This study takes "the multiplication and division of time" unit which is elementary mathematics with multiple-strategies of constructed-response item to develop automated analysis processes which can analyze problem solving strategies, skills, and the types of errors. MS-DINA and DINA Models are used to diagnose and analyze the result and efficiency of the learning process.
There are seven conclusions of this study:
1. In the study, the strategy ,the multiplication and division of compound denominate number time, is used by over 70％ students . The multiplication of compound denominate number time is used by over 96％ students.
2. The students who use the multiplication and division of compound denominate number time strategy and take long division calculation probably make the error type B6, the students take the decimal system instead of the correct numeral system. The researcher recommends teachers give much more practice with long division calculation to make the error type B6 lower.
3. There is the error type B13 because of error computing in every item. The researcher recommends the strengthening of computing ability.
4. The consistency of diagnosis by automated diagnostic analysis and experts is above 0.98.
5. DINA and MS-DINA Models are used to evaluate the cognition of problem solving process. Both of the efficiency of Model4 and Model3 are better than Model1 in DINA Model.
6. Among the efficiency of these four Models, Model4 is greater than Model3, Model3 is greater than Model2, and Model2 is greater than Model1.
7. The efficiency of MS-DINA Model is greater than that of DINA Model.
