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題 名 | 數學資優生的解題歷程分析--以建中三位不同能力的數學資優生為例=A Study on the Problem-Solving Process of Mathematically Talented Students--Using Three Cases |
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作 者 | 劉貞宜; | 書刊名 | 資優教育研究 |
卷 期 | 1:2 2001.12[民90.12] |
頁 次 | 頁97-120 |
分類號 | 529.61 |
關鍵詞 | 社會資源; 後設認知能力; 情意態度; 數學資優生; 數學解題歷程; 數學解題特徵; 數學解題策略; Social resource; Metacognitive abilities; Emotional characteristics; Mathematically talented students; Mathematical problem-solving process; Mathematical thinking methods; Mathematical effective strategies; |
語 文 | 中文(Chinese) |
中文摘要 | 本研究旨在探討不同能力數學資優生的解題歷程,以建中數理資優班老師所命的十道數學題為研究工具,以建國高中二年級三位不同能力的數學資優生為研究對象,以個案放聲思考的方法,蒐集解題內部思考歷程,並以訪談的方式蒐集解題的情意態度,最後以質化的方式方析及統整所蒐集的資料,得到如下的結論: 1.解題歷程:數學資優生解題歷程階段有其相同及不同之處,大都在第二分析題目階段及第三整合及探索階段有所不同。能力越高的學生解題路徑越多,其中能力最高的A生最能覺知、掌握及分析題目及自己的能力;而能力中上的B生常需透過具體表徵及探索後,才會決定解題方法或方向;而能力較弱的C生則較常使用無系統的假設法或嘗試錯誤法來探索題目。 2.數學知識:不同能力數學資優生皆能利用語言知識、基模知識及數學相關概念知識來理解、聯結及應用題目的條件、相關知識、解法及方向。其中能力越高的學生運用的數學知識越多、越廣。 3.數學思維方法:不同能力數學資優生數學思維方法多元,且大多屬於高層次的思考能力,且思考能力靈活、快速。其中能力越高的學生使用的數學思維方法越多,思考也越靈活、快速。 4.解題策略:不同能力數學資優生能利用解題策略來幫助自己理解、思考、探索、聯結及推理,讓整個解變的更順暢及快速,且策略的使用多元。其中能力最高的A生所使用的解題策略最多。 5.後設認知能力:數學資優生能在解題中隨時利用後設認知能力監控其解題,故其對自己的能力及狀況、對解題行為的掌控,以及對解題方法的使用,皆能做到有效的覺知、預測、評估及調整。其中A生最能覺知、預測及評估自己的能力、解題行為及解題方法,並適時的做調整。 6.情意態度:數學資優生在解題中遇到挫折時,大多抱持積極正向的態度及信念,且不易出現較大的負面情緒,縱使出現負面情緒也能很快的將其轉化。 7.資源運用方面:不同能力的數學資優生在解題時,當無法解出題目時,會去尋求資源來協助解題,唯因其個性、家庭背景及習慣等因素,而影響其運用資源的優先順序。 |
英文摘要 | The purpose of this study was to examine ine the problem-solving process of mathematically talented students with different abilities. Participants of this study were three mathematically talented students in their second year at Chien-Kuo Senior High School. They were given 10 math questions conducted by qualified teachers. The researcher collected the information of their thinking process by the "think aloud" method and had interviews with them in order to understand their emotion attitude. The results are as follows. As for problem-solving process, Student A with the highest mathematical ability can best detect and analyze problems as well as his own ability. With regard to Student B with general ability, he made sure the ways how he would solve problems by concrete representation. Student C with lowest mathematical ability would use unsystematic ways to explore questions. In addition, Student A used more mathematical knowledge, mathematical thinking methods, effective strategies and metacognitive abilities than the other two and was relatively faster in solving mathematical problems. Moreover, we can tell that all participants showed positive emotion attitude when encountered with difficulties. Similarly, three participants employed different social resources to help them solve problems; however, both the ways and priorities of using sources were different. |
本系統中英文摘要資訊取自各篇刊載內容。