幾何探索軟體之開發與應用

Abstract

van Hiele提出的幾何學習理論強調操作探索的重要性，然而受到傳統教學工具的限制，老師們很難將幾何圖形動態變化的歷程完整的呈現在學生面前，學生也常缺乏良好的探索工具，協助其能經由建構、操作、實驗、觀察、歸納及推理的學習活動來獲得幾何概念，本研究想藉由蓬勃發展的資訊科技來協助解決這些問題。 在目前的程式軟體中，Flash絕對是最具份量的網頁動畫開發軟體，透過Flash可以設計出富含創意與生命力的網頁動畫，ActionScript程式語言的使用更可以協助開發高互動性的探索軟體，但畢竟Flash主要是為網頁動畫而設計，直接拿它來開發幾何探索軟體有其不便性，本研究針對幾何軟體開發的需求創造出一套函數，並利用這些函數建構一系列的互動元件，使Flash成為開發幾何探索軟體的好幫手。而van Hiele的幾何學習理論、Duval的幾何圖形認知理解理論、Paivio的動態心像理論則提供研究者軟體設計的方向，本研究利用Flash開發一套動態幾何探索軟體—Geometry Player，並詳細介紹它的使用說明及在幾何教學上的應用，希望它能成為老師教學上的好幫手以及學生學習上的好夥伴。 現今的Flash不再只是網頁動畫軟體，也是開發互動式探索教材的利器，除了幾何軟體之外，如何利用Flash開發其它數學主題或領域的教材，根據所研發之軟體配合有效的教學策略進行教學實驗以評估學生的學習成效，是未來值得陸續研究的課題。

van Hiele proposed the geometric learning theory and emphasized that manipulations and explorations are important in geometric learning. Being restricted to instructional tools, teachers often have difficulties to present the dynamic process of geometric figures entirely. Students also are lack of well-designed tools helping them make constructions, manipulations, experiments, observations, inductions and reasoning. Applying information technology into geometric instruction may solve these problems. As we all know, Flash has been a powerful tool to create animations on the web. With Flash, we can design innovative and vital animations in the internet. With its strong functions, Flash ActionScript could be used to create highly interactive software. However, Flash is designed for the creating of interactive web pages. It is inconvenient to use flash to develop digital materials for geometric explorations. The purposes of study are aimed to create mathematics function library and use them to build a series of mathematic interactive symbols. After this development, the designs of geometric digital materials will be easy. Finally a geometry software called “Geometry Player” was developed. In designing this software, we referred to van Hiele’s geometric learning theory, Duval’s cognition comprehension theory of geometric figures and Paivio’s dynamic image theory. Some application examples are also included in this study. It is hoped that Geometry Player can be a good assistant for teachers and also a nice partner for students. Nowadays Flash is not only a software for designing animations on the web but also a powerful tool for creating highly interactive digital materials. How can Flash be used to develop digital materials for other mathematics topics and learning content, what are the effective applications of these digital materials, and what will be the effects on students’ learning, these need future study.