運用派翠西網路『解題是學習數學的重心』，自1980年左右以來這個觀念更是不斷的被各個數學教育研究單位所大力鼓吹，這些建言的目的都是希望把解題作為學生發展數學學習與瞭解的一個方法，藉由解題的情境中學習數學的概念與技能，並且經由解題的經驗發展出高層次的思考。然而，根據調查結果指出，目前大部分數學科方面的電腦輔助教學軟體都缺乏向學習者陳述其中解題步驟的能力，我們認為若系統可以像家教老師一樣來監督學習者的解題過程，必要時並能引導學習者來解題，如此必能使學習者獲得一更有效的學習成果。為了能夠達成此一目的，本研究嘗試應用Petri-Nets來作為學習者解題步驟流向的分析與控制。Petri-Nets是一種兼具數學與圖形的模組化系統分析與發展工具，可適用在具有動態性資料流向性質的系統的分析與控制上。本研究即依循『解題是學習數學的重心』的理念，應用Petri-Nets作為解題步驟流程控制之用，並實際針對高中數學科中的『圓』單元發展一套導引式學習環境的電腦輔助學習系統，在系統的監督下學習者必須一步步陳述對問題的解題步驟，必要時並可向系統要求協助，如此以期能夠達到一個個別化的有效教學目標。

Problem-Solving Based Solving Flow Analys of Mathematics CAI - Using Petri-Nets「Problem solving is the heart in mathematics learning」, and this concept is advocated very often by several mathematical research institutions till 1980. The purpose of the suggestions all hope using problem solving as the method when student develops his mathematics learning and understanding. Depending on the situation in problem solving, student learns the concepts and skills of mathematics and develops high level thinking. However, according to the related investigation results, most of the computer assisted learning softwares in mathematics are short of the ability to express the solving steps to the learner. We think if the system can supervise student's solving steps just as a tutor, and guide the learner to solve question when necessary, student will get more efficient learning results. In order to achieve this goal, our research tries to apply Petri-Nets to analyze and control the learner's solving steps flow.Petri-Nets is both a mathematical and a graphical modelized system analysis and development tool. It is well suited for the analysis and control of the system having the dynamic data flow properties. Our research, in accordance with「Problem solving is the heart in mathematics learning」, applies Petri-Nets to the flow control of the problem solving, and in actuality aiming directly at the unit of "Circle" in mathematics of the senior high school, we develop a computer assisted learning system with a guided learning environment. Under system's supervision, the learner should state the problem solving steps step by step, and can also call for system's help, in order to achieve the individualized effective teaching goal.