透過電腦輔助建構動態學習環境之研究

Abstract

數學教師在教學的過程中常會遇到許多的教學內容，在傳統的教學環境中無法讓學習者利用較為直觀的方式進行學習，然而在電腦及網路發達的現在，正可利用此一工具補充傳統教學模式的不足。 本研究將透過探討van Hiele的幾何思考層次、不同學習理論與CAL的關連性，及利用電腦軟體在數學學習上應用的實例。並藉由這些理論來實際發展數學教材，以及依據所使用軟體的特性，分別探討不同數學問題在教學上的實例及可行性。 在第三章中將利用Cabri Geometry及Cabri Java可在網頁中輕易呈現動態幾何的性質，並透過網頁相關而適當的連結，探索三角形中M-configuration這個問題。第四章中將透過Cabri Geometry、Cabri Java及Cabri3D將歐氏幾何與非歐幾何（上半平面及球面幾何）產生連結，希望讓學習者可透過相關網頁的呈現，由歐氏幾何進入非歐幾何的世界。所有的研究結果均透過網頁的呈現，網址為http://163.19.108.5/~liang/。

Mathematic teachers often encounter the problem that lots of the content cannot be learned by students in an ocular way. Nowadays, computers and network can be used as the supplement to the traditional learning environment and solve the problem. The study will discuss the”van Hiele five-phase learning model”, the correlation between learning theory and CAL , and the examples of using computer software in mathematical learning. Teaching material for mathematics is developed from these theories. Then the feasibility and instances of mathematical instruction are discussed according to the software used. In chapter 3, we explore the problem of “M-configuration in the triangle”, Cabri Geometry and Cabri Java are adopted. Dynamic geometry can be easily presented on the website and guided learning can be correlated through appropriate hyperlinks. In chapter 4, we show how Euclidean Geometries and Non-Euclidean Geometries (The Upper Half-Plane Model and Spherical Geometry) are connected by the use of Cabri Geometry, Cabri Java and Cabri3D. Learners can enter the domain of Non-Euclidean Geometries from Euclidean Geometries through the presentation of related hyperlinks. All results of study are presented on http://163.19.108.5/~liang/.