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Making Mathematics Vital: Proceedings of the Twentieth Biennial Conference of the Australian Association of Mathematics Teachers

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Making Mathematics Vital: Proceedings of the Twentieth Biennial Conference of the Australian Association of Mathematics Teachers Proceedings of the Twentieth Biennial Conference of The Australian Association of Mathematics Teachers Edited by M. Coupland, J. Anderson & T. Spencer © The Australian Association of Mathematics Teachers Inc., 2005 ISBN 1-875900-58-6 Published by The Australian Association of Mathematics Teachers Inc. GPO Box 1729 Adelaide SA 5001 Phone: (08) 8363 0288 Fax: (08) 8362 9288 Email: [email protected] Internet: www.aamt.edu.au MAKING MATHEMATICS VITAL: PROCEEDINGS OF THE TWENTIETH BIENNIAL CONFERENCE OF THE AUSTRALIAN ASSOCIATION OF MATHEMATICS TEACHERS Preface In these proceedings of the twentieth biennial conference of The Australian Association of Mathematics Teachers, Making Mathematics Vital, are many insights from people from all over the country and also overseas who enjoy meeting the challenge of that endeavour — making the learning and teaching of mathematics a vital enterprise. In these pages you will read about successes and also of indications where more effort and imagination is needed. You will read that the work continues and is unlikely to be any easier as we find new challenges in our paths. You will also read of the rewards for both teachers and learn- ers when connections are made and real learning occurs. The editors wish to thank the editorial committee for their support and hard work in bringing this proceedings to such a high standard in a short time. Members of the edito- rial committee are: Janette Bobis, Michael Cavanagh, Beth Southwell, Steve Thornton, and Paul White. We were greatly assisted in our task by Merrilyn Goos, who shared her experiences from the 2003 conference; and by Ann Belperio in the AAMT office. The panel of people to whom papers were sent for peer review was extensive and we wish to thank them all: Steve Arnold Sandra Frid Carolyn McGinty Howard Reeves Cathy Attard Sue Garner Mal McLean Noemi Reynolds Mary Barnes Vince Geiger Diane McPhail Dianne Siemon Dawn Bartlett Ann Gervasoni Ken Milton Len Sparrow Bernice Beechey Peter Gould Mike Mitchelmore Max Stephens George Booker Jim Green Will Morony Gloria Stillman Elizabeth Burns Peter Grootenboer Sharyn Moses Chris Stocks Rosemary Callingham Holly Gyton Greg Murty Paul Swan Mohan Chinnapan Anthony Harradine Denise Neal Jenny Tayler Garry Clark Judy Hartnett Zeffie Nicholas Sue Thomson Barbara Clarke Chris Horley Steven Nisbet David Tynan Rae Deeley David Keanan-Brown Peter Osland Elizabeth Warren Judith Falle Barry Kissane Kay Owens Jane Watson Rhonda Faragher David Leigh-Lancaster Cath Pearn Jenni Way Helen Forgasz Kym Linke Ray Peck Leigh Wood Pat Forster Tom Lowrie Thelma Perso Robert Yen Andrew Fraser Karen McDaide Cyril Quinlan Robyn Zevenbergen Editors: Mary Coupland, Judy Anderson, Toby Spencer. [ PREFACE ] ii MAKING MATHEMATICS VITAL: PROCEEDINGS OF THE TWENTIETH BIENNIAL CONFERENCE OF THE AUSTRALIAN ASSOCIATION OF MATHEMATICS TEACHERS Review process Submissions to the conference were called for in two formats, seminar papers and work- shops, with the possibility of either being subjected to peer review. These papers were reviewed blind by at least two reviewers. Papers were assessed as: 1. suitable for presentation at the conference and for publication in the proceedings, identified as ‘accepted by peer review’, 2. suitable for presentation at the conference and for publication in the proceedings, and 3. not suitable for the conference. Papers that were designated as (1) have been identified with an asterisk (*). [ REVIEW PROCESS ] iii MAKING MATHEMATICS VITAL: PROCEEDINGS OF THE TWENTIETH BIENNIAL CONFERENCE OF THE AUSTRALIAN ASSOCIATION OF MATHEMATICS TEACHERS Contents Keynote papers 2 Challenging mathematics and its role in the learning process Peter Taylor 11 Improving statistical literacy: The respective roles of schools and the National Statistical Offices Dennis Trewin 20 Keeping learning on track: Formative assessment and the regulation of learning Dylan Wiliam 35 Oversights and insights: Mathematics teaching and learning Sue Willis Seminar papers 43 Students’ conceptual understanding and critical thinking? A case for concept maps and vee diagrams in mathematics problem solving* Karoline Afamasaga-Fuata’i 53 Working mathematically in NSW classrooms: An opportunity to implement quality teaching and learning* Judy Anderson 60 The teacher’s role in collaborative learning* Mary Barnes 66 The empty number line: Making children’s thinking visible* Janette Bobis & Emily Bobis 73 Working mathematically to revitalise assessment* Rosemary Callingham 80 Working mathematically: The role of graphics calculators* Michael Cavanagh 87 Assessing highly accomplished teachers of mathematics* Barbara Clarke 93 Written algorithms in the primary years: Undoing the ‘good work’?