以SVG動態演示幾何證明題之研究
Abstract
數位學習的發展愈來愈成熟，應用的層面也愈來愈廣。其中除了具有文字資訊外，更有豐富的圖形展示。而在國中數學幾何證明題的學習上，學生常常只能透過純文字的方式來理解，往往缺少動態的圖形輔助說明。因此我們設計出一個可以模擬幾何證明演繹過程的自動化系統，並配合圖形和文字說明。系統讀取題目之後，會自動產生證明的過程，並呈現證明步驟文字和圖形。透過這個系統，希望能對幾何證明題的學習有所幫助。
本研究參考專家系統的原理，以XML的技術建立了幾何知識庫，配合SVG圖形的動態變化，以及AJAX的傳輸方式，成功的發展出一套自動化幾何證明系統。以幾何標記符號和規則表示式來建立XML規則庫，以及使用後向鏈結的方法來進行證明推論，並以證明樹的原理來呈現證明步驟，是本研究的重要成果。
The development of e-learning is more and more mature, and the applied level is also more and more wide. Among them, in addition to having text information, there are also abundant diagrammatic demonstrations. On the learning of geometry proof problems in mathematics in junior high school, student can only comprehend through pure literalness method, and usually be in need of a dynamic illustration with graph.So we design an automatic system that can simulate deductive process of geometry proof, and match with explanation with graph and text. After reading the topic of a problem, the system will produce the process of deduction automatically, and present the text and graph of deductive step.Through this system, we hope it is helpful to the learning of geometry proof problems. We develop an automatic system of geometry proof successfully on this research by making reference to the principle of expert system, building a geometry knowledge base by XML technique, matching with dynamic transformation of SVG graph, and the AJAX transmission way. We build up a XML rule base by using geometry symbol and rule expression, deduce by backward chaining method, and present proof step according to the principle of proof tree. These are the important results of this research.
The development of e-learning is more and more mature, and the applied level is also more and more wide. Among them, in addition to having text information, there are also abundant diagrammatic demonstrations. On the learning of geometry proof problems in mathematics in junior high school, student can only comprehend through pure literalness method, and usually be in need of a dynamic illustration with graph.So we design an automatic system that can simulate deductive process of geometry proof, and match with explanation with graph and text. After reading the topic of a problem, the system will produce the process of deduction automatically, and present the text and graph of deductive step.Through this system, we hope it is helpful to the learning of geometry proof problems. We develop an automatic system of geometry proof successfully on this research by making reference to the principle of expert system, building a geometry knowledge base by XML technique, matching with dynamic transformation of SVG graph, and the AJAX transmission way. We build up a XML rule base by using geometry symbol and rule expression, deduce by backward chaining method, and present proof step according to the principle of proof tree. These are the important results of this research.
Description
Keywords
數位學習, 幾何證明, XML, SVG, AJAX, E-learning, Geometry Proof, XML, SVG, AJAX