| Summary: | 碩士 === 國立臺中教育大學 === 數學教育學系 === 95 === The purpose of this study is to investigate the performance on correlation problems for pupils. The study shows the correct ratio of each item, and comparisions on rule graphs between grade and gender. The individualized hierarchical structures for rules based on ordering theory are discussed. Besides, the researcher classifify the examinee with latent class analysis according to the rule usage of examinee.
In this study, there are 431 objects of fifth and sixth graders from Tai-chung city of Taiwan. The results are as follows.
1. For the correct ratio of all items in three kinds of problems, the highest is in subordinate problems, the second is in conflict-equal problems, and the lowest is in conflict-dominant problems.
2. As to the rules usage on all items, there is significant difference between grade. Moreover, the performance of 6th graders is better than that of 5th graders. The pupils of 6th graders use rule3 and rule4 the most. On the contrary, the pupils of 5th graders used the rule1 and the rule2 the most. But there is no significant difference between gender for the rule usage. In the same way, there is also no significant difference between the interaction of grade and gender.
3. About hierarchical structures on rule usage, the similarity index between different graders is different. It shows that hierarchical structures of sixth garders are more similar to expert than that of fifth graders. However, the similarity index does not vary with gender. Besides, the interaction of gender and grade on similarity index is not significantly different.
4. The hierarchical structures on rule usage vary with subjects of different total score and response patterns. Therefore, total score can not explain the knowledge structure.
5. There are four latent classes with respect to laent class analysis. Cluster I consist of mixture the rule 1, rule 2, and rule 3. Cluster II, III, IV represent rule 4, rule 1, and rule 4. There is significant difference on the frequencies of clusters for varied graders. Most fifth graders belong to cluster I and III, while most sixth graders belong to cluster I and cluster II.
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