-Won Son); (20) Exploring the Role Played by the Remainder in the Solution of Division Problems (Alina Galvao Spinillo and Sintria Labres Lautert); (21) Incomplete or Incorrect Understanding of Decimals: An Important Deficit for Student Nurses (Vicki Steinle and Robyn Pierce); (22) Proportional Reasoning: Variable Influencing the Problems Difficulty Level and One's Use of Problem Solving Strategies (Olof Bjorg Steinthorsdottir); (23) The Impact of the Intuitive Rule "If A Then B, If Not A Then Not B" in Perimeter and Area Tasks (Lambros Stephanou and Demetra Pitta-Pantazi); (24) Process-Object Difficulties in Linear Algebra: Eigenvalues and Eigenvectors (Sepideh Stewart and Michael O. J. Thomas); (25) Conceptual Changes as Dialectical Transformation (Nadia Stoyanova Kennedy); (26) Content Knowledge for Mathematics Teaching: The Case of Reasoning and Proving (Andreas J. Stylianides and Gabriel J. Stylianides); (27) "Making Proof Central to Pre-High School Mathematics Is an Appropriate Instructional Goal": Provable, Refutable, or Undecidable Proposition? (Gabriel J. Stylianides and Andreas J. Stylianides); (28) Power and Poverty--Whose, Where, and Why?: School Mathematics, Context and the Social Construction of "Disadvantage" (Dalene M. Swanson); (29) Documenting Learning in School-Based Mathematics Communities of Teachers (Paola Sztajn); (30) Research and Teaching--Can One Person Do Both? A Case Study (MichalTabach); (31) Computer "Knowledge" and Student's Images of Figures: The Case of Dragging (Varda Talmon and Michal Yerushalmy); (32) Graphics Calculators for Mathematics Learning in Singapore and Victoria (Australia): Teachers' Views (Hazel Tan and Helen J. Forgasz); (33) Vague Language in Greek and English Mathematical Talk: A Variation Study in Face-Work (Konstantinos Tatsis and Tim Rowland); (34) Teachers Using Computers in Mathematics: A Longitudinal Study (Michael O. J. Thomas); (35) Analysing Classroom Interactions Using Critical Discourse Analysis (Steve Thornton and Noemi Reynolds); (36) Pre-Service and In-Service Mathematics Teachers' Concept Images of Radian (Tahsin Topcu, Mahmut Kertil, Hatice Akkoc, Kamil Yilmaz, and Osman Onder); (37) Adaptive Expertise in the Number Domain 20-100 (Joke Torbeyns, Lien Vanderveken, Lieven Verschaffel, and Pol Ghesquiere); (38) Mathematical Activity in a Technological Workplace: Results from an Ethnographic Study (Chrissavgi Triantafillou and Despina Potari); (39) Pupils' Over-Use of Proportionality on Missing-Value Problems: How Numbers May Change Solutions (Wim Van Dooren, Dirk De Bock, Marleen Evers, and Lieven Verschaffel); (40) Arithmetical Procedures in the Solution of a Problem Involving Velocity (Veronica Vargas and Jose Guzman); (41) Introducing Algebraic Thinking to 13 Year-Old Students: The Case of the Inequality (Petros Verikios and Vassiliki Farmaki); (42) Why Is a Discontinuous Function Differentiable? (Antti Viholainen); (43) Overgeneralization of Linear Models: Presence and Characteristics among University Students (Monica Villareal, Cristina Esteley, and Humberto Alagia); (44) Educational Design Research in Mozambique: Starting Mathematics from Authentic Resources (Pauline Vos, Tiago G. Devesse, and Assane Rassul); (45) "The Big Test": A School Community Experiences Standardized Mathematics Assessment (Fiona Walls); (46) Numeracy Reform in New Zealand: Factors that Influence Classroom Enactment (Margaret Walshaw and Glenda Anthony); (47) An Investigation of Factors Influencing Teachers' Scoring Student Responses to Mathematics Constructed-Response Assessment Tasks (Ning Wang and Jinfa Cai); (48) Teacher Actions that Assist Young Students to Write Generalizations in Words and in Symbols (Elizabeth Warren); (49) Promoting Pre-Service Teachers' Understanding of Decimal Notation and Its Teaching (Wanty Widjaja and Kaye Stacey); (50) Impetus to Explore: Approaching Operational Deficiency Optimistically (Gaye Williams); (51) Generating and Evaluating Geometry Conjectures with Self-Directed Experiments (Chao-Jung Wu, Wing-Kwong Wong, Ying-Hao Cheng, and Yunn-Wen Lien); (52) The Distributions of van Hiele Levels of Geometric Thinking among 1st and 6th Graders (Der-bang Wu and Hsiu-Ian Ma); (53) Elementary Teacher Education and Teacher Efficacy toward Mathematics and Science (Su-Chiao Wu and Yu Liang Chang); (54) Spatial Rotation and Perspective Taking Abilities in Relation to Performance in Reflective Symmetry Tasks (Xenia Xistouri and Demetra Pitta-Pantazi); (55) Elementary Teachers' Mathematics Beliefs and Teaching Practices after a Curriculum Reform (Shirley M. Yates); (56) Inquiry Activities in a Classroom: Extra-Logical Processes of Illumination vs. Logical Process of Deductive and Inductive Reasoning. A Case Study (Oleksiy Yevdokimov); (57) Developments of a Child's Fraction Concepts with the Help of Psychological Tools: A Vygotsky's Cultural-Historical Perspective (Kaori Yoshida); (58) A Teacher's Treatment of Examples as Reflection of Her Knowledge-Base (Orit Zaslavsky, Guershon Harel, and Alfred Manaster); and (59) Cognitive Conflict and its Resolution via Pivotal/Bridging Example (Rina Zazkis and Egan Chernoff). (Individual papers contain references.)

