Developing an Integrated Learning Environment to Foster "Function Sense" by Using Technology in an e-Learning System

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More than 20 years have passed since technologies were incorporated into mathematics education, and now everybody can use these technologies at any place and time. Many researchers have showed the effects of learning with technology. And yet this methodology is not widely used in schools. These days the pace of change is so fast and we are surrounded daily by all kinds of quantitative information, about which we have to make judgments depending on the situation. For students living in such a changing world, developing the ability to model real phenomena with quantitative information and to analyze various types of patterns and functional relationships. Technology is a very helpful tool to foster this kind of ability. We call the ability to use numerical data, graphs and expressions appropriately as a tool, "Function Sense". An e-textbook on a CD-R and web pages (http://www.tsukuba-g.ac.jp/t/kakihana/kansu/) was developed to foster "Function Sense". The materials developed in this study provide many opportunities to use technology for observing changing situations. Many interesting materials are included. Through these materials, students can explore the characteristics of many kinds of functions in daily life and solve problems. To do these activities, students need Microsoft Office Excel, Cabri Geometry II plus and Cabri 3D (developed by Cabrilog) with the plug-ins. Each of these softwares is accessible to all learners. Through spreadsheets, both students and teachers can change numeric data linked to the graph to explore the characteristics of functions and to solve a problem. In addition, by using DGS they can explore a function drawn by moving geometric figures on a computer screen. As a result, students can tackle each problem thoroughly and can observe the change of graph, numeric data and mathematical expression simultaneously and thus find the characteristics of functions.