以追趕問題為例探討資優個案的解題表現

Analysis of Problem Solving Performance for a Gifted Case: Examples from the Type of Running and Catching up of Speed Problems

江奇婉(Chi-Wan Chiang) ； 劉祥通(Shiang-Tung Liu)

《資優教育季刊》 116期 (2010/09) Pp. 18-24+6

https://doi.org/10.6218/GEQ.201009_(116).0004

摘要

本研究旨在探討一位國中資優生，面對追趕非例行性問題的非代數法之解題表現。本研究先以資源、捷思和控制分析其解題表現，後來發現個案憑藉了他優越的直觀能力，早已從問題的脈絡看到解題的線索，降低了問題的複雜性，而逐步為問題找到一條解答的捷徑。研究者深信個案在解研究問題中所利用的相關線索，可以幫助學生在解題中建構更好的理解力。因此本文針對個案解題表現中在資源、捷思、控制三面向以及直觀能力加以討論並據此提供建議。

關鍵字

資優生 ； 解題表現 ； 直觀能力

並列摘要

The purpose of this study was to analyze problem solving performance for a gifted student of the seventh grader. We were mostly interested in his spontaneous (non-algebraic) method of solving non-routine problems. Originally, our attention and efforts were placed on his performance from the various dimensions of resources, heuristics, and control. Later on, we found he has excellent intuitive ability to see the problem solving clues from the problem context. Therefore, the level of problem complexity was often decreased and the shortcut of problem solving was found. Indeed, it was our belief that approaching problem as he did in this study, by gaining an appreciation of the use of relevant clues, may help students construct an understanding in problem solving. Finally, some discussions and suggestions about the viewpoints of resource, heuristic, control, and intuitive ability were provided as well.

並列關鍵字

gifted students ； problem solving performance ； intuitive ability

參考文獻

Barba, R. H.(1990).Problem solving pointers.Science Teacher.57(7),32-35.

Burton, L.(1999).Why is intuition so important to mathematicians but missing from mathematics education.For the Learning of Mathematics.19(3),27-32.

Charles, R. L.(ed.),Silver, E. A.(ed.)(1988).The Teaching and assessing of mathematical problem solving.Hillsdale, NJ:Lawrence Erlbaum Associates.

Garofalo, J.(1987).Metacognition and school mathematics.Arithmetic Teacher.34(9),22-23.

Hersh, R.(1998).What is mathematics, really?.London, UK:Vintage Books.