This conference proceedings contains 65 presentations and 3 colloquiums from a conference that dealt with knowledge at work and knowledge that works and with how education can be successfully integrated into work and work into education. The papers are "Reading the Contexts of Complex Incidents of Adult Education Practice" (Apte); "Models of Work Based Learning for Undergraduates" (Armsby et al.); "Just-in-Time Training as Anticipative Action and as Inferential Understanding" (Beckett); "Learning to Compete" (Beckett et al.); "Co-Participation at Work" (Billett); "Globalization, Work, and Education" (Boland); "Work as the Curriculum" (Boud, Solomon); "Working Towards a Curriculum Framework for Work-Related Learning" (Brown); "Evaluating Organizational Change" (Butler et al.);"New Knowledge and the Construction of Vocational Education and Training (VET) Practitioners" (Chappell); "Facing Realities" (Cornford); "Subcontractors in the Australian Construction Industry" (Crowley et al.); "Learning; Design; Practice; Practitioner Perspectives of Workplace Learning" (Cys); "Learning at the Point of Production" (Daly, Mjelde); "Teaching Online" (Dewar, Whittington); "Spirituality of Work" (Dirkx); "Learning to Work" (Eames); "A Working Ethic?" (Edwards); "Transforming Management Education's Working Knowledge" (Elliott); "Negotiating Knowledge in the Knowledge Economy" (Farrell); "Work Knowing on the Fly" (Fenwick); "Productive Learning at Work" (FitzSimons); "Teachers Redefining Professionalism and Professional Development" (Gambell, Hunter); "Modelling the Invisible" (Gamble); "The New Capitalism" (Gee); "Conceptions of Learning" (Hager); "Recognition of Prior Learning in Higher Education" (Harris); "Promoting Knowledge Sharing in a Training and Further Education Organization" (Hill); "Incentives and Barriers to Learning in the Workplace" (Hodkinson et al.); "Reflections on Empowerment, Workplace Language and Literacy Policy, and Professional Development in England" (Holland); "Enabling Productive Learning at Work" (Holland, Leggett); "Learning Through Working" (Hopkins, Maglen); "Supervisor and Facilitation" (Hughes); "Writing-Up People at Work" (Jackson); "Whiteness as a Social Construct That Drives Continuing Education" (Johnson-Bailey, Cervero); "Knowledge Workers and the Office Economy" (Kurth); "Teaching with Global Awareness" (Lekoko); "Accrediting and Assessing Learning at Work" (Lyons); "Working Knowledge and Work-Based Learning" (McIntyre); "Working Knowledge in Management and Medicine" (Mulcahy); "Workplace Learning from a Curriculum Perspective" (Munby et al.); "The 'Good' Teacher?" (Nicoll); "Professional Identity as Learning Processes in Life Histories" (Olesen); "Local Perspectives on Globalization and Learning" (Payne); "Implementing Work-Based Learning in Higher Education" (Reeve, Gallacher); "Working Knowledge, Economic Metaphors, and the 'Cogito-Economic' Subject" (Rhodes, Garrick); "Technical and Vocational Education in China" (Rongguang); "Preparing Undereducated and Unemployed Parents for the Workplace Through Effective Family Literacy Programs in Texas" (Seaman, Seaman); "Working Knowledge of Online Learning Amongst VET Practitioners" (Schofield et al.); "Working Knowledge for New Educational Landscapes" (Seddon); "Links Between Corporate and Academic Research" (Shannon, Sekhon); "Towards a Definition of Work Based Learning" (Shaw); "Relationships Between R (Research) & D (Development) and Decision-Making in VET" (Smith); "Context Variety Means Four Stories?" (Smid); "Reflecting upon Experiences" (Staley); "Ordering the Menu" (Symes); "Critical Literacy, Cultural Inclusiveness, and Text Selection in English for Academic Purposes Courses" (Thompson); "Communicative Practices in Web-Enhanced Collaborative Learning" (Treleaven et al.); "Role of Emotion in Situated Learning and Communities of Practice" (Turnbull); "Alternative Conception of Competence" (Velde); "Learning in/Through/with Struggle" (von Kotze); "More Things Change" (Wallace); "Deschooled Learning" (Whittington, McLean); "Quality Online Participation" (Wiesenberg, Hutton); and "Emergence of New Types of Communities of Practice" (Young, Mitchell). (YLB)