| Summary: | 碩士 === 國立臺中教育大學 === 教育測驗統計研究所 === 98 === The purpose of this study is to explore and compare the concept structures of annual details of the concept of “numbers and quantities” for fifth graders of elementary school by using the analysis of fuzzy clustering and polytomous item relational structure (PIRS). The sample includes 646 students from fifth graders of elementary school by using self-designed “number and quantity” concepts test. Secondly, the researcher analyzed examinees’ response patterns. The researcher appropriately classify examinees into groups by fuzzy clustering and used PIRS to draw the concept structure graphs of each group. The study explores the characteristics and differences of concept structures of students under each concept. The results of this study are as follows.
1. The examinees is classified into groups by fuzzy clustering, and the results show that three groups is the best.
2. Precondition relationship among some of the concepts of “numbers and quantities” conform to the development of mathematical concepts.
3. Under different concepts, the concept structure graph of each group has its own characteristics.
4. The linkages between concept structures could provide some references for teachers.
According to the findings of the study, the methods of the study could be helpful for understanding concept structures of students and being references of grouping and remedial instruction. Finally some suggestions and recommendations are provided for future research and teaching.
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