合作學習為一種有效之學習方式，而如何將學生分成多個結構優良的合作小組則為合作學習的一個重要議題。由於概念圖可以用來顯現與組織學生學習的知識架構，透過此工具更可以了解各個學生的學習狀況，而小組成員的各個概念之學習狀況越是互補，其學習進步的空間將越大，因此本研究以個人的概念圖為基礎，由知識架構方面更詳細地制定一套可評估小組成員間概念互補情形的計算方式，並由整體成員的互補程度、概念結構的互補情形、小組間公平性等面向，提出數種分組策略。
本研究以作業研究領域中之整數規劃技巧針對各分組策略加以模式化，並由分組問題中常見的兩種角度提出數學模式Ⅰ與數學模式Ⅱ以求出最佳的分組方式。其中，模式Ⅰ直接以決策變數來決定學生i是否與學生j同組；而模式Ⅱ則以學生i是否屬於第r組之變數來間接判斷學生i是否與學生j同組。此外，為更符合使用者使用的需求，我們提出透過整數規劃中不同的目標式與限制式搭配求解的想法，以增加使用者選擇彈性，並更進一步說明如何將文獻中提及之各類分組因素轉換成本研究提出之整數規劃數學模型，以及解釋如何應用所提之分組規則以讓使用者可更彈性地運用各種分組策略。
為能更快速地分組，我們亦提出一個改良式的基因演算法機制，以在各種情境中找出一組可行解，此外，我們亦針對最常使用之分組情境提出一貪婪式演算法，經測試比較後發現，此改良式基因演算法能在合理的時限內找出求解品質不錯的分組方式，且其求解的穩定性亦優於貪婪式演算法。

Cooperative learning is a useful way for learning, whereas how to divide learners into adaptive groups becomes an important issue. In this study, we use the conceptual maps to evaluate the learning performance for each student and propose a mechanism to gauge the conceptual complementarities between two individuals. We then set several grouping strategies based on complementary scores, coverage of concepts and fairness between groups.
We propose two mathematical models based on integer programming (IP) formulations by different grouping strategies. We illustrate our grouping mechanisms by examples and show how previous group composition strategies can be integrated into our proposed grouping mathematical models.
To effectively grouping students within short period of time, we propose a genetic algorithm (GA) and a greedy algorithm (GREEDY) and compare their performances with the formulations solved by a state-of-the-art IP solver. The test results indicate GA and GREEDY can efficiently deal with larger problems, and GA is more robust with better performance than GREEDY.

中文部份：
余民寧(1997)，有意義的學習：概念構圖之研究，商鼎文化出版社。
黃政傑，吳俊憲(2006)，合作學習發展與實踐，五南文化出版公司。

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