使用貝氏網路分析不同背景變項及學習風格之學生學習成果

Using Bayesian Network to Analyze Performance of students with Different Learning styles and Background situations

蔣順興(Chiang Shun Hsing)

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

研究背景與目的
近年來貝氏網路廣泛的應用在教育領域，根據汪端正（2006）研究，以貝氏網路為基礎的測驗，是一種很好的診斷工具；另外，Sternberg（1997）指出，學生的思考風格是可測量的。因此，本研究的目的要探究不同思考風格的學生，在數學上面的學習困難，所呈現的狀況會形成什麼差異，而診斷學生的不同學習狀況，即是使用貝氏網路來預測。
研究方法
透過專家與富教學經驗之教師，編制「面積」單元的知識結構、貝氏網路及試題，施測的同時，學童必須填寫學習思考風格量表（林鎂惠、陳易芬，2008），利用量表診斷出學生風格，包括層次的巨觀、微觀型或功能的評析、自主、程序型。收回試卷及問卷後，配合學生的作答過程及結果做比較分析，找出不同思考風格學生，在試題的錯誤類型與子技能的表現情形。
研究結果與討論
1.貝氏網路適用於診斷面積單元，其錯誤類型精準度平均達86.4%；能力指標與
子技能精準度平均達85.5%。
2.功能與學習、層次與學習情況區辨：
（1）程序型學生發生面積周長混淆、誤用梯形公式情形，較自主型為高。
（2）自主型應用公式解決平行四邊、三角形面積試題情形，優於程序型。
（3）整體自主型學生具備學習基本概念情形，優於其他兩型。
（4）整體程序型發生學習困難狀況情形，高於其他兩型。
3.以高、中、低分組風格與學習：
（1）高分組微觀型誤用平行四邊形公式情形，較巨觀型為高。
（2）自主型利用公式正確解決3種複合圖形試題情形，優於程序型。
（3）評析型發生誤用平行四邊形公式情形，較自主型為高。
（4）中分組程序型發生誤用梯形面積公式情形，較自主型為高。
（5）低分組巨觀型發生未將梯形公式除以2、未看清題意而使用錯誤計算，
較微觀型顯著。
4.以6種複合風格類型與學習情況區辨
（1）評析-微觀型發生錯誤類型面積、周長混淆情形，較自主-微觀型為高。
（2）程序-巨觀型發生錯誤類型誤用梯形公式情形，較自主-微觀型為高。
（3）自主-巨觀型具備子技能應用公式解決平行四邊形試題，優於評析-巨觀
（4）整體程序-巨觀型學生發生錯誤類型的情況高於其他5種類型，自主-微
觀型學生發生錯誤類型情形低於其他5種類型。
（5）整體而言，自主-巨觀型學生具備子技能情形優於其他5種類型，自主-
微觀型學生具備子技能情形低於其他5種類型。
5.以複合風格類型與性別、得分區辨
（1）男學童偏向自主-巨觀型，女學童偏向程序-微觀型。
（2）男學童以評析-巨觀型平均分數最高，女學童以自主-巨觀型平均最高。
（3）整體而言，本研究中的女學童的平均分數略高於男學童。
6.以背景變項與學習成就區辨
（1）女學童在子技能達成情形較男學童略高。
（2）有補習學生平均分數高於無補習者。
（3）主動提問學生平均分數高於不主動提問者。

關鍵字

貝氏網路 ； 思考風格 ； 面積

並列摘要

Research background and purposes
Bayesian network has been widely applied in educational field. According to the research of D.C. Wang (2006), tests based on Bayesian network can be on of the best instrument in diagnosis. In addition, as Sternberg (1997) pointed out, the thinking styles of students are measurable. Thus, the purpose of this study was to examine learning difficulties in math for students with differential thinking styles. The study further analyzed the differences among various situations to diagnose different learning situations of students by applying Bayesian network to predict the results.

Research Methods
Incorporating with specialists and well-experienced teachers, the knowledge framework of “square measurement” unit, Bayesian network and test items were constructed. Students were required to fill in thinking style scale form, which diagnoses thinking styles of students. The scales include global level, local or functional judicial, legislative and executive styles. Test sheets and questionnaires along with processes when students were doing the test and the test outcomes were compared and analyzed to find out the error types of test items and sub-skill performances among students with different thinking styles.

Results and discussion
1. Bayesian is suitable for diagnosis of “square measurement” unit. The preciseness degree of error type prediction has reached 86.4% averagely. The preciseness degree of ability index and sub-skills has reached 85.5% averagely.
2. Distinguishing based on styles and learning conditions.
(1) Students with executive styles tend to apply formula incorrectly more significantly than those with legislative style whereas students with legislative style tend to correctly apply formula to solve problems more significantly than those with executive styles.
3. Distinguishing based on scores with low, medium, and high groups.
(1) Group with high scores applying incorrect formula is more significant than other two groups.
(2) Group with low score with global style tends to apply incorrect formula and to misunderstand meaning of test items than those with local style.
(3) Groups with medium and high scores with executive style tend to apply formula more significant than those with legislative style.
(4) Groups with high scores with legislative style tend to apply formula correctly to solve complex graphs more significantly than those with executive style.
4. Distinguishing based six learning style combination and learning conditions.
(1) Errors made by students with executive and global styles were more significant than those with legislative and local styles.
(2) Students with legislative and global styles with sub-skills were more significant than those with legislative and local styles.
(3) Groups with medium and high scores tend to incline to legislative and global styles whereas groups with low scores tend to incline to executive and local styles.
5. Distinguishing based on sex and learning condition
(1) Boys tend to incline to executive and local styles whereas girls tend to incline to legislative and global styles.

並列關鍵字

Bayesian network ； thinking styles ； square measurement

參考文獻

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