在台灣的九年一貫數學課程綱要中，對於圖形與空間的學習，強調從生活經驗中著手，發現形體的組成要素及其與形體之間的關係，進而確立空間的概念。近年來虛擬實境等技術日趨成熟，廣泛的被應用到軍事訓練與娛樂產業上，但卻少有利用在學校基礎教育上。而且在數學幾何的學習上，不能單只靠公式的記憶，而是要透過豐富的操作、點數、切割、比較、拼湊等活動的進行，來建構其知識。所以，本研究發展『Web3D虛擬教室系統』來整合Virtual Manipulatives與多媒體電子白板來進行研究。本系統用使用Java來實作，並以Web3D的標準去建立幾何模型與場景，讓使用者可以透過網路來存取本系統的功能，因此學習者與教學者可以透過電腦以非同步的方式進行出題與解題的動作。並讓學習者在進行解題的過程，藉由操作3D的幾何物件，以建構式學習的方式來達成知識由具像到心像的過程。同時本系統整合白板工具至虛擬的場景中，讓學習者統整後的知識可以用多種表徵方式表達出來，進行問題解題或概念說明，也可以讓同儕以非同步的方式進行合作與互評，做到知識由心像到抽像的過程。 這篇文章最主要分成兩個部分。第一個部分是系統的開發與設計，以及相關文獻的探討，而第二部分是本研究對本系統進行兩次系統接受度的調查，並對學習者在使用本系統進行解題的作品做了初步的分析。結果顯示使用者同意本系統是有用的，並對易用性方面有正面的評價。 In this paper, an innovative and manipulative learning tool was proposed. We called it “Web3D Virtual Classroom System”. We used it to improve geometry problem solving based on the pedagogical theory: “The learning representation mode is from the concrete items to abstract ideas through physical or mental manipulation“. In Taiwan 9-year integrated curriculum syllabus, emphasizing the importance of learning geometric concept through real life experience. By that we hope for children can find the factors and relations from different kinds of geometric objects, and then to construct correct geometric concept. In recent years, the Virtual Reality technology has been applied in military training and video games etc., but it was rarely employed in formal educational context. And especially for geometry learning, learners should promote their understanding through coordination, integration and structuring activities with geometric objects. For above reasons, we have developed “Web3D Virtual Classroom System” by integrating virtual manipulative and multimedia whiteboard. That was mean learners can solve geometric problems with manipulating objects, and propose their solution on multimedia whiteboard. Furthermore. And we also involved the asynchronous cooperation by introducing peer assessment and solution revision mechanism. This paper was divided into two parts. In first part, we described literature discussion, system design and system development. In the second part, we investigated perceived acceptance of proposed system and students' solving methods from two system studies. The questionnaires' result showed that subjects agreed our proposed system is useful and they also had positive attitude to ease of use.
