篇名 | 國小六年級學童未知數解題類型之個案研究:介於算術與代數階段的約估策略 |
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卷期 | 22:2 |
並列篇名 | A Case Study of a Sixth Grader's Problem Solving Patterns of the Unknown: Using the Approximation Strategy for the Cognitive Gap Between Arithmetic and Algebra |
作者 | 陳維民 |
頁次 | 101-130 |
關鍵字 | 未知數概念 、 約估解題類型 、 根本建構主義 、 基模論 、 教學晤談法 、 Conceptions of the unknown 、 the approximation strategy 、 radical constructivism 、 scheme theory 、 teaching interview 、 TSSCI |
出刊日期 | 201112 |
本研究的主要目的在探討1 位國小六年級學童面對同一未知數出現在方程式單側兩次的問題時,學童所展現的未知數解題類型。本研究透過教學晤談法,對國小六年級學童―小威(化名)進行六次的教學晤談。根據分析結果,小威在面臨常數項為加數問題、常數項為減數以及合併常數項為負的未知數合成問題時,採用合併數字項及合併未知數項的策略來進行解題,但面臨其他類型問題時,小威則展現以下六項約估解題類型:一、以倍數進行約估後調整策略;二、以公倍數進行約估後調整策略;三、約估未知數的線性組合;四、以最大整數進行約估後調整策略;五、嘗試約估算則策略;六、約估局部未知數總量」。研究中對小威約估解題類型以及「面對問題―策略選擇」的描述可以作為課程與教學上的參考。
This study examines a sixth grader's problem solving patterns of the unknown when encountering the same unknown twice on one side of the equation. Six teaching interviews were conducted with a sixth grader, Shaw-Wei (pseudonym), to collect data of his performance through videotaping. According to the analysis results, Shaw-Wei used strategies of grouping numerical terms and grouping unknown terms when encountering problems of basic type; however, he used the strategy of approximation when encountering problems of other types. The problem solving patterns of the approximation have the following attributes: (1) use the multiple as the initial approximation, and subsequently adjust; (2) use the common multiple as the initial approximation, and subsequently adjust; (3) estimate the linear combinations of the unknown; (4) use the greatest integer that satisfies the conditions as the initial approximation, and subsequently adjust; (5) use trial and error to formulate the algorithm; and (6) estimate a part of the values of the linear combinations. The problem solving patterns of the unknown can be used as the reference for the curriculum and teaching.