小六學生不同代數表徵的解題表現、教師布題順序與代數教學信念之研究

The Study of Six Graders' Problem-Solving Performance, Teachers' Problem Posing and Teaching Beliefs in Different Algebra Problems

10.6151/CERQ.2012.2002.03

劉家樟(Chia-Chang Liu)；楊凱琳(Kai-Lin Yang)；許慧玉(Hui-Yu Hsu)

符號優先教學觀 ； 代數教學信念 ； 符號題 ； 文字題 ； 故事題 ； symbol-precedence view ； teaching beliefs in algebra ； equation problems ； word-equation problems ； story problems

當代教育研究季刊

20卷2期（2012 / 06 / 30）

93 - 133

繁體中文

本研究主要探討三個問題，包括：第一是臺灣國小六年級學生在不同代數試題表徵（故事、文字、符號）的解題表現：第二是國小數學教師對這三類試題表徵的教學布題序列及背後的教學信念：第三是學生的解題表現與教師信念間之一致性檢驗。研究結果發現：一、在相同數學內涵之下，國小六年級學生在符號題表現最好，故事題表現最差。但進一步分析後發現，學生雖在符號題的答題較佳，代數思維的發展仍未臻成熟。二、約80%國小數學科教師的布題順序為符號、文字、故事，且具有符號優先教學觀（symbol-precedence view）。這些教師認為，學生在符號題表現較好，文字題應直接教導正確解題法或先熟悉符號操作過程，也較贊同代數方程式是解決故事或文字題最有效的方法。剩下20%的教師則是認為，應先教學生故事題， 其教學信念明顯偏向非符號優先與非示純解題法的教學觀。三、進一步比較教師布題順序及代數教學信念與學生解題表現間的一致性，結果發現，教師無法完全準確地預測學生的答題表現。更有甚者，教學信念偏向非符號優先與非清楚示範解題法的教師，預測學生的答題表現最不準確。

This paper presents three investigations related to algebra problems: (1) Taiwanese sixth graders' problem-solving performance on story problems, word-equation problems, and equation problems; (2) Taiwanese mathematics teachers' posing sequences towards these problems and their hidden teaching beliefs: and (3) the relationship between students' performance and teachers ' beliefs. These analyses revealed that sixth graders performed the best on equation problems and the worst on story problems. Further investigation indicated that although students performed better on equation problems, their algebraic thinking was still not well-developed. Second, about 80% mathematics teachers posed problems with the sequences of equation problems, word-equation problems, and story problems, respectively; they preferred the symbol-precedence view. They thought equation problems were easiest for students, and that word-equation problems should teach students how to directly find algebraic solutions and the procedures of algebraic operations. They also agreed that algebraic equations were the most effective way to solve story problems and word-equation problems. The remaining teachers, who expressed a non-symbol-precedence view, believed that story problems should be taught first. Third, the comparisons showed the inconsistency between students' performance and teachers' predictions, especially those teachers with a non-symbol-precedence belief made the worst predictions.

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