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題 名 | 以建模觀點詮釋國中資優生的數學解題活動=Using Modeling Perspectives to Interpret Mathematic Problem Solving Activities of Junior High School Gifted Students |
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作 者 | 顏富明; 張靜嚳; | 書刊名 | 科學教育研究與發展季刊 |
卷 期 | 60 2011.03[民100.03] |
頁 次 | 頁91-131 |
分類號 | 529.61 |
關鍵詞 | 解題; 建模; 資優生; 詮釋; Problem solving; Modeling; Gifted student; Interpretation; |
語 文 | 中文(Chinese) |
中文摘要 | 本研究目的是以建模觀點詮釋國中資優生的數學解題活動,包含思維內涵、模型、建模循環與模型發展系列的關係。本研究採個案研究法,在一班30人的國中資優生進行小組合作解題,全班共分成八組,每組3至4人,以其中四組為本研究之個案,資料收集包含小組討論及其發表、學生的學習日誌、教學現場摘記、教學日誌及任務導向的臨床晤談。研究結果發現:1.國中資優生的解題活動是一種建模思維取向的歷程,而不是描述式或規範式的歷程;2.以建模觀點詮釋國中資優生數學解題活動,有助於了解國中資優生的數學思維特徵;3.模型、建模循環與模型發展系列也有一些特定的關係與蘊涵,包括(1)模型與建模循環的一對一對應關係;(2)在每個問題的模型發展系列的主要活動中,所建構的模型數量是依問題解決者所經歷的建模循環次數而定;(3)問題的本質與模型建構、模型發展系列的關聯性;(4)所建構的模型數量的多寡,不是代表題目的難易,而是代表不同解題者企圖貼近問題,所經歷的建模循環次數的差異。 |
英文摘要 | The purpose of this paper was to interpret the mathematical problem solving activities of junior high school gifted students from modeling perspectives, focusing particularly on the relationships among the intension of thinking, models, modeling cycles and model-development sequences. Using a case study approach, the study examined the cooperative problem solving of a class of 30 students. The subjects were divided into eight small groups of 3 to 4 students. Four groups were chosen as the cases. Data were collected from the discussions and presentations of the groups, the students’ learning journals, the teaching notes, the teaching journals, and the task-based clinical interviews. The main findings of the study were as follows. First, the problem solving activities of junior high school gifted students were a process of modeling thinking orientation, rather than a descriptive or prescriptive process. Second, interpreting the mathematical problem solving activities of junior high school gifted students from modeling perspectives, the study also showed insight into the characterizations of the students’ mathematical thinking. Third, there were some specific relationships and implications among models, modeling cycles and model-development sequences, including (1) the one-to-one correspondences between models and modeling cycles; (2) the dependence of the quantities of constructed models on the number of times of modeling cycles that problem solvers experienced during the main activities of model development sequences of each problem; (3) the relationships among the nature of the problem, model construction and model-development sequences; (4) the various quantities of constructed models, which represent the discrepancy of the number of times of modeling cycles experienced by different problem solvers who attempt to approach problems, rather than the difficulty levels of problems. |
本系統中英文摘要資訊取自各篇刊載內容。