The Longitudinal Research on Integer Addition and Subtraction Concepts for Junior-Grade Elementary School Students －An Integrated Application Using Fuzzy Cluster Analysis and Ordering Theory

Autor: HSIU-YU HUANG, 黃秀玉
Rok vydání: 2008
Druh dokumentu: 學位論文 ; thesis
Popis: 96
Addition and subtraction are not only the key points of math for elementary schools beginner students, but also are fundamental factors for students to learn math. Therefore, this research sampled total of 413 junior-grade elementary school students as subjects and is conducted by using “Self-Designed Addition and Subtraction Word Problems Tests” integrated with fuzzy clustering and generalized ordering theory. This paper is to explore the cross-time variations in terms of solving representation, clusters in which the students are categorized, the knowledge structure of every student in the same and across different clusters under each categories. The results of this research reveal that： 1. Pupils are most proficient in type 5 (Change/ Decrease/ Change quantity unknown), and least proficient in type 19 (Compare/ Less than/ Referent quantity unknown) on both tests. The places and the directions of the unknowns do cause significant differences on each type. 2. Change problems have the highest mean in of both tests while combine and compare problems have the lowest mean scores. Furthermore, the second-year students are more proficient than the first-year students in terms of problem solving ability in every category. 3. For both tests, pupils do less well than before on type 1 (Compare/ More than/ Referent quantity unknown) but perform significantly better in the 17 types and 4 categories except for type 15 (Equalize /Join/ Compared quantity unknown) and type 17 (Equalize/ Separate/ Referent quantity unknown). 4. For both tests, the number of clusters is the same in 4 categories. However, there are characteristics in its knowledge structure for different clusters in the same categories and different groups of pupils in the same test. 5. In the first year pupils are most proficient in type 5 (Change/ Decrease/ Change quantity unknown) and least proficient in type 20 (Change/ Increase/ Change quantity unknown). This remains true for the second year. Pupils that are most proficient in all of the change problems in the first year will deal with the change problems well in the second year. 6. Most of the pupils will be proficient in all of combine problems in the second year regardless of how they performed on the problems in the first year. 7. In compare type of problems, pupils that are most proficient in types of compared and difference quantity unknown, and least proficient in those types of in referent quantity unknown in the first year are most likely still most precise and least precise in the same types in the second year. Pupils are least proficient in type 19 (Compare/ Less than/ Referent quantity unknown) only are most likely to be proficient in all types. 8. Most of the pupils who are proficient in type 2 (Equalize/ Join/ Referent quantity unknown) and type 17 (Equalize/ Separate/ Referent quantity unknown) and who are least proficient in type 7 (Equalize/ Separate/ Compared quantity unknown) in the first year will show similar mathematical problem solving results in the second year. Pupils who are most proficient in all of equalize problems in the first year are most likely to perform are same in the second year. 9. Population proportion by every cluster in both tests for all examinees in change, compare and equalize is significant. There are important cognitive meanings of mathematics in each result group. There are particularity in learning behaviors and cognition in mathematics. The knowledge structure changed for both tests. However, the base and upper types always are the base and upper. 10. For both tests, both hierarchy structure and number of people are different for pupils who belong to each of the 4 categories. Not only the results are in complete accordance with difficulty levels (base to upper), but also shows the hierarchical characteristics of knowledge structure. Diagnostics for cognitive abilities should be based on the characteristics and different knowledge structures. Moreover, this research provides useful information for as of how to design teaching materials, what are the remedial procedures for future research and studies.
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