數學動態學習環境製作之研究

Abstract

本研究主要根據研究者為教育第一線的高級中學數學老師，藉由數學輔助軟體GSP, Cabri 3D, GeoGebra，根據教學經驗，融合教學與視覺思考，藉此讓教學更有效果，讓學生更容易吸收所需要的知識，利用具體的圖像協助學生學習抽象的定理，彌補傳統教學上的不足。

本論文分兩部分，第三章是數位內容的開發。圓錐截痕在以往的傳統教材中，大部分採三維模擬二維的方式講解，本研究用目前在三維空間使用最好的軟體--- Cabri 3D做為工具，不僅方便教師的教學，也讓學習者可不斷的重複觀看直到瞭解為止。

第四章是根據不同軟體製作的數位教材內容的比較，把同一題目，用三個目前普遍使用的數學軟體呈現--- GSP, Cabri 3D, GeoGebra做為工具來呈現，發現其彼此的優點，並補足彼此的劣勢，希望能妥善運用得宜，讓教學更有成效。

How to prepare course materials efficiently so that the students can easily catch abstract mathematical concepts in friendly environments is usually the main concern of high school teachers in mathematics. For efficient teaching and learning, how to prepare course materials by using appropriate packages of software is the theme of this research.

Based on teaching experiences in classes, the evolutions of courses materials from the traditional ways to the current information days are surveyed in Chapter 3. The evolutions is illustrated by the topic of conic sections; in particular, we show in detail how the classification of conic sections in traditional way in paper, and then gradually transformed into the presentation in GSP. Finally the classification is presented in Cabri 3D, three types of conic sections are presented efficiently, and the student hopefully will be convinced clearly and friendly.

Comparisons of course materials for various topics in high school level mathematics prepared by the packages of software including GSP, Cabri 3D, GeoGebra, commonly used in campus currently, are given in Chapter 4. Some prototype problems chosen from texts, entrance examinations, and mathematics competitions illustrated in various packages of software are given. Some procedures for preparing related course materials in detail are included.