合作學習是團隊工作的開始，經由互助、分享達到彼此盡責、發揮個人能力與團隊進步的獎勵。分組，是合作的第一步，為了讓合作能更順利，我們提出一個分組技術，採用社會網絡關系及過往的測驗成績為分組依據，以強化學生學習及改善測驗結果。本方法基於合作學習中，互動的需求及合作的渴望。以學生的學習成就及社會關系為基礎，本方法將社會關系良好的同學分在同一組，作為互相學習或者模彷的對象。如此一來，學生的學習成就渴望被提升。我們的實驗結果顯示這樣的分組而學習，可以得到較佳的學習成果，對比以隨機分組的學生而言，較好的社會關系能增加合作的協調性。更確切的說，以社會關系為基礎的分組的學生，有17.64%的同學提升了學習成就，同時，整個班的平均分數提升，標準差也集中了。學生於合作學習中互相參考，也同時被組長所影響。一位好組長能引導全組良好溝通，分享彼此的建議。在我們的方法裡，父母、老師、及同組成員對組長的支持，直接影響全組的學習成果。尤其是家中父母的支持，更是提升全組成績的最好支援。另一方面，題目難易度直接影響成績走向，我們提出另一種檢驗題目難度的方法，以數學題目為例，提出四個要素：理解、公式、計算、及單位轉換。這個檢驗方法，能對那些尚未被試題反應理論測試過的題目，定義出屬於題目本身的難度。

A team work begins with cooperative learning, the responsibility of associators, abilities of individuals, and team progress are rewarded for helping and sharing to each other. Grouping takes the first step of cooperation. For better cooperation, we propose a grouping strategy to enhance the learning and testing results of students based on the relationship of social network. The proposed method stems from the need of interactivity and the desire of cooperation in cooperative learning. Basing on the society relationships and the learning results of students, our method provides members of the groups to learn from or mimic learners who have good relationships with them. As such, the learning achievement can be raised. Our experimental results show that the proposed method can provide a better learning result, especially when compared to grouping at random, because it enables low achievers to find more appropriate collaborators. More precisely, the experimental results show that the learning achievement of approximately 17.64\% of the students is increased. The average score is also increased. Cooperative learning are also influenced by the leader and the learning achievements. A good leader leads a better communication and shares the advisement among members. We have found the supports, including parents, teachers, and relationships, for a leader leading the group to a higher achievement. The specific factors are also discussed, that the parents' support is the biggest among the others. In another factor, achievement trend, the item difficulty of a question can affect the difference of achievement trend. We provide a method, difference from item response theory, can sensibly calculate the difficulty of item-self by four factors, recognition, formula, calculation, and unit transformation. This method takes mathematics as instance and can be applied to question items in which is not tested before.

Contents
Acknowledges c
List of Tables iii
List of Figures iv
Chapter 1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Chapter 2 Related Works 6
2.1 Social Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Cooperative Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 E-Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.1 Learning Management System . . . . . . . . . . . . . . . . . . . . . 13
2.3.2 Remedial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 Grouping and Social Network . . . . . . . . . . . . . . . . . . . . . . . . . 16
Chapter 3 Grouping Strategy 18
3.1 Friendship Rank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.1.1 Extracting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1.2 Ranking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 Achievement Trend . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2.1 Normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.2 Regressing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Grouping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3.1 Computing Center of Attraction . . . . . . . . . . . . . . . . . . . . 29
3.3.2 Building Quadratic B’ezier Curve . . . . . . . . . . . . . . . . . . . . 29
3.3.3 Selecting Partner . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.4 Leader Originality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.5 Multiplayer grouping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Chapter 4 Experimental Results 36
4.1 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.2 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.3.1 Status Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.3.2 Relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.3.3 Leadership . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.4 Experimental Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Chapter 5 Discussion 53
5.1 Complexity and limitation . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.2 Course Grouping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.3 Item Difficulty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Chapter 6 Conclusion 62
References 64
Appendix A Questionnaire 78
Appendix B Scores of Experiment 81

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