doi:10.1093/teamat/hrp003 Advance Access publication 13 March 2009

GeoGebra ç freedom to explore and learn*

LINDA FAHLBERG-STOJANOVSKAy

Department of Mathematics and Computer Sciences, University of St. Clement of Ohrid, Bitola, FYR Macedonia Downloaded from http://teamat.oxfordjournals.org/ at University of Melbourne Library on October 23, 2011

VITOMIR STOJANOVSKI

Department of Mechanical Engineering, University of St. Clement of Ohrid, Bitola, FYR Macedonia [Submitted November 2008; accepted January 2009]

We start by visiting the maths section of the web site answers.yahoo.com. Here, anybody can ask a question from anywhere in the world at every possible level. Answers are given by anyone who wants to contribute and then askers/readers rate the responses. A brief look here and it is starkly clear that our young people are struggling and their ability to think logicallyçthat is understand a problem, organize data into knowns and unknowns, explore possibilities and assess solutions is definitely on the decline. In our opinion, this is more insidious than the actual decline in their overall mathematics skills. Further, one is struck by the fact that technology seems to be contributing to this decline when in fact it should be the opposite. We then examine two question/answer cycles in detail and show how the freeware GeoGebra (www.geogebra.org GeoGebraWiki: www.geogebra.org/ wiki GeoGebraForum: www.geogebra.org/forum)çwhich gives the freedom to explore and learn to everyone, everywhere and at any timeçcan be of tremendous value to pupils and students in their understanding of mathematics from the smallest ages on up.

1. Introduction

There is no question that there is a decline both in the skill and interest level in mathematics and science among our young people. Many argue that these skills are not needed in everyday life and others argue that without these skills, we cannot compete in a global economy. Regardless of our thinking on this, the following is certainly true. Given any problem in life, one needs to be able to think about it logically. This means, understand what the problem is, organize data into knowns and unknowns, explore possibilities and assess solutions. These are crucial life skills. By its very nature—the process of learning and doing mathematics should significantly increase these capabilities. However, it seems that our students are not learning these skills and the integration of technology has not increased the development of these skills, as we had hoped. Why do we say this? What is the reason for this? What can we do to reverse this process and (hopefully) at the same time increase both their interest and actual skills in mathematics?

*For additional information see http://math247.pbwiki.com/GeoGebra y Email: lindas@t-home.mk ß The Author 2009 Published by Oxford University Press on behalf of The Institute of Mathematics and its Applications. . All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

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L. FAHLBERG-STOJANOVSKA AND V. STOJANOVSKI

2. Facing the Facts: answers.yahoo.com

Where do our young people go for help with their mathematics? Check out the mathematics questions at answers.yahoo.com. The questions come in every minute and range from the absolute most simple to complex questions from calculus and beyond. Answers are given by anyone who wants to contribute and again the range in quality and quantity is immense. Finally, the askers and readers rate the answers. This is a breathtaking view into what is happening with our young people and their mathematics education throughout the world. It is also an incredible opportunity for all kinds of mathematical exploration and we will show this through detailed consideration of two examples. Downloaded from http://teamat.oxfordjournals.org/ at University of Melbourne Library on October 23, 2011

3. Sample Problem 1...