套裝軟體支援下之高中數學教學的動態呈現與探究

Abstract

資訊科技的蓬勃發展，讓我們的教學模式更加地多元化。如何運用資訊科技融入數學教學之中，是教育工作者目前主要的課題之一，亞洲方面尤其以中國大陸和新加坡最為積極。本研究主要針對高中數學教學的動態呈現與探究學習兩方面，作資訊科技融入教學設計的探討。 我們在第三章裡，選擇適合網路學習的單元，並依據所使用軟體的特性，以資訊科技的優勢，設計以學生為核心的教學模組和方法，取代傳統的教學內容。我們使用 MathPS 設計了視覺化動態圖說證明 (Dynamic Proofs Without Words) 的例說，讓學生在正規嚴謹的數學證明之外，亦能從其他不同的觀點來體會數學之美。此外，我們並利用 Excel 軟體設計了「改變參數看圖形變化」單元，希望學生透過實驗及觀察，對於參數與圖形的關係能有進一步的理解。 圖形與代數兩者相輔相成的結合，對學生在思考數學時，會有更佳的學習效果。在第四章中，我們先針對若干問題培養學生多樣化的思維。接著將透過 Cabri-3D 軟體以動態立體幾何的方式，模擬呈現立體的實物圖形，幫助學生建立清楚的空間觀念。最後，我們在動態平面幾何軟體 GSP 的環境下，藉由觀察探索與解決問題的過程，提供學生進一步體會數學探究活動中的創造性研究。

The innovation of information technology nowadays accelerates the variety of our teaching styles. It has became current major concerns for how instructors integrating the information technology with subject contents for mathematical teaching and learning in class worldwide for the past decades, especially in China and Singapore. The focus of this thesis is to study how info-technology contributes to mathematical exploring and its dynamic presentations in mathematics teaching in high school. In Chapter 3, some units that manifest internet-learning are chosen to develop student-centered teaching modules and methods. The advantages of old teaching style are replaced by the advantages of info-technology depending on the software used. Therefore, some examples of “Dynamic Proofs Without Words” show us dynamical ways of mathematical proofs within the environment of MathPS. In addition to strict mathematical proofs, it enables learners to appreciate the insights of mathematics from various view points. Moreover, the subjects “The change of graphs by changing the parameters” is developed by Excel. We hope that students will further understand the relationship between parameters and graphs by observing through various experiments. It contributes to better learning kind on thinking mathematics question by the combination of the graph and algebra. Students’ versatile ways of thinking for various questions are given in Chapter 4. We also show how to build clear ideas about the presentations of three dimension through dynamic solid geometry using the dynamic geometry software Cabri-3D. Finally, we will show how to be benefited from the process of mathematical exploring together with problem solving under the dynamic geometry software GSP, so that students can successfully experience themselves the creative thinking of mathematical exploring.