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題 名 | Analogical Reasoning in Mathematical Problem Solving: The Effects of Problem Similarities and Domain Knowledge=解決數學問題的類比推理思考--問題相似性與領域知識的影響 |
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作 者 | 黃幸美; 鄭晉昌; | 書刊名 | 臺北市立師範學院學報 |
卷 期 | 31 2000.04[民89.04] |
頁 次 | 頁135-159 |
分類號 | 523.32 |
關鍵詞 | 解決數學問題; 類比推理思考; 問題相似性; 領域知識; 兒童; |
語 文 | 英文(English) |
中文摘要 | 本文包含兩個研究,主要目的在探討兒童解決數學問題的類比推理思考。第一個研究,探討來源與標的問題之間的特徵相似性,對於兒童類比推理解決數學問題表現的影響。研究結果發現,當來源與標的問題之間的表面特徵與結構特徵皆相似時,兒童的解題表現最理想;當來源與標的問題之間只具表面特徵相似性而結構特徵不相似時,兒童的解題表現最不理想。第二個研究,探討來源與標的問題之間的相似性,對好與差的問題解決者推理解題表現的影響,同時分析不同能力的解題者其類比遷移與解題表現的差異。研究結果顯示,當來源與標的問題之間的表面特徵與結構特徵皆相似時,解題者傾向表現正向遷移,此現象尤多見之於好的解題者;反之,當來源與標的問題之間只具表面特徵相似性而結構特徵不相似時,解題者傾向錯誤對應與空白未答,此現象尤多見之於差的解題者。分析解題者的解題錯誤類型結果發現,問題基模建構不良是好的解題者最常見的錯誤類型;缺乏問題領域知識則為差的解題者最常見的錯誤類型。 |
英文摘要 | This research project consisted of two related studies which investigated children's analogical reasoning in solving mathematical problems. The first examined how children's analogical problem solving performance was affected by similarities shared by the source and target problems. Results indicated that children had superior problem solving performance when the source and target shared both surface and structural similarities and had poorer performance when they shared both surface and structural similarities and had poorer performance when they shared merely surface similarities. The second examined how similarities shared by the source and target affected good and poor problem solvers' problem solving performance. The research focus concerned the analogical transfer that primarily resulted from the similarities of problem features and learners' capabilities in representating problems. Results indicated when the source and the target possessed the same structural features, positive transfer was more likely, particularly for good problem solvers. On the other hand, when the two shared the same superficial but not structural features, misapplying knowledge and blank without transfer was more likely, particularly for poor problem solvers. Most instances of failure of analogical transfer made by good problem solvers resulted fro ill-constructed problem schemas whereas those of poor problem solvers' resulted from a lack of domain knowledge needed to obtain solutions. |
本系統中英文摘要資訊取自各篇刊載內容。