因數與倍數之解題溝通能力測驗編製及其實證探究

本研究旨在根據因數與倍數之數學解題溝通能力的內涵，編製因數與倍數解題溝通能力測驗，以分析學生的因數與倍數的解題溝通能力。研究對象為國民小學六年級學生，計342名。採用自編的「因數與倍數的解題溝通能力測驗」為研究工具，經統計分析後，研究結果發現：一、本研究之溝通層次分為「表達自我想法」、「理解他人想法」與「評價他人想法」，整體而言，「表達自我想法」與「理解他人想法」優於「評價他人想法」；「因數」的溝通能力優於「倍數」的溝通能力。二、在「表達自我概念」上，「符號表徵」的了解優於「理解題意」，「解題」優於「表達溝通」。在「理解他人想法」中，其能力表現依次為「判斷」、「轉化」、「認同說明」、「質疑辯證」。在「評價他人想法」中，「辨別」優於「澄清與補充」和「評鑑」。三、本研究溝通類型分為內向表達型、外向理解型、全能優越型及多層障礙型；其中多層障礙型的人數百分比最高，全能優越型最少。四、因數與倍數概念之錯誤類型分析可分為：（一）語言概念錯誤，包括題意了解錯誤、語意知識不足、專有名詞概念混淆；（二）認知概念錯誤，包括運思能力不足、粗心錯誤、運算系統錯誤、直觀法則影響；（三）策略概念錯誤，包括解題策略錯誤、計劃監控失誤；（四）個人態度錯誤，包括厭惡思考、猜測。最後，研究者根據研究結果提出對於教學、評量實務及未來進一步的建議。

關鍵字

因數與倍數；解題溝通能力；溝通類型

並列摘要

The purpose of this study was to design the testing tools of mathematics communication on factor and multiple problems and investigate pupils' ability of mathematics communication on factor and multiple problems. There are totally 342 sixth graders. According to the data analysis, there were some results as follows: 1. There were three levels of mathematics communication. They were ”expressing one's own concepts”, ”comprehending thinking of others” and ”evaluating thinking of others.” 2. As to ”expressing one's own concepts”, the performance of ”the symbolic representation” was better than that of ”realizing the meaning of problems.” The performance of ”problem-solving” was better than that of ”expressing”. As to ”evaluating thinking of others”, the performance of ”identification” was better than that of ”clarifying and addition” and the ”estimation.” 3. There were four kinds of mathematics communication. They were ”interior-expressing”, ”exterior-comprehending”, ”overall-excellence” and ”multiply-obstacle.” The ”multiply-obstacle” was the highest of percentage and the ”overall-excellence” was the least of percentage. 4. According to the analysis of the misconception of communication, they were misconception of language, the wrong cognition, the fault of tactics and the fault of individual attitude. Finally, according to the results of this research, some suggestions for teaching, practical assessment and future research were recommended by the researcher.