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   免費試閱

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

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.