* Doug M. Clarke [ CONTENTS ] iv MAKING MATHEMATICS VITAL: PROCEEDINGS OF THE TWENTIETH BIENNIAL CONFERENCE OF THE AUSTRALIAN ASSOCIATION OF MATHEMATICS TEACHERS 99 Supporting the Standards for Excellence in Teaching Mathematics in Australian Schools through the Specialist Schools Network in England and iNET, International Networking for Educational Transformation Graham Corbyn 106 Teaching trend and regression with computer technologies* Craig Davis & Pat Forster 113 Take ’em out of the equation: Student understandings of ‘cancelling’* Judith Falle 120 SAFEly does it with CAS: Where have we been, where are we going? Sue Garner 133 Drawing sense out of fractions* Peter Gould 139 Improving mental computation skills* Jim Green 146 Getting school maths online: Possibilities and challenges* Boris Handal & Tony Herrington 153 Evaluating online mathematics resources: A practical approach for teachers* Boris Handal, Parvin Handal & Tony Herrington 166 Mathematics and computers as ‘cognitive tools’ Rebecca Hudson 173 New York City school mathematics: What are the vital outcomes? Brian Lannen, Rhonda Horne, Neil Davis & Tom Frossinakis 179 Multiples of three and saving Australia in 1942* John Mack 186 Mathematical knowledge of some entrants to a pre-service education course* Heather Mays 194 The rewards and difficulties of working mathematically* Heather McMaster & Michael Mitchelmore 201 Improving whole class teaching: Differentiated learning trajectories* Judy Mousley, Robyn Zevenbergen & Peter Sullivan 209 Algebra outcomes for your K–9 class Thelma Perso 217 Box plots: Issues for teaching and learning* Romaine Saunders & Pat Forster 223 Mathematics: Dead or alive!* Beth Southwell 229 Action research for improving professional standards in mathematics* Beth Southwell 235 Relational thinking about numbers as a bridge to algebraic reasoning* Max Stephens 243 Mathematics for everybody: Implications for the lower secondary school* Steve Thornton & John Hogan 253 Lessons from research: Students’ understanding of statistical literacy* Jane M. Watson 261 Quality pedagogy and teaching in K–12 mathematics* Paul White 268 The year in which my love of maths changed: Pre-service primary teachers’ self-image as mathematicians* Sue Wilson & Steve Thornton [ CONTENTS ] v MAKING MATHEMATICS VITAL: PROCEEDINGS OF THE TWENTIETH BIENNIAL CONFERENCE OF THE AUSTRALIAN ASSOCIATION OF MATHEMATICS TEACHERS Workshop papers and notes 276 Geometer’s Sketchpad: Some basics Anna Austin 285 Constructing better mathematics classroom tests Priscila C. De Sagun 292 Activities to develop fraction concepts Richard Evans 300 Changing the focus of computation instruction in primary schools: Putting the research into practice Judy Hartnett 308 Algebra revisited* Marj Horne 316 Numeracy development: What it looks like in the classroom Chris Hurst 324 Exploring space and measurement with the ClassPad 300* Barry Kissane 333 The role of manipulatives in developing mathematical thinking* Linda Marshall & Paul Swan 338 Houdini, Fibonacci and Pythagoras: The link Mal McLean 344 From arithmetic to algebra: Helping to give the ‘letters’ arithmetic meaning — A consideration of algebra and algebraic thinking within the realm of arithmetic Ken Milton 348 Technology enhanced mathematics education Karim Noura 357 The Ethnomathematics website Kay Owens 363 Refreshing ideas for secondary mathematics lessons Cyril Quinlan 370 Let ’em fight it out: Arguing in my constructivist classroom Noemi Reynolds 375 Maths on a mat with Matt Matt Skoss 380 Benford’s Law Brett Stephenson 384 Decide, select, perform and make sense: Computation in primary mathematics* Paul Swan & Len Sparrow 392 Making ‘cents’ of spinners Ed Staples 395 Exact answers, old problems, and a new elementary function Seán Stewart 402 Energising secondary school mathematics through modelling with the graphics calculator* Allan White 409 Mathematical simulations using a spreadsheet Paul White 414 Mathematics Challenge for Young Australians Sue Wilson [ CONTENTS ] vi MAKING MATHEMATICS VITAL: PROCEEDINGS OF THE TWENTIETH BIENNIAL CONFERENCE OF THE AUSTRALIAN ASSOCIATION OF MATHEMATICS TEACHERS Keynote papers 1 MAKING MATHEMATICS VITAL: PROCEEDINGS OF THE TWENTIETH BIENNIAL CONFERENCE OF THE AUSTRALIAN ASSOCIATION OF MATHEMATICS TEACHERS Challenging mathematics and its role in the learning process Peter Taylor Australian Mathematics Trust Challenge is not only an important component of the learning process but also a vital skill for life. People are confronted with challenging situations each day and need to deal with them. Fortunately the processes in solving mathematics chal- lenges (abstract or otherwise) involve certain types of reasoning which generalise to solving challenges encountered in every day life. Mathematics has a vital role in the classroom not only
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