臺灣博碩士論文加值系統

專家學者認為教學者鼓勵學生在數學課時能使用多種不同方式來解決問題，可引導學生發現不同的思維。因此研究探討國小數學資優生與一般生進行數學幾何方面的多元解題時，在解題歷程中使用的解題策略變化情形。本研究採個案研究法，研究對象分別為新加坡華僑中學所舉辦小學奧林匹亞競賽的金牌選手和臺北市某國小六年級一般學童，透過紙筆測驗、錄影和訪談進行研究，從研究過程中反映出學生面對非例行性作答方式時，在解題歷程、創造力的展現以及多元解題策略的正確性及關連性。
研究結果指出數學資優生在進行多元解題時，其優異表現於正確性及解題策略的多樣性，且進行多元解題的教學有助於產生不同知識基模的聯結。而低中高數學學習成就的一般學生與數學資優生的表現情形均有明顯差異，其正確率及解題策略表現偏低，而高學成就學童的表現亦優於中低成就的學童。探究其原因可能與缺乏足夠的知識基模有關，使得解題歷程的計劃階段無法擬定正確的策略，導致錯誤的執行結果。而且一般生對於自己所完成的解題歷程無法透過多元的解題策略反覆驗證答題的正確性，導致學習成就越低的學生表現越差的結果。因此本研究建議在進行多元解題的教學過程時，對於低學習成就的學童仍應同時提升學童的數學知識基模。

This dissertation mainly discusses (compares) that the differences of the strategies in geometry between talented students and average students. It regards that in mathematics courses teachers could inspire students to explore various ideas, when they ask the students to solve problems in lots of different ways.
The research is a case study and focus on paper tests, videos and interviews to compare two cases. It shows that the relationship between students’ creativities, various strategies influences how the students solve problems, when they try to answer non-routine math problems. The cases are from two groups: one is the competitors of the Asia-Pacific Mathematical Olympiad for Primary Schools (APMOPS) in Hwa Chong Institution, the other is sixth graders in a elementary school in Taipei City.
In the result, it points out the talented students perform well on correctness and variety of strategies, when they are using various ways to solve problems. Besides, it helps them to develop the connection between different knowledge patterns. There is a huge difference between talented students and average students who are separated into three levels; the talented students perform better than average students, especially on correctness and problems solving strategies. In addition, in average student group, higher-level ones could do it better than lower ones. Probably, the reason of students’ failures is without enough patterns and incorrect strategies. Moreover, it is hard to double check correctness through various strategies for average ones; it means that the lower-level students perform worse then others. Therefore, this dissertation suggests that teachers increase knowledge patterns for low-level students during various problems solving teaching process.

目 次
第一章 緒論 1
第一節 研究動機 1
第二節 研究目的與待答問題 4
第三節 名詞釋義 5
第四節 研究範圍與限制 6
第二章 文獻探討 9
第一節 創造力之意涵 9
第二節 數學創造力 15
第三節 數學資優生 22
第四節 解題策略及歷程 31
第五節 多元解題 48
第六節 幾何學習之探究 53
第三章 研究設計 59
第一節 研究方法 59
第二節 研究對象 59
第三節 研究工具 60
第四節 研究架構與流程 63
第五節 資料的處理 64
第四章 研究結果與討論 67
第一節 數學資優生的解題結果總表現 67
第二節 三位數學資優生的解題策略表現 69
第三節 數學資優生與一般生的表現 134
第四節 回顧與省思 155
第五章 結論與建議 159
第一節 結論 159
第二節 建議 162
參考文獻 165
附錄 171
附錄一：本研究施測題目 171
附錄二：家長同意書 173

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