教學的目的之一是在於培養學生具有分析問題與解決問題的能力。因此許多研究都致力於改進教學方法以提高教學效果，並安排適當的學習環境來培養學生問題解決的能力。然而，很多因素會影響數學解題的進行，解題策略的使用便是其中重要的因素之一。
基於上述原因，本研究設計一套教學系統來教導學生解題策略的使用，選擇的主題是國中數學--「因式分解」單元。本系統依據Bruner [1996]的三個表徵模式（動作、影像、符號）為理論基礎來設計，分成「具體操作」以及「符號思考」兩階段，而「符號思考」階段又區分成【直接引導】以及【間接引導】兩種教學模式。在具體操作階段，讓學生於「做」中學。在符號思考階段，依據完成式策略以填充、修改、擴充的設計方式，引導學生學習，配合學生的認知狀態，讓學生學習解題策略的使用，以期改善學生的因式分解解題能力。
本系統在實作完成後藉由實驗來評估三種教學模式對於一般問題解決能力和關於因式分解的特殊問題解決能力的教學成效，並調查學生使用系統的態度。
實驗結果發現，具體操作對於因式分解中十字交乘法策略的使用有相當大的幫助，而且具體操作也是系統中學生最感興趣的部分。此外間接引導教學模式對於各個解題能力的提升（十項問題解決能力）大於直接引導的方式。但整體而言，兩者對於學生因式分解解題能力以及一般問題解決能力的提升都很有幫助。

Developing student's ability of problem - analyzing and problem - solving is one of the main purposes of teaching. Most researches are devoted to improve the teaching ways increasing the effects of teaching and arranging proper learning environments to develop student's ability of problem - solving. However, many factors will influence the mathematical problem - solving. TO use problem - solving strategies is one of the important factors.
This research proposed and implemented a learning system for students to practice the strategies of problem - solving. The factorization in mathematics was selected as the subject of this system. The system is designed according to Burner's three Representation Modes (Enactive representation mode, Iconic representation mode and Symbolic representation mode. The learning processes were divided into two stages, "concrete operational stage" and "symcbolic thinking stage" The symbolic stage is also divided into two options, "direct - guidance" learning mode and "indirect - guidance" learning mode. In "concrete operational stage", learning by doing theory is adopted. In "symbolic thinking stage", the system provides a environment based on completion strategy. The strategy presents three operators such as "cloze", "modification", "extension". The state of students' cognition are also considered to guide them.
After the system was designed and developed, Student's ability of common problem - solving and special factorial problem - solving was evaluated by several experiments. In theses experiments, the effects of three learning modes are tested, and students' attitudes to the system are also investigated.
According to the results of these experiments, we found that "concrete operation" improved students' ability to use Cross - Multiplication strategy very much and it was also the most interesting function to the students. Besides, In "symbolic thinking stage", "indirect - guidance" learning mode had better effects than "direct - guidance" learning mode in all strategies of factorization. Overall, both of the learning modes were helpful to raise the ability of common problem - solving and special factorial problem - solving.