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MathCAL-II is a piece of software for students to practice solving mathematical word problems in trigonometry. At the core of the system is a database that stores experts’ problem-solving paths. These solution paths are stored as Petri net graphs internally. MathCAL-II also dynamically records a learner’s solution path during a practicing session. Thus it can compare a learner’s partial solution path against all correct solution paths to identify a best match, which can then be used to provide guidance to a learner in case s/he requests help. In a series of experiments that we conducted in a local high school, 58 students who participated voluntarily were divided randomly into the treatment group and the control group. The treatment group used MathCAL-II to practice solving trigonometric word problems, whereas the control group used the traditional pencil-and-paper approach. Results revealed that the students in the treatment group made significantly more progress than those in the control group. A questionnaire survey also showed that MathCAL-II not only improved students’ understanding of mathematical concepts in trigonometry but had positive influence on students’ attitudes toward learning trigonometry.



派特里網路, 電腦輔助學習, 電腦輔助解題系統, 數學解題, Petri net, Computer assist learning, Mathematical problem solving