# 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

 dc.contributor.author 劉家樟 楊凱琳 許慧玉 zh_tw dc.contributor.author Chia-Chang Liu Kai-Lin Yang Hui-Yu Hsu en_US dc.date.accessioned 2014-10-27T15:14:50Z dc.date.available 2014-10-27T15:14:50Z dc.date.issued 2012-06-?? zh_TW dc.description.abstract 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-precedenceview) 。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(憂先與非示範解題法的教學觀。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o zh_tw dc.description.abstract This paper presents three investigations related to algebra problems: (I) Taiwanese sixth graders' problem-solving performance on story problems, wordequation 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-symbolprecedence 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. en_US dc.identifier DE75C4CB-A151-65B2-8CEE-6599C9E31F9E zh_TW dc.identifier.uri http://rportal.lib.ntnu.edu.tw/handle/20.500.12235/13191 dc.language 中文 zh_TW dc.publisher 教育研究與評鑑中心 zh_tw dc.publisher Center for Educational Research and Evaluation en_US dc.relation 20(2)，93-133 zh_TW dc.relation.ispartof 當代教育研究 zh_tw dc.subject.other 符號優先教學觀 zh_tw dc.subject.other 代數教學信念 zh_tw dc.subject.other 符號題 zh_tw dc.subject.other 文字題 zh_tw dc.subject.other 故事題 zh_tw dc.subject.other symbol-precedence view en_US dc.subject.other teaching beliefs in algebra en_US dc.subject.other equationproblems en_US dc.subject.other word-equation problems en_US dc.subject.other story problems en_US dc.title 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 zh-tw dc.title.alternative The Study of Six Graders' Problem-Solving Performance, Teachers' Problem Posing and Teaching Beliefs in Different Algebra Problems zh_tw

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