一個數學解題練習系統之設計理念

Abstract

本文所描述的是一個網路化數學解題練習系統之雛型及其設計理念。我們使用派特里網路圖記錄數學解題知識，將解題所需運用之數學公式，定理，概念等，經分析整理而成一組解題函式，並將其對應至派特里網路之「轉變」；至於觸發每一個解題函式所需之輸入條件與輸出結果則對應至派特里網路之「位置」。使用者利用這些解題函式進行解題，其解題過程則由系統動態地逐步記錄。當使用者於解題過程中遭遇困難並要求系統協助時，系統可將其解題過程與系統所儲存之專家解題知識加以比對，並根據比對結果提供適當之引導。本系統亦提供網路上同步與非同步溝通功能，使學習者得以透過網路獲得教師或同儕的協助解題。本系統之庫存題目及各題目之解法均具有可擴充性，使用者可利用題目編輯器隨時新增題目及其解法，而系統亦能動態偵測並儲存原有題目之新增解法。

This paper describes the prototype of an Internet-based computer- assisted-learning system that allows learners to practice mathematical problem solving. Petri nets are used by the system as its knowledge representation model. Math knowledge within a chosen domain is pre-analyzed to derive a set of macro functions for use in solving problems. Each macro function typically embodies a math concept or rule that may be applied to transform a math problem from a state to another. The macro functions correspond to transitions in a Petri net graph, while the conditions for triggering those functions correspond to places. With Petri net graphs, the system can store experts' static problem-solving knowledge as well as learners' dynamic problem-solving procedures. The graphs may then be used effectively for diagnosing learners' problem-solving difficulties and for offering guidance. The system also supports synchronous and asynchronous network communication functions that may be used by learners to solicit help from other system users. Users may add new problems to the problem bank with the system-provided editor. In addition, me system can automatically detect new solution paths to any old or new problem and augment the system's knowledge base accordingly.