國小數學領域分數的加減單元之電腦適性學習系統研發

The Research and Development of Computerized Adaptive Learning System for“Addition and Subtraction of Fractions＂in Elementary School Mathematics

郭致穎(kuo chih ying)

指導教授 ： 劉湘川

亞洲大學/資訊學院/資訊工程學系碩士班/碩士(2007年)

摘要

本研究擬研發一套以國小四、五、六年級數學領域「分數的加減」單元為評量內容的電腦適性學習系統，探討應用知識結構分析，並結合貝氏網路機率推論工具的評量診斷模式是否方便有效。 這套系統包括了線上診斷測驗及電腦化適性補救教學系統，讓學生透過網際網路參加測驗並立即得知自己的測驗結果、作答情形以及出現錯誤類型的診斷報告，並根據錯誤類型的分布情況，進行線上適性化、個別化、即時化的補救教學。 根據本研究實驗流程進行及結果分析，主要得到以下結論： 1. 利用貝氏網路結合知識結構作為推論工具有提昇辨識率的效果，其中以結合專家與學生知識結構的貝氏網路表現最佳。 2. 研究中可發現傳統的固定決斷值選取法來選取錯誤類型或子技能的決斷值，整體之辨識率不及動態決斷值選取法的方式能有效提高整體之辨識率。 3. 此系統可有效的診斷個別學生在四、五、六年級數學領域之「分數的加減」須補救的概念，且可以節省施測題數，其補救動畫能達到補救迷思概念的目的，學生在前、後測驗表現上具有顯著差異，平均分數進步達到顯著的水準。

關鍵字

貝氏網路、知識結構、電腦化適性診斷測驗、適性化補救教學、子技能

並列摘要

The main idea of the study is to research and develop the computerized adaptive learning system for “Addition and Subtraction of Fractions” in Elementary School mathematics in Grade4、5 and 6.The research want to know which integrates the method of knowledge structures with the test diagnosis model of Bayesian Networks analysis tool whether is convenient and effective or not.
The system includes both on-line Computerized Adaptive Diagnosing Test and Adaptive Remedy Instructions, students can immediately know the calculation ,the status of their is answering, and a comprehensive diagnosis of their own problems patterns by taking this Internet exam. According to the distribution of the problems patterns, they can also have an adaptive, individual, instant remedy instruction online.
We have conclusions as below.
1. It is helpful to move up the recognition rate by taking advantage of Bayesian networks evaluation mode as a conclusion tool, and the Bayesian networks linked up with professionals’ and students’ knowledge structure is the best tool.
2. In this research , it’s can be discovered that using the traditional fixed critical ratio to choose problems patterns or sub-skills decisive values is not good as using dynamic threshold, which means we can improve recognition rate by using dynamic threshold .
3.This learning system can diagnose individual student needs the concept of remedy instructions for “Addition and Subtraction of Fractions” in Elementary School mathematics in Grade4、5 and 6 or not. Besides, the system can reduce the amount of the questions in tests. Students make marked differences between former test and post-test, and the grade-point average reaches an outstanding level by this Adaptive Remedy Instructions.

並列關鍵字

Bayesian networks、knowledge structures、Computerized Adaptive Diagnosing Test、Adaptive Remedy Instructions、Sub-skills

參考文獻

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