The ordering hierarchies on solving the proportional problem for pupils

• Main Authors: WEI-SHIH LIN, 林瑋詩
• Other Authors: 林原宏
• Format: Others
• Language: zh-TW
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/90747111723397974753

碩士 === 國立臺中教育大學 === 數學教育學系在職進修教學碩士學位班 === 95 === The purpose of this study is to apply ordering theory in analyzing the hierarchical structures of problem-solving rules of proportional problems for individualized subjects. Besides, the author also compares rule graphs according to grade and gender. There are 876 subjects in this study. The proportional problem test is designed by the author. In the data analysis, individualized rule hierarchies are discussed and rule graphs are compared. Through the procedure of the analysis, the following conclusions were found. 1. Subjects of different total score exhibit different characteristics of rule-hierarchies. 2. Subjects of the same total score exhibit different rule-hierarchies due to distinct response patterns. 3. Characteristics of rule-hierarchies in three number types of proportional problems within one subject are different. 4. Characteristics of rule-hierarchies in three semantic types of proportional problems within one subject are different. 5. Rule usages between fifth and sixth graders are different. Rule usages utilized by six graders are more similar to that of expert than fifth graders. 6. Rule usages between male and female are not different. The findings of this study should be helpful for cognition diagnosis and as references for remedial instruction. Finally, some recommendations and suggestions for future research are provided.