國小數學情境文字題解題推理之研究

Research on Reasoning of Solving Mathematical

白文宗

指導教授 ： 葉耀明

國立臺灣師範大學/教育學院/資訊教育學系在職進修碩士班/碩士(2005年)

摘要

全球資訊網的蓬勃發展與寬頻網路的快速普及，帶動一股數位學習的熱潮。數位學習是不受時間、空間限制的一種學習方式，其符合現代多元社會不同的學習需求和模式，能真正落實全民教育、終身學習的目標。因此，如何應用資訊科技來建立良好的數位學習環境，是近年重要的研究議題。
在國小數學問題類型中，情境文字題是一般學童感到困難的題型，而透過資訊技術的輔助，可以協助學童運用推理能力，採取適當的策略來解題，發揮學習的動機及成效，建立解題性知識方面的數學能力。但是受到HTML網頁語法的設計限制，過去很少有成功的教學系統能在網頁上實作數學解題推理的教學。有鑑於此，本研究結合人工智慧研究領域中的自然語言處理技術，經由詞法分析、句法分析、語義分析、規則判斷等步驟來推論情境文字題的語意結構與運算結構，並採用XML應用技術領域中的MathML（數學標記語言）與SVG（可縮放向量圖形）語言規範技術，動態地將運算結構轉換為MathML及SVG文件標籤，在網頁上呈現情境文字題解題推理的運算過程與結果。
本研究進一步將上述情境文字題的自動推理建模應用到國小數學的整數加減法、分數加減法、整數乘法與除法等四個單元主題，共十五種題型類別合計489個文字題進行解題推理與呈現建模。透過推理建模效能評估，結果顯示本系統在上列的題型中已具備良好的推論能力。本研究期望國小學童可以透過本系統提供的自動推理建模來協助建立其解題性、概念性及程序性的數學能力，培養學童從推理中提昇邏輯理解與擴展知識延伸的深度及廣度。

關鍵字

數位學習 ； 情境文字題 ； 自然語言處理 ； MathML ； SVG ； AJAX

並列摘要

The fast development of World Wide Web and popularization of broadband network have driving an upsurge of e-learning. E-learning is a kind of study way that can not be limited by the time and space. It accords with modern plural society’s different study demand and way, can really implement the whole people’s education and goal of lifetime study. So, how to use information science and technology to set up good environment of elearning is the important research topic in recent years.
Students in primary school feel that the situation word problems are difficult among assessment problems of the mathematics. Experts believe that through the assisting of information and computer technology can help students to improve their reasoning ability, and to adopt the proper tactics to solve a problem. It can also bring the motive, improve the effect of study and set up the mathematics ability of solving a problem. In the past, with the restriction of HTML language, it is very difficult to develop a successful web-based tutoring system that can provide reasoning of solving mathematical problem. In view of this, this research develops a web-based reasoning of mathematical word problem using the natural language processing technology. Our system provides the steps of the morphological analysis, syntax analysis, semantic analysis and rule judgement to infer the semantic structure and operational structure of situation word problem. It also adopts the language of MathML and SVG to provide the web-based illustration of solving procedure in mathematical situation word problems.
In addition, this research applies above-mentioned system to the automatic reasoning and modeling of the mathematics situation word problem in primary school. The scope of our application includes addition and subtraction of the integer, addition and subtraction of the fraction, multiplication and division of the integers. There are 489 mathematics situation word problems among 15 problem types developed in the system. The result shows that this system has already possessed good inference ability in the above-listed question types. This research expects the automatic reasoning and modeling to be used for setting up students’ capability in solving a problem, and in building the mathematical conceptual and procedural knowledge in primary school with the development of this system. It can train students to promote their logical understanding and expand the depth and scope of mathematical knowledge.

並列關鍵字

E-learning ； situation word problem ； natural language processing ； MathML ； SVG ； AJAX