Fuzzy Approach of Interpretive Structural Model on Mathematics Competence Indicators of Numbers and Quantities for Pupils

• Main Authors: Shin-fen Shih, 施杏芬
• Other Authors: Y.H., Lin
• Format: Others
• Language: zh-TW
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/46824929527131063355

碩士 === 國立臺中教育大學 === 教育測驗統計研究所 === 96 === The purpose of this study is to apply the Fuzzy Approach of Interpretive Structural Model (FAISM) to analyze the individualized hierarchical structures of numbers and quantities concepts for third graders. In order to explore the individualized structure of numbers and quantities concepts, the sample includes 1086 third graders of elementary schools and the testing is self-designed numbers and quantities concepts test first. Secondly, the researcher analyzes students’ response patterns through FAISM software to get the individualized hierarchical structures of concepts. Thirdly, the researcher compares qualitively and quantitatively the differences of the individualized hierarchical structures among examinees of high, middle, low ability with the experts. Finally, the researcher explores the differences among groups by fuzzy cluster analysis and IRT latent trait. Through the procedures of the analysis, the following conclusions are found. 1. The FAISM is a feasible way for analyzing the individualized concepts structures of numbers and quantities. 2. The ISM graphs of examinees are varied with different ability. 3. The ISM graphs are different from those who have the same total scores but different response patterns. 4. According to individualized ISM graphs, the links among concepts could be as references for group teaching and remedial instruction. 5. Based on the referenced standard of experts’ concept structures, the similarity indices of the ISM graphs of examinees of different ability are significantly different. 6. The higher IRT theta values of examinees have, the higher similarity indices of the ISM graphs will be. 7. All examinees are divided into two groups, higher ability and lower ability. The examinees in the same group have similar mastery concepts. The findings of this study should be helpful for understanding the learning process of numbers and quantities and could be as references for remedial instruction or group teaching. Finally, some recommendations and suggestions for future research are provided.