在電腦套裝軟體環境下經營數學探究之研究

Abstract

現代科技在基礎教育改革的道路上，一直扮演著重要的角色。尤其數學探究活動在電腦應用軟體和網路環境的有力支持下，能有一個可供實作的學習環境，來幫助學生快速有效獲取有用的資料、以從事自主學習為導向的數學探索，並能促進合作學習與交流。 在第一、二章裡，我們回顧探究式學習的意義、特點及其歷史脈絡；並闡明應用電腦軟體輔助數學探究的學理上的依據。我們特別指出結合現代科技的數學探究所具備的自主性、探究性及實踐性等三項特色。 融合教育學習理論，參照“問題教學法”的教學模式，輔以多年的教學經驗，設計一項以學生為主體，以問題探索為核心，來進行數學探究活動的示例。在這項數學探究活動的示例□，我們將探討如何將實作的研究，應用到高中數學的専題研究與科展等兩項活動，提供學生有機會初步體驗數學研究的創造性過程。 利用電腦軟體GSP和Cabri 3D所提供的具有創新溝通機制與動態呈現兩項特點的環境，我們在第三、四兩章裡，透過一些數學的解題模組，設計模擬真實情境，來進行模擬與實驗，快速獲取資訊；根據觀察所獲得的結論，作進一步的猜想，在進行後續的推理與證明。希望在電腦軟體所營造的環境下，藉由問題的提出，經歷探索與解決問題的過程，讓學生體會數學的應用價值，並藉以培養學生應用資訊科技的能力。

Modern science and technology have been always playing a vital role in the reform of school education. In particular, the activities of mathematical exploring has been benefited from the learning environments supported by computer softwares together with nowadays web technology. Within these environments, students can retrieve necessary data efficiently, they can also conduct oriented study independently, followed by cooperative study and communication as well. The meaning and the feature of exploratory study together with its historical vein will be first recalled in Chapter 2. We explain the theoretical basis of computer-based mathematical exploring; we also point out that exploratory study of mathematics by using modern science and technology is characterized by the features of independency, exploration and practicality. Based on educational learning theory and the teaching module of "problem methodology", together with our teaching experience, a student oriented and problem centered illustrative example is proposed to demonstrate the processing of mathematical exploration. We show how to turn this style of training into student oriented programs of topic project and scientific research activity, so that students will successfully experience themselves the creative process of mathematical research. Taking advantage of the creative and dynamic learning environments provided by software including GSP and Cabri 3D, We will show in Chapters 3, 4 that students can be stimulated by imitating real situations, so that the students will obtain abundant information efficiently. Based on these observations, the students can make their own conjectures and then finally leads to their verifications. We hope that the students will be benefited from the performance of computer-based mathematical exploring together with computer-based problem solving, and lead finally to the appreciation of mathematics and its applications.