以分眾分類法為基礎建造國小數學應用問題

Abstract

讓學生解數學應用問題可以訓練學生的算數應用能力，然而，要建造新的數學應用問題需要耗費時間以及成本，因為要以合理、多變的問題情境來描述應用題的數學算式是很複雜的。本篇論文，我們以分眾分類法收集老師的知識，這些知識包含問題情境以及問題結構。我們提出了階層式數學應用問題框架式知識表達法來表示問題結構，因為框架的繼承性質適合表示數學應用問題的分類結構。我們提出的數學應用問題文法可促進維護數學應用問題以及問題的演化，包含自我演化以及合作式演化。自我演化改變問題的邏輯來產生不同的題目。合作式演化將兩個問題結構整合成一個新的問題結構。此外，框架中的規則可將不同的問題情境套用在問題結構上;以此大量產生數學應用問題。我們建構了以分眾分類法為基礎的題庫管理系統，來評估系統的使用滿意程度，實驗結果顯示，大多數的國小數學老師都很滿意我們的系統。

The arithmetic word problem enables students to apply their arithmetic skills to solve the problem in application level arithmetic of Bloom’s taxonomy. However, it is costly and time consuming to construct new arithmetic word problems due to the complexity of combining the different arithmetic questions with the various and reasonable scenario. In this thesis, we aim to apply Folksonomy-Based approach to collecting teachers’ knowledge consisting of Question Scenario and Question Structure. We proposed an Arithmetic Word Problem Frame Hierarchy knowledge representation to represent these question structure because inheritance property of frames is appropriate to represent the category structure of arithmetic word problems. The proposed Arithmetic Word Problem Grammar can facilitate the maintenance of arithmetic word problems and their evolutions including Self-Evolution and Collaborative-Evolution. Self-evolution changes the arithmetic logic to generate different problems. And collaborative-evolution integrates two question structures into a new question structures. Besides, the rules embedded in the frame can be used to apply different scenario to the question structure; thus a large amount of arithmetic word problems can be generated. We have also constructed a Folksonomy-Based Item Bank management system (FIB) to evaluate the satisfaction degree of FIB. The evaluation results show that most of elementary school teachers satisfy with our proposed system.