融合不同專家貝氏網路優勢進行國小六年級數學領域代數之適性學習系統研發

Integrating Advantages of Diverse Expert Bayesian Networks in Developing an Adaptive Learning System for the Sixth-Year Elementary School Algebra Class

張見銘(chang chien ming)

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

本研究為解決教師在診斷、補救學生數學上迷思概念所產生的負擔，嘗試 以國小數學領域六年級代數能力指標（6-a-01、6-a-02、6-a-03）為例，以貝氏網路為推論工具，輔以知識結構的概念，建立一快速、準確且有效的電腦適性學習系統。
本研究首先分析能力指標內容，找出子技能及錯誤類型後建立單一貝氏網路模組，並依此命題，進行紙筆測驗。測驗完成後，建立五組不同專家貝氏網路，以預試的資料當作訓練樣本，透過融合不同專家貝氏網路的方法提升診斷的辨識率。接著同樣利用預試的資料，分析學生的試題結構後，在系統中加入知識結構的概念，使得此診斷測驗具備有適性的功能。最後再依適性測驗診斷報告連結可引起學生學習興趣且配合子技能節點的補救教學動畫，而使系統成一個以國小六年級代數為例的電腦適性學習系統。適性學習系統經過線上施測實驗後，將前、後測資料分析與討論所得結論歸納如下：
一、透過融合不同專家貝氏網路可提升辨識率，所使用的六種融合演算法中，以結構融合演算法所提升的辨識率效果最為顯著。
二、可將紙筆測驗成功的轉換成電腦適性測驗，且電腦適性測驗能節省大量的測驗時間、對於節點的有無具有良好的推論效果。
三、此系統可有效的診斷個別學生在六年級代數須補救的概念，且補救動畫能達到補救迷思概念的目的。

關鍵字

貝氏網路 ； 代數 ； 診斷測驗、補救教學、適性學習系統、知識結構

並列摘要

The study aimed at reducing the teachers’ burden when they diagnosed and remedied students’ misconceptions in math and at developing a fast, precise and effective computerized adaptive learning system by integrate Bayesian Network as an instrument of inference and knowledge structures as concepts to help the sixthyear elementary students in learning algebra. At first, after analyzing the contents of the competence indicators and finding out the sub-skills and bugs, the study set up a model of Bayesian Network and developed a standardized test accordingly. After implementing the pre-test, five different Expert Bayesian Network were thus established. All the data collected from the pre-test were used as training samples to elevate classification results by integrating diverse Expert Bayesian Networks. Next, the study used the same data from the pre-test to analyze the students’ structure concepts when receiving tests. Then, the study added the knowledge structures to the system to make the diagnosis test adaptive. Finally, the study linked the diagnosis reports of the adaptive test to the animated remedial instructions which would arouse students’ interests in learning and would match the nodes of sub-skills. Eventually, the whole system became a computerized adaptive learning system for the sixth-year elementary students in algebra classes. After the on-line pre-tests and post-tests, the results of the adaptive learning system were as below:
1. Integrating diverse Expert Bayesian Networks elevated the classification results. Among the six fusion methods, the classification results of the Structure Fusion Method were elevated most highly.
2. It could be successfully transferred from paper tests to computerized adaptive tests. Besides, computerized adaptive tests not only saved time but they also brought about good inference results as to the existence of nodes.
3. The system could effectively diagnose the concepts which needed remedying for each individual six-year student in their algebra learning. In addition, the animated remedial instructions could serve the purpose for remedying those misconceptions.

並列關鍵字

Bayesian Newwork ； Algebra ； Diagnostic Test, Remedial instruction, Adaptive Learning System, Knowledge Structure

參考文獻

教育部（2003），國民中小學九年一貫課程綱要數學學習領域。台北：教育部。

馮齡儀（2003）。電腦輔助子宮頸抹片異常細胞辨識之初期研究，中原大學醫學工程研究所碩士論文，未出版，桃園縣。

戴文賓（2000）。國一學生由算術領域轉入代數領域呈現的學習現象與特徵。彰化師範大學科學教育研究所碩士論文，未出版，彰化縣。

方建良（2003）。「合」樂融融的數學課－以四年級「四則運算」之補救教學為例。國教世紀，208，85-100。

施皇嘉（2001）。利用貝氏信度網路來解釋運動節目。國立清華大學電機工程學系，未出版，新竹市。