Barry Kissane

These collected papers are a record of the proceedings of the 33rd Annual Conference of the Mathematics Education Research Group of Australasia entitled, Shaping the Future of Mathematics Education. The conference is held in Fremantle, as was the previous conference a decade earlier. Keynote speakers are discussing issues that are emerging more sharply at the present time as the mathematics education community focus on the education of Indigenous children, the scope of the mathematics curriculum and ways in which the content might be taught effectively, and the significant role of technologies in teaching and learning in the twenty-first century. Research papers are featured from mathematics educators from all states and territories of Australia, from colleagues in New Zealand, and from overseas — United Kingdom, Singapore, United States of America, India, Thailand, South Africa, and Indonesia. Some participants are not only new researchers but also new to the conference. Many have been aided by experienced colleagues via the supervision process within their university and also by the Early Bird system coordinated by MERGA and the Organising Committee. I wish to acknowledge the advice, comments, and suggestions given as part of the Early Bird system by experienced MERGA researchers. Their generosity in many ways repays the help and advice they received from the MERGA community earlier in their own careers. All papers submitted for publication have been ‗double blind‘ reviewed by at least two experienced researchers and writers organised into review groups for the purpose. In some cases a third person also reviewed the paper. Only papers that have been accepted by two reviewers are published in these proceedings. In the ‗double blind‘ review process, neither the reviewer nor the author was named. Reviewers worked with a set of review guidelines produced by MERGA to work for consistency of outcome. My thanks are offered to the group coordinators, the reviewers, Emeritus Professor John Malone for his coordination of the process, and to the local Organising Committee. This set of proceedings includes abstracts and full papers for refereed research presentations, short communications of developing research, roundtable discussions, and symposia. Thanks are due to the co-editors, Barry Kissane and Chris Hurst, for their diligence and support in editing and compiling these proceedings. The conference has been organised by a group of mathematics educators from each of the five universities in Perth, the main education systems, and the Curriculum Council of Western Australia. There has been a wonderful sense of collaboration typical of mathematics educators in Western Australia. All has been achieved under the experienced and watchful eye of conference organiser, Dr. Jack Bana. My thanks and appreciation is offered to all. Len Sparrow Chair, Conference Organising Committee

This book is intended for use with the Casio fx-9860G AU graphics calculator. It includes a substantial revision to previous publications of MAWA over the past decade concerned with the earlier Casio cfx-9850G series of calculators. Over that decade, graphics calculators have continued to be the major opportunity for secondary school students to have regular access to technology for mathematical work, both in Australia and elsewhere. The exercises in each chapter have been designed to help develop specific calculator skills to know thoroughly where to find things on the calculator. The activities in each chapter serve a wider variety of purposes. In some cases they suggest some of the kinds of mathematical problems and situations that can be tackled using the calculator

Calculators are too often regarded as devices to produce answers to numerical questions. However, a graphics calculator like the Casio CFX-9850GB PLUS is much more than a tool for producing answers. It is a tool for exploring mathematical ideas, and we have written this book to offer some suggestions of how to make good use it when exploring ideas related to algebra. We assume that you will read this book with the calculator by your side, and use it as you read. Unlike some mathematics books, in which there are many exercises of various kinds to complete, this one contains only a few ‘interactions’ and even less ‘investigations’. The learning journey that we have in mind for this book assumes that you will complete all the interactions, rather than only some. The investigations will give you a chance to do some exploring of your own. We also assume that you will work through this book with a companion: someone to compare your observations and thoughts with; someone to help you if you get stuck; someone to talk to about your mathematical journey. Learning mathematics is not meant to be a lonely affair; we expect you to interact with mathematics, your calculator and other people on your journey. Throughout the book, there are some calculator instructions, written in a different font (like this). These will help you to get started, but we do not regard them as a complete manual, and expect that you will already be a little familiar with the calculator and will also use our Getting Started book, the User’s Guide and other sources to develop your calculator skills. Algebraic Modelling is one of the topics in General Mathematics, mainly because it is a fundamental idea in mathematics and in the applications of mathematics to the real world. Using algebra, we can build models of everyday situations and then use the models to help answer questions we may have. Producing tables of values, graphs and solving equations are all useful to this end. You will experience how the graphics calculator is a useful tool to aid us in these processes. Although we have sampled some of the possible ways of using a graphics calculator to learn about this topic, we have certainly not dealt with all of them.

As its title suggests, this book is intended to be a resource to help you to start using your calculator effectively. If you have never used your calculator at all, we suggest that you begin by working through the first few pages of this book with your calculator at your fingertips. Expect to make a few mistakes here and there, as the calculator is a very sophisticated device, and is capable of doing many more things than we will use in this series. If you have used the calculator before, you might still find it useful to refer to the book, in case there are things described here that you have not yet encountered. If you are an experienced calculator user, you may need to refer to the book only for particular purposes (such as to find out how to enter a program into the calculator). Many details of the more sophisticated aspects of using your calculator (such as statistical work) are dealt with in other books in this series. This book is only intended to be the first step. As well as advice on how to use the calculator, there are a few mathematical interactions for you to try, for which answers have been provided. These will allow you to make sure that you understand thoroughly how to use the calculator in the ways described. In addition to this book, there are other resources that you may find useful if and when you get stuck. Your fellow students and your teacher are likely to be the quickest way of getting the help you need. There is also a very detailed User’s Guide that comes with each calculator; you may be able to find a copy of this to use, particularly when you have a little experience with the calculator. We hope that you find this book a useful assistant for your early work with the calculator.