| Abstract: | In the traditional test, it is tend to diagnose the “ability” of students. But the multiple-choice items used in the tradition test are influenced by those factors such as carelessness and guessing. Therefore, it is difficult to diagnose the sub-skills of students and the misconceptions stemmed. The defect of the multiple-choice items, to be compared, becomes the benefit of the constructed-response items. But the constructed-response test has its own problems that it takes a lot of time to conduct the test and is not easily to grade. To solve those problems, in this research, based on the unit of multiplication and division of fraction, both test of total multiple-choice items and total constructed-response items are developed. Automatic analysis mechanism is designed for the constructed-response items and the DINA and DINO models are used to analyze those data collect to avoid the defects of the multiple-choice items which is easily influenced by guessing and carelessness and thus to lower the uncertainty of the counting of concept and error type. Furthermore, to upgrade the accuracy rate of the diagnostic classification, four different arrangements of the six constructed-response items are used: superordinate concept, subordinate concept, most concepts in one item, and most bugs in one item. As a result, the best efficient way of items arrangement is found. The main conclusions of this research are as follow:1. The average diagnostic accuracy rate of the constructed-response items through the automatic analysis mechanism is 98.01%.2. Under the DINA model, the concept diagnostic accuracy rate of the total constructed-response items is 97.93% which is better than that of 73.66% of the total multiple-choice items.3. Under the DINO model, the error type diagnostic accuracy rate of the total constructed-response items is 89.45% which is better than that of 78.56% of the total multiple-choice items.4. The best way of items arrangement: the concept diagnostic accuracy rate is 0.8703% under the DINA model, and the error type diagnostic accuracy rate is 0.8669% under the DINO model. It is not only has the improvement in time saving but also has the upgrading of the accuracy rate of the diagnostic classification under both cognitive diagnostic models of DINA and DINO.Key words: multiplication and division of fraction, constructed-response items, cognitive diagnostic model, DINA, DINO |
