An Exploration of Applying Bayesian Networks for Mapping the Learning Processes of Composite Concepts

本研究以貝氏網路作為表示教學領域中各個學習觀念的關係的語言。教學領域中的學習觀念包含了基本觀念與綜合觀念，綜合觀念是由兩個以上的基本觀念所衍生出來的觀念，而綜合觀念的學習歷程即為學生在學習的過程中如何整合這些基本觀念的過程。了解綜合觀念的學習歷程可以幫助教師及出題者了解學生的學習路徑，並修改其教學或出題的方針，以期能提供適性化的教學及測驗。為了從考生答題資料中尋找出這個隱藏的綜合觀念學習歷程，我們提出一套以mutual information以及一套以chi-square test所發展出來的研究方法，希望能夠藉由一個模擬環境中模擬考生的答題資料來猜測考生學習綜合觀念的學習歷程。 初步的實驗結果顯示出，在一些特殊的條件假設下，我們的方法有不錯的機會找到暗藏在模擬系統中的學習歷程。因此我們進而嘗試提出一個策略來尋找較大規模結構中的學習歷程，利用搜尋的概念嘗試是否能較有效率的尋找出學生對於綜合觀念學習歷程。雖然在實驗中並沒有十分理想的結果，但是在實驗的過程中，我們除了發現學生答題資料的模糊程度為系統的正確率的主要挑戰之外，另外也發現了學生類別與觀念能力之間的關係也是影響實驗結果的主要因素。透過我們的方法，雖然不能完美的找出學生對於任何綜合觀念的綜合歷程，但是我們的實驗過程與結果也對隱藏的真實歷程結構提供了不少線索。 最後，我們探討如何藉由觀察學生接受測驗的結果來分類不同學習程度與狀況的學生之相關問題與技術。我們利用最近鄰居分類法與k-means分群法以及基於這些方法所變化出的方法，探討是否能透過學生的答題資料有效的分辨學生能力的類別。實驗結果顯示出，在每個觀念擁有多道測驗試題的情況下，利用最近鄰居分類法與k-means分群法以及基於這些方法所變化出的方法，藉由考生答題資料來進行學生能力類別的分類可以得到不錯的正確率。我們希望這些探討和結果能對適性化教學作出一些貢獻。In this thesis, I employ Bayesian networks to represent relations between concepts in pedagogical domains. We consider basic concepts, and composite concepts that are integrated from the basic ones. The learning processes of composite concepts are the ways how students integrate the basic concepts to form the composite concepts. Information about the learning processes can help teachers know the learning paths of students and revise their teaching methods so that teachers can provide adaptive course contents and assessments. In order to find out the latent learning processes based on students’ item response patterns, I propose two methods: a mutual information-based approach and a chi-square test-stimulated heuristics, and examine the ideas in a simulated environment. Results of some preliminary experiments showed that the proposed methods offered satisfactory performance under some particular conditions. Hence, I went a step further to propose a search method that tried to find out the learning process of larger structures in a more efficient way. Although the experimental results for the search method were not very satisfactory, we would find that both the uncertainty included by the students’ item response patterns and the relations between student groups and concepts substantially influenced the performance achieved by the proposed methods. Although the proposed methods did not find out the learning processes perfectly, the experimental processes and results indeed had the potential to provide information about the latent learning processes. Finally, I attempted to classify students’ competence according to their item response patterns. I used the nearest neighbor algorithm, the k-means algorithm, and some variations of these two algorithms to classify students’ competence patterns. Experimental results showed that the more the test items used in the assessment, the higher the accuracy of classification we could obtain. I hope that these experimental results can make contributions towards adaptive learning