應用貝氏網路認知診斷模式進行國小五年級小數單元學習診斷之研究

Abstract

本研究的主要目的在於以貝氏網路的方法論著手，發展學生模式與證據模式，建立一個以貝氏網路為基礎的錯誤類型與子技能認知診斷模式，並以國小五年級數學學習領域中「小數」單元作為特定應用領域，而後評估此貝氏網路認知診斷模式應用於實際數學學習診斷的有效性。在評估貝氏網路認知診斷模式應用之有效性的過程中，本研究將探討加入子技能變項、測驗資料型態、分類決斷值以及訓練樣本大小等四個因素對貝氏網路認知診斷模式診斷正確率之影響，以進一步了解如何建立最佳的貝氏網路認知診斷模式，使其未來能與電腦科技結合，發展以貝氏網路為基礎的適性診斷系統，以便更有效地應用於實際教學情境，進而提昇學生的學習成效。 研究結果發現： 一、應用貝氏網路認知診斷模式於數學學習領域中國小五年級「小數」單元，可建構出一套能同時診斷錯誤類型及子技能，適用於單元教學的認知診斷模式。 二、專家診斷結果與訪談診斷具有統計上的一致性，因此，以專家診斷結果作為本研究模式評估之效標是適當的。 三、貝氏網路認知診斷模式應用於國小五年級「小數」單元內四種評量重點，在錯誤類型與子技能部分皆可達到良好的診斷結果，惟子技能的診斷正確率低於錯誤類型。 四、加入子技能的貝氏網路認知診斷模式對錯誤類型的診斷正確率有些許提昇，但影響的程度很小。 五、以多選項記分資料作為證據的貝氏網路之診斷正確率最佳，以二元記分資料為證據的貝氏網路次之，以二種IRT選答率為證據的貝氏網路診斷正確率最差。 六、使用由訓練樣本所選取的動態分類決斷值之診斷正確率優於採用固定式的分類決斷值。 七、在使用動態分類決斷值的前提下，訓練樣本之大小對錯誤類型與子技能的診斷正確率影響程度均不大。 最後，研究者針對研究結果提出建議，作為本研究貝氏網路認知診斷模式在教學應用以及未來研究的參考。The main purpose ofthis study is to develop the cognitively diagnostic model based on Bayesian networks that include the student model and the evidence model, and to explore the efficiency of using Bayesian networks for modeling assessment data and identifying bugs and sub-skills of decimals after students have learned the related contents. Four factors are involved in this study: the effects of using sub-skill nodes in addition to bug nodes, the effects of various scoring type of assessment data, the effects of various cut-points, and the effects of setting various size of training sample. By varying these factors to assess the effectiveness of the generated Bayesian network models work in predicting the existence of bugs and sub-skills in order to find the best cognitively diagnostic model based on Bayesian networks. The results of this study will lay a foundation for building a computerized adaptive diagnostic mathematics test based on Bayesian networks for elementary schools successively. The major findings of this study are summarized as follows: 1.The cognitively diagnostic model based on Bayesian networks can be constructed and employed in the diagnosis of bugs and sub-skills of decimals in the fifth grade mathematics of elementary school successfully. 2.Experts’ diagnostic results are agreed with interview statistically, so, it is suitable to assess the effectiveness of the generated Bayesian network models using experts’ diagnostic results as criterion. 3.The results show that using the cognitively diagnostic model based on Bayesian networks to diagnose the existence of bugs and sub-skills of students can get good performance, but the sub-skill prediction rates are lower than the bug prediction rates. 4.The increased bug prediction rates for adding sub-skill nodes are minimal. 5.The prediction rates for employing specific multiple-choice answer information are better than binary-answer Bayesian network. The prediction rates for employing the probability of item response theory information are worst. 6.The dynamic cut-points based on the response data of training samples can get better performance than the fixed cut-points. 7.The value of prior distribution is the important factor in Bayesian networks estimation. In this study, the prediction rates of bugs are increasing with the size of training sample, but the effects are minimal. Based on the findings, some suggestions regarding instructional application and future research also offer.