The first volume of this proceedings contains the papers presented at the 21st annual meeting of the Mathematics Education Research Group of Australasia. Papers include: (1) "Research, Rhetoric and Reality" (Lyn English); (2) "I Keep Six Honest Serving Men" (Peter Galbraith); (3) "The Intension/Intention of Teaching Mathematics" (Stephen Lerman); (4) "One Teacher's Problem Solving Beliefs and Practices: Influences and Coherence" (Judy Anderson); (5) "Towards the Study of the Processes and Effects of Internationalisation in Mathematics Education" (Bill Atweh, Phil Clarkson, and John Malone); (6) "The Use of Action Research To Assist the Transition into Teaching" (Bill Atweh and Ann Heirdsfield); (7) "The Effectiveness of a No Goal Approach in Solving Pythagorean 2-Stage Problems" (Paula Ayres); (8) "Factors Influencing Predictions about Randomly Generated Sequences" (Paula Ayres and Jenni Way); (9) "Towards a Framework for Analyzing Power Relationships in Small Group Discussions" (Mary Barnes); (10) "Year 5 Students' Available and Accessible Knowledge of Decimal-Number Numeration" (Annette Baturo); (11) "Mathematics Curriculum and Development" (Andy Begg); (12) "The Impact of An Early Number Project on the Professional Development of Teachers" (Janette Bobis and Peter Gould); (13) "Arithmetic, Pre-Algebra, and Algebra: A Model of Transition" (Gillian Boulton-Lewis, Tom Cooper, H. Pillay, and L. Wilss); (14) "The Invisible Wall Project: Problem Solving Processes of Pupils Who Work on Problems with a Goal Which Cannot Be Reached" (Birgit Burchardtz and Martin Stein); (15) "'Why Are We Assessed in Mathematics?': The Views of Students" (Ken Carr); (16) "Developing a Framework for Viewing Affective and Knowledge Factors in Teaching Primary Mathematics" (Jean Carroll); (17) "Teachers' Understandings of the Role of Learning Activities" (Min-Pyng Chen); (18) "Showing and Telling: Primary Students' Outcomes in Data Representation and Interpretation" (Helen Chick and Jane Watson); (19) "Representing the Connectedness of Mathematical Knowledge" (Mohan Chinnapan, Michael Lawson, and Rod Nason); (20) "Beginning Teachers' Problems with Fundamental Mathematics" (Phil Clarkson); (21) "Investigating Students' Understanding of the Relationships among Quadrilaterals" (Penelope Currie and John Pegg); (22) "Rethinking What It Means To Understand" (Lyn English); (23) "New Times for Mathematics in Vocational Education and Training" (Gail FitzSimons); (24) "Exploring Avenues of Reflective Practice with Pre-Service Mathematics Teachers" (Sandra Frid, Ted Redden, and Chris Reading); (25) "Students' Perspectives on Using Computers and Graphing Calculators during Mathematical Collaborative Practice" (Vince Geiger); (26) "Identifying the Dilemmas in Early Mathematics Teaching" (Ann Gervasoni); (27) "'I Don't Know If I'm Doing It Right or I'm Doing It Wrong!' Unresolved Uncertainty in the Collaborative Learning of Mathematics" (Merrilyn Goos); (28) "Visual Reasoning and Teaching Styles in Mathematics Classrooms" (Kevin Hannah); (29) "Flexible/Inflexible: Clare and Mandy's Story" (Ann Heirdsfield); (30) "We Really Put Our Minds To It: Cognitive Engagement in the Mathematics Classroom" (Sue Helme and David Clarke); (31) "Maori Mathematics Education: The Challenge of Providing Immersion Programmes For Preservice Maori Primary Teachers" (Leeana Herewini); (32) "Towards an Explanation of Curriculum Control" (John Horwood); (33) "How Sixth Grade Students Explaining Connections between Common and Decimal Fractions" (Robert Hunting, Lauren Oppenheimer, Cath Pearn, and E. Nugent); (34) "Mathematics Curriculum Change in the Northern Territory: What Do Teachers Really Think?" (Rosemary Jacob and Sandra Frid); (35) "The Effective Use of Calculators" (Sonia Jones and Howard Tanner); (36) "New Knowledge/New Teachers/New Times: How Processes of Subjectification Undermine the Implementation of Investigatory Approaches to Teaching Mathematics" (Mary Klein); (37) "Affective Factors and the Improvement of Algebraic Problem Solving" (Saraswathi Kota and Mike Thomas); (38) "Tertiary Mathematics: Perceptions of School Levers and Mature-Age Students" (Gilah Leder and Helen Forgasz); (39) "There's More Than Meets the Eye: The Relationships between the User, the Teacher and the Technology" (Tom Lowrie); (40) "Pre-Service Teachers' Understandings of Word Problems" (Kevin Maguire); (41) "Protasis: A Technique for Fostering Professional Development" (John Mason); (42) "Towards a Psychology of Knowing-To" (John Mason and Mary Spence); (43) "School-Based Assessment in VCE Mathematics: Ten Years On" (Barry Mccrae, John Dowsey, and Max Stephens); and (44) "A New Trilemma" (D.F. Mckenzie). (ASK)