Conference Proceedings Contents Foreword v Keynotepapers Professor David Clarke 3 Speaking in and about mathematics classrooms internationally: The technical vocabulary of students and teachers. Mr Phil Daro 8 Standards, what’s the difference?: A view from inside the development of the Common Core State Standards in the occasionally United States. Professor Kaye Stacey 17 Mathematics teaching and learning to reach beyond the basics. Professor Paul Ernest 21 The social outcomes of school mathematics: Standard, unintended or visionary? Concurrentpapers Professor Robyn Jorgenson 27 Issues of social equity in access and success in mathematics learning for Indigenous students. Professor Tom Lowrie 31 Primary students’ decoding mathematics tasks: The role of spatial reasoning. Professor John Pegg 35 Promoting the acquisition of higher order skills and understandings in primary and secondary mathematics. Associate Professor Rosemary Callingham 39 Mathematics assessment in primary classrooms: Making it count. Dr David Leigh-Lancaster 43 The case of technology in senior secondary mathematics: Curriculum and assessment congruence? Associate Professor Joanne Mulligan 47 Reconceptualising early mathematics learning. Professor Peter Sullivan 53 Learning about selecting classroom tasks and structuring mathematics lessons from students. Mr Ross Turner 56 Identifying cognitive processes important to mathematics learning but often overlooked. Associate Professor Robert Reeve 62 Using mental representations of space when words are unavailable: Studies of enumeration and arithmetic in Indigenous Australia. Professor Merrilyn Goos 67 Using technology to support effective mathematics teaching and learning: What counts? Dr Shelley Dole 71 Making connections to the big ideas in mathematics: Promoting proportional reasoning. Dr Sue Thomson 75 Mathematics learning: What TIMSS and PISA can tell us about what counts for all Australian students. Posterpresentations 81 Conferenceprogram 85 CrownConferenceCentremapandfloorplan 89 Conferencedelegates 93 Research Conference 2010 Planning Committee Professor Geoff Masters CEO, Conference Convenor, ACER Dr John Ainley Deputy CEO and Research Director National and International Surveys, ACER Professor Kaye Stacey Professor Mathematics Education, University of Melbourne Dr David Leigh-Lancaster Mathematics Manager, Victorian Curriculum and Assessment Authority Mr Ross Turner Principal Research Fellow, ACER Ms Kerry-Anne Hoad Director ACER Institute, ACER Ms Lynda Rosman Manager Programs and Projects, ACER Institute, ACER Copyright © 2010 Australian Council for Educational Research 19 Prospect Hill Road Camberwell VIC 3124 AUSTRALIA www.acer.edu.au ISBN 978-0-86431-958-6 Design and layout by Stacey Zass of Page 12 and ACER Project Publishing Editing by Carolyn Glascodine and Kerry-Anne Hoad Printed by Print Impressions Research Conference 2010 iv Foreword GeoffMasters Australian Council for Educational Research Research Conference 2010 is the fifteenth national Research Conference. Through our research conferences, ACER provides significant opportunities at the national Geoff Masters is Chief Executive Officer and a level for reviewing current research-based knowledge in key areas of educational member of the Board of the Australian Council policy and practice. A primary goal of these conferences is to inform educational for Educational Research (ACER) – roles he has policy and practice. held since 1998. He has a PhD in educational measurement from Research Conference 2010 brings together key researchers, policy makers and the University of Chicago and has published teachers from a broad range of educational contexts from around Australia and widely in the fields of educational assessment and overseas. The conference will explore the important theme of teaching and learning research. mathematics. The conference will draw together research-based knowledge about Professor Masters has served on a range of effective teaching and learning of mathematics and explore approaches to teaching bodies, including terms as founding President of that develop the mathematical proficiency of students and catch their interest in the Asia-Pacific Educational Research Association; President of the Australian College of Educators; mathematics from the early years through to post-compulsory education. Chair of the Technical Advisory Committee for We are sure that the papers and discussions from this research conference will the International Association for the Evaluation of Educational Achievement (IEA); Chair of make a major contribution to the national and international literature and debate on the Technical Advisory Group for the OECD’s key issues related to the effective teaching and learning of mathematics. Programme for International Student Assessment (PISA); member of the Business Council of We welcome you to Research Conference 2010, and encourage you to engage Australia’s Education, Skills and Innovation in conversation with other participants, and to reflect on the research and its Taskforce; member of the Australian National connections to policy and practice. Commission for UNESCO (and Chair of the Commission’s Education Network); and member of the International Baccalaureate Research Committee. He has undertaken a number of reviews for governments, including a review of examination procedures in the New South Wales Higher School Certificate (2002); an investigation of options for the introduction of an Australian Certificate of Education (2005); a national review Professor Geoff N Masters of options for reporting and comparing school Chief Executive Officer, ACER performances (2008); and a review of strategies for improving literacy, numeracy and science learning in Queensland primary schools (2009). Professor Masters was the recipient of the Australian College of Educators’ 2009 College Medal in recognition of his contributions to education. vii Research Conference 2010 viii Keynote papers Speaking in and about mathematics classrooms internationally: The technical vocabulary of students and teachers Abstract Presentation summary This presentation takes patterns of Classroom discourse (and professional language use as the entry point for discourse about classrooms) is a form the consideration of discourses in and of social performance undertaken about the mathematics classroom. within affordances and constraints These patterns of language take the that can be both cultural and linguistic. form of discourses performed within The nature of these discourses, as mathematics classrooms around the performed in mathematics classrooms, world and among the international provides a key indicator of pedagogical DavidClarke mathematics education community principles underlying classroom practice University of Melbourne about the mathematics classroom. and the theories of learning on which Cross-cultural comparisons reveal these principles are implicitly founded. David Clarke is a Professor of Education and how discourses in and about the The discourses about mathematics the Director of the International Centre for Classroom Research (ICCR) at the University mathematics classroom have developed classrooms give expression to these of Melbourne. Over the last 15 years, Professor in different cultures. Research is used pedagogical principles sometimes Clarke’s research activity has centred on capturing to explore the role of spoken language explicitly and sometimes through the complexity of classroom practice through a in mathematics classrooms situated embedding privileged forms of program of international video-based classroom research. The ICCR is unique in the facilities in Asian and Western countries. In practice in the naming conventions by it offers for the manipulation and analysis of conceptualising effective learning, which the mathematics classroom is classroom data and provides the focus for researchers, teachers and curriculum described. From research undertaken in collaborative activities among researchers from developers need to locate proficiency classrooms situated in different cultures, China, the Czech Republic, Germany, Hong Kong, Israel, Japan, Korea, New Zealand, Norway, the with mathematical language within it appears that both mathematical Philippines, Portugal, Singapore, South Africa, their framework of valued learning discourse and professional discourse Sweden, the United Kingdom and the United outcomes. Further, different cultures, take different forms and are differently States of America. Under Professor Clarke’s employing different languages, have valued in different communities. This direction the ICCR has developed a system for web-mediated, secure, high-speed data chosen to name and therefore privilege presentation draws on and connects entry, retrieval and analysis on an international different classroom activities. Research research into these two discourses. scale (videoPortal). Other significant research is reported into how language is has addressed teacher professional learning, and might be used to describe the The spoken metacognition, problem-based learning, and events of mathematics classrooms assessment (particularly the use of open- mathematics study ended tasks for assessment and instruction in in different cultures. Research and mathematics). Current research activities involve theorising undertaken in and about Research was conducted into the multi-theoretic research designs, cross-cultural those mathematics classrooms must situated use of mathematical language analyses and the