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Mathematics: Shaping Australia Proceedings of the Eighteenth Biennial Conference of the Australian Association of Mathematics Teachers Inc Proceedings of the Eighteenth Biennial Conference of The Australian Association of Mathematics Teachers Inc. 15–19 January 2001 Australian National University, Canberra ACT Mathematics: Shaping Australia Proceedings of the Eighteenth Biennial Conference of The Australian Association of Mathematics Teachers Inc. © The Australian Association of Mathematics Teachers Inc. 2001 ISBN 1 875900 47 0 Published by The Australian Association of Mathematics Teachers Inc. GPO Box 1729 Adelaide South Australia 5001 Telephone (08) 8363 0288 Facsimile (08) 8362 9288 Email [email protected] Internet http://www.aamt.edu.au All papers in these proceedings were subject to a blind review process. Mathematics: Shaping Australia Contents PAPERS No More (Red-Pen) Marking!............................................................................................ 8 Tony Allan Learning about Learning in Mathematics ...................................................................... 15 Anna Austin Mathematics Education in Thailand: From Kindergarten to Graphics Calculators .................................................................. 29 Nittayaporn Bunyasiri and Peter Jones Unsolved Problems and the Mathematics Challenge for Young Australians............. 38 John Dowsey and Mike Newman I Can Do Maths Too — Count Me In! ............................................................................. 45 Rhonda Faragher Reading the World with Math: Goals for a Criticalmathematical Literacy Curriculum........................................................................................................................ 53 Marilyn Frankenstein Curriculum Integration in the Middle School: Mathematics Meets History............... 65 Merrilyn Goos and Martin Mills Mathematics and Visual Literacy in the Early Years..................................................... 77 Rachel Griffiths Information Texts: a Road to Numeracy and Literacy .................................................. 81 Rachel Griffiths Enrichment In Mathematics: Catering for Able Students in Years 4 to 6.................... 86 Anne Joshua Open-ended Questions and Investigations for Years 7 to 10....................................... 95 Anne Joshua Parent Perceptions of the Teaching and Learning of Primary School Mathematics ............................................ 109 Paulene Kibble Algebra and Technology: Emerging Issues.................................................................. 120 Barry Kissane 3 Mathematics: Shaping Australia Assessing the Impact of CAS Calculators on Mathematics Examinations ................ 131 Barry McCrae and Peter Flynn Modelling Growth and Decay with the TI-83 and Excel............................................ 140 Frank Moya Literally Teaching Literacy In Maths: The Thebarton Senior College Experience.................................................................... 149 Derek Nash Indigenous Mathematics — A Rich Diversity.............................................................. 157 Kay Owens Mathematical Expectation in Gambling and Games of Chance ................................. 168 Robert Peard Counting On: An Evaluation of the Learning and Teaching of Mathematics in Year 7 ................... 179 Bob Perry and Peter Howard Assessing Numeracy in the Middle Years — The Shape of Things to Come........... 188 Dianne Siemon and Max Stephens Numeracy for National Development .......................................................................... 201 Beth Southwell Calculators: Shaping the Way Children Think ............................................................ 209 Len Sparrow and Paul Swan How Might Computer Algebra Change Senior Mathematics: The Case of Trigonometry.............................................................................................. 217 Kaye Stacey and Lynda Ball Mathematics is Stuffed ................................................................................................... 226 Paul Swan Strategies for Going Mental ........................................................................................... 236 Paul Swan and Len Sparrow Shaping Mathematical Ideas Visually........................................................................... 245 Steve Thornton What is the Value of Professional Journals for Shaping Teacher Development? ................................................................................................................. 255 John Truran 4 Mathematics: Shaping Australia WORKSHOPS The Victorian Early Years Numeracy Strategy ............................................................ 264 Cathy Beesey and Kim Hamilton Mental Computation: Shaping Our Children’s Success in Mathematics................... 265 Janette Bobis Shaping Assessment for Effective Intervention ........................................................... 271 Rosemary Callingham and Patrick Griffin Using Literacy Strategies in Mathematics Lessons ...................................................... 281 Leslie Casey Practical Activities in the Middle School Classroom................................................... 283 Leslie Casey How Much Algebra Do We Need to Teach Our Students? ........................................ 287 David Driver Polar Bears and Popcorn: Building Confidence in Low Achievers ............................ 295 Alison Flannery The Rule of 3 Comes Alive! Graphic, Numeric, and Analytic Representations in Real Time................................. 301 Mark Howell Asia Counts — Studies of Asia and Numeracy ........................................................... 310 Jan Kiernan and Howard Reeves Activities to Support the Shaping of Number Sense ................................................... 314 Brian J. Lannen Numerical Methods in Senior Secondary Mathematics .............................................. 330 David Leigh-Lancaster and Michael Evans BoxCars Hands-On Maths Games................................................................................. 338 Sharyn Livy Using Algebra in the Early Stages of its Learning ....................................................... 341 Ken Milton and Howard Reeves The Bicentennial Conservatory in Adelaide................................................................. 350 Carol Moule Working Mathematically: What Does It Look Like in the Classroom?...................... 352 Thelma Perso 5 Mathematics: Shaping Australia Aboriginal Numeracy..................................................................................................... 357 Thelma Perso Developing Skills in Writing Proofs Throughout Secondary School ......................... 363 Diane Resek Problem Solving Approach to Teaching Mathematics................................................ 368 Katrina Sims Characteristics of a Good Mathematical Investigation................................................ 370 Beth Southwell Not Another Worksheet! — Activities for Bright Maths Students ............................ 378 Jenny Tayler Listening to Children’s Learning — Using Conversation to Shape Children’s Understanding of Mathematics................ 387 John Truran Data For Primary Classrooms: Making Shape Out Of Chaos..................................... 395 Kath Truran Shaping Primary Teachers’ Beliefs About Mathematics ............................................ 403 Kath Truran Chaos and Disorder........................................................................................................ 411 Michael Wheal Shaping Mathematical Conflict in Australian Classrooms Using Peaceful and Humorous Means ......................................................................... 428 Allan White Index of presenters ......................................................................................................... 438 6 Mathematics: Shaping Australia PAPERS 7 Mathematics: Shaping Australia No More (Red-Pen) Marking! Tony Allan Can computers be used to test students of mathematics and mark their answers? Issues include: • What hardware is available? What software? • How secure is the software/hardware configuration? • Which kinds of questions can be tested by a computer? Which cannot? • What level of difficulty can be achieved in computer testing? • What about part marks for working out? • What can computers do that mere mortals cannot? (Like giving each student different numbers in the questions). This paper describes one product which addresses some of these issues. No more marking (with a red pen) sounds like one of those over-blown claims for the computer age that pop up periodically in the techno sections of newspapers and from the minds of populist television pundits. The holy grail of teachers! It reminds me of the confident claim made by the IT outfit I worked for in the 1980s in England. We were at the forefront of Image Processing. The software and hardware engineers were developing circuit boards, ROM chips and programs to implement the first tools for manipulating images — on some of the very first IBM-compatible PCs that were then emerging. We demonstrated a computer with a scanner card, an Image Processing card, a high-resolution video card, an optical disk reader and a printer card. A hand-written letter was scanned in; it appeared on the screen; we moved the word ‘not’ to a different part of the letter and printed the ‘fake’. The machine got too warm to demonstrate for more than a few minutes, but on this premise we trumpeted the first steps towards the paperless office. We also dabbled in optical character recognition; I do not think voice-recognition
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