資訊科技融入高中數學資優教育的實務研究

Abstract

資訊科技融入各科教學已是時代趨勢，高中數學資優教育中的加速教育與充實教育更是需要資訊科技的輔助，本研究主要針對加速教育與充實教育此二方面，作資訊科技融入教學設計的探討。 加速教育部分，運用資訊科技作教學素材的開發，以提升教學素材品質與學生學習效率，包含平面環境下與立體環境下的教學素材開發。範圍包括積化和差與餘弦定理的動態圖說證明(Dynamic Proof without Words)，讓學生在正規嚴謹的數學證明之外，多些不同的觀點去體會數學之美；並利用MathPS提供的準確定位與按鈕式互動功能，實作了排容原理等重要觀念。立體環境下的教學素材開發，以Cabri-3D為主要開發工具，用動態立體幾何的方式，模擬呈現立體圖形，協助學生培養清楚的空間概念。 充實教育部分，在GSP動態平面幾何環境下，引導學生作專題導向式學習研究，選定的題材是圓錐曲線，讓學生透過自己動手實作，對圓錐曲線的各種基本性質有更深刻的體會，再探討圓錐曲線的各種進階性質。並將圓錐曲線的性質應用到面積平分的研究，進而推廣到體積平分。體積平分部份改以Maple軟體環境下作立體曲面的呈現。

It is an inevitable tendency to apply info-technology to the school teaching. This is especially true to mathematical gifted education in high schools. With the assistance of info-technology, it becomes easy to accelerate the teaching programs and enrich the teaching materials. In this thesis, there are particular discussions referring to how info-technology contributes to the acceleration and enrichment in mathematical gifted education. To accelerate learn programs, the application of some softwares such as PowerPoint with MathPS, GSP, Cabri-3D are recommended. With these softwares, mathematics teaching materials are not only presented on plane but also displayed in three-dimensional pictures, which no doubt enhances the quality of teaching materials and students’ learning efficiency. For example, in addition to strict mathematical proofs, Dynamic Proof without Words of Product-Sum/Difference Identities enables learners to appreciate the insights of mathematics from various view points. Moreover, the mighty interactive functions in MathPS make it easier to illustrate some important concepts such as inclusion-exclusion principle, while Cabri-3D can help students to build clear ideas about dimension through dynamic solid geometry. As for the enrichment of teaching materials, GSP is a quite powerful dynamic geometry software to encourage students to explore projects. For instance, students would understand conic sections better by sketching the geometric patterns on their own with the help of this software. If students gain better understanding about the properties of conic sections, they could go further to such categories as area bisection and volume bisection. Besides, by using Maple, students can even sketch solid geometric patterns to help themselves comprehend the solid curves in volume bisection.