A Study of The Relationship between Integer Multiplication-Division Knowledge Structure and Cognitive Style for Sixth Graders Elementary School Students

• Main Authors: Chung Shih Fan, 鐘世帆
• Other Authors: 易正明
• Format: Others
• Language: zh-TW
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/33106913097171790785

碩士 === 臺中師範學院 === 數學教育學系 === 93 === The purpose of this study was to apply Pathfinder Method to investigate the relationship between knowledge structure and cognitive style when the elementary school students sloved multiplication-division problems. In the meantime, this study also analyzed both the patterns difference of knowledge structure graph representation, with which it aimd to provide the consultation for teaching diagnosis and teaching design. The subjects came from 379 sixth-grade students of three elementary school in Taichung district. The tools of this study included the “Group Embedded-Figures Tests” and “Math Tests of multiplication-division concept” designed by the author.. The main findings and conclusions were as follows: 1. Students had different ability of the problem-solving when dealing with multiplication-division problems. (1) In the performance of multiplication-division problems, the students performed best on the type of the product of measures and the type of comparison. The next was the isomorphism of measures and the multiple proportion was the worst . (2) There were differences in the places of the unknown quantity in the problems of different multiplication-division types of students. (3) The field-independent pupils were superior to the field-dependent pupils in the ability of solving multiplication-division word problems. 2. The knowledge structure indices could effectively predict subjects with different patterns of multiplication-division. The most prediction of high multiplication-division group is PFC index; secondly, the most prediction of middle multiplication-division group is PRX index. Furthermore, the most prediction of low multiplication-division group is GTD index. And the PRX index was the most prediction for all students. 3. The knowledge structure indices could effectively predict the Group Embedded-Figures Tests score of the patterns difference of multiplication-division pupils. The most prediction of all pupils, field-independent pupils and field-dependent pupils was the same and it was GTD index. 4. The knowledge structure indices could effectively discriminate subjects with different patterns of multiplication-division. 5. From the analysis the knowledge structure graph of students, the result were as follows: (1) With the knowledge structure graph of different multiplication-division ability, the low group is affected mainly by the types of the assessment questions,but the high group and mid group are not. (2) With the knowledge structure graph of different cognitive styles, the field-dependent pupils were affected mainly by the types of the assessment questions, but the field-independent pupils were not. (3) The pupils of the same test score didn’t have the same the knowledge structure graph. The results and findings can offer the consultation for teaching diagnosis and teaching design. Some recommendations for further research were provided by the researcher.