CAL對學習的幫助有正面的評價，然而一般數學CAL中，常常以題組的方式作為系統的選擇方法，換言之，學習者作錯時，系統會再從相似的題組中選擇一題出來，對學習者而言，這樣的題目選擇常常是不恰當的，因為學習者往往不是對此類型題目不了解，而只是對其中的某些步驟不熟悉罷了。在我們的研究中，我們應用Petri - Net 的理論於題目的分析中，將題目的解題過程分析出來，並成為我們的知識核心，我們讓學習者利用我們所設計的核心函式來解答問題，令學習者將學習心思完全放在解題的邏輯思維上，不用去顧慮人為計算疏失。因此，我們設計了39個系統核心函式提供學習者使用，並將題庫中的題目依此39個函式來歸類，使得學習者可以快速查出使用過該步驟（即該函式）之題目，並對函式作詳細之解說，以利學習者對解題步驟能有較清晰概念。

Assessment is an essential aspect of all instruction. A CAL system usually administers the computerized test by storing a set of test questions in the item banks which can be accessed according to some pre - defined selection strategy. However, the selection strategies adopted by most mathematics CAL systems are often quite naive. When a learner gave an incorrect answer to a question, it is usually the way that the system would pick a similar question for the learner to work on without proper diagnosis of the learner's possible problem spots. This is very ineffective with more advanced mathematical problem - solving. The solution of a more sophisticated math problem must involve a sequence of steps, and each step typically corresponds to the application of some important concept in the problem domain. Therefore, if the system can be designed to keep track of the learner's problem - solving process, it can easily detect where the learner gets stuck and offer proper guidance. In this research we applied the Petri - Net theory to the analysis of mathematical problem - solving. We limited our knowledge domain to the topic of "Circle" found in a typical high - school mathematics textbook. We compiled a total of 39 generic functions which our analysis shows are necessary for solving most of the questions in the domain. There 39 functions form the kernel of our system, and the concept involved in applying each function is explained in detail. Whenever a learner chooses a pre-stored question from the item banks and starts working on it, the system keeps a log file of the functions the learner applies in each step of the problem - solving process. A Petri - net is also constructed along the way to detect if the learner is going in the right direction by being matched against the pre - stored "correct" Petrinet. In addition to the pre - stored test questions and solutions, the system includes an editor which an instructor or a learner can use to enter new questions together with the corresponding solving processes (which are converted by the system into Petri - nets).