比較適性與非適性貝氏網路診斷測驗及補救教學系統之成效－以國小數學領域分數的乘法為例

The Comparison of the effects of adaptive and non-adaptive diagnostic test and adaptive remedial teaching by Bayesian Network Theory: The multiplication of fraction in elementary school math classes

張宏文(chang hung wen)

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

本研究以分數的乘法為例，利用學生試題結構分析的子技能上下位關係加入貝氏網路做為診斷測驗推論的模式，又以學生試題結構為適性測驗的選題策略，另以電腦多媒體元件設計補救教學動畫，依此比較適性及非適性的診斷測驗及適性化補救教學的成效，期望能有效的診斷學生在學習上的錯誤概念，透過系統節省測驗的時間，並給予學生適性化、個人化的補救教學，也希望能同時達到評量、診斷、補救的功能。
研究結果發現：
一、 比較後顯示，順序理論之閾值為0.045 時所得之架構加入貝氏網路推論可以得到最高的辨識率。
二、 以學生試題結構加入貝氏網路為推論工具可以獲得最高的辨識效果，有效地診斷學生的錯誤類型發生和子技能通過的有無。
三、 補救教學系統實施後，學生的平均成績、子技能的平均通過率有顯著進步，錯誤類型的平均發生率亦有降低。
四、 經由比較，適性的診斷測驗除了可以節省試題，在預測精準度和全測的推論具有一致性。

關鍵字

貝氏網路 ； 學生試題結構 ； 電腦適性測驗、電腦化適性補救教學

並列摘要

This research aims to investigate the effectiveness of different model of inference, with Bayesian Network Theory, in the sub-skills of item structure analysis, using multiplication of fraction as an example. It also compares the effects of adaptive vs. non-adaptive diagnostic tests and adaptive remedial teaching, using students’ item structure as the strategy for the adaptive diagnostic test and computer multimedia animation as the design for the adaptive remedial teaching. Through this system, it is expected that wrong concepts in the process of students’ learning can be diagnosed more effectively, giving students adaptive and individual remedial teaching, and at the same time, achieving the functions of tests, diagnosis and remedial teaching.
The results of this research include:
1. With the inference of Bayesian Network Theory, the structure obtained from ordering Theory when the threshold value is 0.045 can achieve the highest differentiability. when the threshold value in Ordering Theory is 0.045 can achieve the highest differentiability.
2. Students’ item structure with Bayesian Network Theory, as the mode of inference, obtains the highest effectiveness in diagnosing students’ error types and sub-skills pass rate.
3. After the implementation of remedial teaching, students’ average grades and the average sub-skills pass rate are increased significantly. The percentage of the average occurrences of error types is also decreased.
4. The adaptive test saves the use the test items, and in comparison with the full answers in Bayesian Network Theory, the likelihood is over 90% Besides saving the test items, the adaptive diagnostic is also consistent with both the degree of accuracy in anticipation and inference in non-adaptive.

並列關鍵字

Bayesian Network Theory ； item structure ； computer adaptive test,computerized adaptive remedial teaching

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。台北市：教育部。

吳仁奇(2006)。以貝氏網路為基礎之能力指標測驗編制及補救教學動畫製作－以五年級數學領域分數相關能力指標為例。臺中亞洲大學資訊工程研究所碩士論文。未出版，台中縣。

沈俊達（2003）。以知識結構為主的電腦適性診斷測驗系統之研究－以國民小學數學領域為例。臺中健康暨管理學院資訊科技研究所碩士論文。未出版，台中縣。

蕭文欽（2003）。知識結構為基礎的電腦適性診斷測驗系統。臺中健康暨管理學院資訊科技研究所碩士論文。未出版，台中縣。

Almond R. G., Mislevy R. J.(1999). Graphical models and computerized adaptive testing. Applied Psychological Measurement, 23(3),223-237.