國小六年級學童發現數列樣式的推理歷程之分析研究
| Autor: | Pei-wen Li, 李佩玟 |
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| Rok vydání: | 2005 |
| Druh dokumentu: | 學位論文 ; thesis |
| Popis: | 93 The study was to investigate children’s reasoning process in solving sequence problems. The researcher established the cognitive process of sequences problems solved by reorganizing literature: encoding → looking for patterns (unitizing → computation and inference → mapping) → application∕generalization→ response, and used two experimental results to support the existence of “unitizing”, “computation and inference”, “mapping” in the stage of “looking for patterns”. The first experiment was designed to operate “number of the string” and “nature of the string”, and formed three types of sequences. The second one was designed to operate “nature of differences between terms－ interval & multiple, lower-order & higher-order relations ”, and formed four types of sequences. Subjects are 319 six grade children from ten classes in five schools in Taipei and Keelung. They were asked to provide the next term for a given sequence and list the mathematic formula. Results consisted of the correct rate (Part Ⅰ) and strategy (Part Ⅱ) involved in solving these problems. Part Ⅰ of the first experiment: Subjects’ performance in sole sequences was better than compound sequences and has no difference between two types of compound sequences by t-test. Part Ⅱ of the first experiment: It was easier for subjects to solve compound sequences by using grouping approach than adjacent approach. In other words, they must divide compound sequences into two strings and then look for patterns. Part Ⅰ of the second experiment: Subjects’ performance in sequences with interval relations was better than sequence with multiple relations and in linear sequences (with lower-order relations) was better than quadratic sequences (with higher-order relations) by two-way ANOVA analysis. Part Ⅱ of the second experiment: Few subjects used plus-minus method fixedly to look for patterns of all sequences. Some subjects intended to neglect the mapping step and then patterns of quadratic sequences. Meanwhile, researcher selected four subjects’ written record for qualitative data analysis. From above mentioned, it showed that the importance of “unitizing”, “computation and inference”, “mapping” steps. Finally, researcher made the flow diagram for solution of sequences and provided suggestion about researches and teaching. |
| Databáze: | Networked Digital Library of Theses & Dissertations |
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