Apply the polytomous item relational structure (PIRS) to analyze the hierarchical structures of Numbers and Quantities concepts for third graders

• Main Authors: PEI-YI, CHEN, 陳沛儀
• Other Authors: Tian-Wei, Sheu
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/75110346459549522256

碩士 === 國立臺中教育大學 === 教育測驗統計研究所 === 97 === Numbers and Quantities are very important in mathematics curriculum. Mathematics learning is step-by-step. To grasp the structures of Numbers and Quantities concepts is conducive teaching. The purpose of this study is to apply the polytomous item relational structure (PIRS) to analyze the hierarchical structures of Numbers and Quantities concepts for third graders. In order to investigate the structure of Numbers and Quantities concepts, the researcher first tests 614 third graders of elementary schools by using self-designed Numbers and Quantities concepts test according to the mathematics content in Grade 1-9 Curriculum. Secondly, the researcher analyzes students’ response data matrix and item-concept matrix through PIRS software to get the hierarchical structure of Numbers and Quantities concepts. Thirdly, the researcher applies fuzzy clustering to classify task-takers into groups, and gets the concept structures of each group by PIRS. Finally, the researcher compares characteristics and differences of each group’s hierarchical structure of Numbers and Quantities concepts. Through the procedures of the analysis, the following conclusions are found. 1. The diagrams of conceptual hierarchical structures of different groups are different. 2. For third graders, the structure of Number concepts are hierarchical, but the structure of Quantity concepts are not. 3. Classifying task-takers into two groups is helpful for remedial instruction. The findings of this study may be helpful for teachers to understand the conceptual structures of Numbers and Quantities, and as references for remedial instruction or group teaching. Finally, some recommendations and suggestions for future research are provided.