以貝氏網路為基礎之能力指標測驗編製及補救教學動畫製作－以六年級數學領域之「代數」相關指標為例

Competence Indicators Test and Remedial Instruction Developments Based on The Structures of Bayesian Networks－The “algebra ” Related Indicator of Mathematics in Grade 6

梁家鳳(Liang Jia Feng)

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(2006年)

摘要

本研究主要以自編電腦診斷測驗試題與電腦補救教學，以國小六年級代數相關能力指標為研究範圍，以台中縣及南投縣3 所國民小學為研究對象，共66 名學生，診斷並分析國小六年級學生學習數學代數的錯誤類型，並以適切的電腦補救教學實施教學補救，以期改善學生的錯誤概念，提升其能力指標。
研究結果摘
1、以證據為中心的評量設計結合貝氏網路，建構以概念性為主的評量模式，可有效應用於診斷學生的錯誤類型。
2、在錯誤類型的分析上，學生經前測診斷分析後，具有的錯誤類型以不會「四則運算」為最多，經電腦動畫補救教學後，關於「驗算」的錯誤類型可明顯改善。在能力指標方面，經電腦補救教學後，對於「使用未知數符號」
3、比較經前、後測的學生錯誤類型進步情形發現，錯誤類型進步最多者為兩步驟未知數符號應用相關錯誤類型，進步最少者為代數應用文字題列式、解題及驗算的部份。自編補救教學動畫可有效降低學生的學習錯誤，特別是中、高分組的學生最為顯著，低分組學生則無明顯差異。
4、資料統計分析上，使用平均數差之t 檢定(0.05 顯著水準下)，結果發現學生經電腦補救教學後具有顯著的改善效果。
5、貝氏網路為基礎的國小六年級代數電腦診斷測驗具有良好的信度和效度，協助學生正確的數學概念學習。結合電腦診斷測驗及適性電腦補救教學稱得上是一個值得的推廣的教學診斷系統。
【關鍵詞】貝氏網路、能力指標、診斷測驗、錯誤類型、電腦補救教學、代數

關鍵字

貝氏網路 ； 能力指標 ； 診斷測驗 ； 錯誤類型 ； 電腦補救教學 ； 代數

並列摘要

ABSTRACT
The purpose of this research is to analysis how to establish a computerized diagnostic test system that can be used to identify the error patterns of a student by Bayesian network and is applicable to make a remedial online teaching. It is very important to improve students’ wrong concept in algebra after computer remedial instruction. Therefore, the research is to seek for further understanding and to improve student’s key competencies.
The assessment task of error patterns was administered to 66 sixth-grade students from Taichung and Nantou County. The key points are described as follows：
1. A study of using evidence process to construct a concept evaluation model, the related contents can be applied to diagnosis error patterns of students.
2. The study found that the most causes of the error patterns were the conception of 「4 Basic Arithmatic Operations」in first diagnostic test. After computer remedial instruction, the error patterns of 「Algorithm」was reduced obviously. The results indicated that the student exhibits a substantial increase in the ability index.
3. The mistake was evidently improved for high-score group students in second diagnostic test, but there was no significant improved for low-score group students. Results suggest that the computer remedial instruction was affected those who have better learning ability according to the high-score group part.
4. Data analysis is conducted by the utilization of t-test, the findings generated that the computer remedial instruction was exhibited a significant effect on improving error patterns and increasing score.
5. Based on the Bayesian Network, there is high level of trustworthiness and applicability using the computer diagnostic assessment for six-grade student’s subject of algebra. We can find the better learning method for mathematics concepts in the future.
【Ked Words】：
Bayesian Network, Key competencies, Diagnostic assessment, Error patterns, Computer remedial instruction, Algebra

並列關鍵字

Bayesian Network ； Key competencies ； Diagnostic assessment ； Error patterns ； Computer remedial instruction ； Algebra

參考文獻

liu hsiang ch'uan