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

技术融入数学教育已经过去了20多年，现在每个人都可以在任何地点和时间使用这些技术。许多研究人员已经展示了利用技术学习的效果。然而这种方法并没有在学校中广泛使用。如今，变化的速度如此之快，我们每天都被各种定量信息包围，我们必须根据情况做出判断。对于生活在这样一个不断变化的世界中的学生来说，培养用定量信息模拟真实现象以及分析各种类型的模式和函数关系的能力。技术是培养这种能力的非常有用的工具。我们将正确使用数值数据、图表和表达式作为工具的能力称为“函数感”。开发了 CD-R 和网页电子教科书 (http://www.tsukuba-g.ac.jp/t/kakihana/kansu/) 来培养“功能感”。本研究中开发的材料提供了许多使用技术来观察不断变化的情况的机会。其中包括许多有趣的材料。通过这些材料，学生可以探索日常生活中多种函数的特点并解决问题。要完成这些活动，学生需要 Microsoft Office Excel、Cabri Geometry II plus 和 Cabri 3D（由 Cabrilog 开发）及其插件。所有学习者都可以使用这些软件。通过电子表格，学生和教师都可以更改与图形链接的数字数据，以探索函数的特征并解决问题。此外，通过使用 DGS，他们可以探索通过在计算机屏幕上移动几何图形绘制的函数。这样，学生就可以彻底解决每一个问题，并能同时观察图形、数值数据和数学表达式的变化，从而发现函数的特征。

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.