本研究在探討五年級數學資優生及普通生在數學解題(非例行性問題時)的思考歷 程，並探索比較兩類學童思考模式的異同。本研究以兒童解題策略，解題行為，所使用的思 考方式以及答題比率作為探討的重點。本研究以三大類問題的解題來進行，其目的為希望以 不同類的題型來探索兒童解題時的思考歷程以便尋求其解題模型，並比較兩類學童的異同處 。實驗進行時，學童被要求以放聲思考 (thinking aloud) 方式來解釋其所有的解題活動及 內在思考歷程。實驗結果發現：兩類學童在解邏輯概念題時差異最大，題組及創意題及數概 念題則在伯仲之間。兩類學童在答題率上的差異依數概念題，邏輯概念題，題組及創意題之 次序依次為 14 ％，28.3 ％及 16.5 ％。 他們在顯示解題策略，解題行為及所使用的思考 方式的題題層次上的差異則依次為 20 ％，42 ％及 24 ％ (此差為 A 類層次比率之差 )， 此結果顯示數學資優生不僅在答題率上優於普通生，在思考品質，層次上亦有較大的優異性 。在兩類學童的解題模型方面，數學資優生通常 (70 ％左右 ) 較能掌握題目的全面性，以 系統的，有計劃的方式來設計策略解決問題。他們能有效的整合題目中各類資訊，條件，並 運用原有認知做出正確的判斷。在所有三類題型中，資優生的解題行為有其一致性，以一致 的思考模型進行。 普通生則通常 (一半以上 ) 以局限的，部分的條件作為思考，解題的依 據。他們通常不能有效地整合題中各類條件，如此不週全的思考模式常導至錯誤或部分答案 產生。在所有三類題型中，普通生的解題行為也均有一致性。

　　　　　This study explores the differences between the thought processes of mathematically advanced fifth grade students with the thought processes of average students of the same level, when solving a variety of mathematics problems. Students were presented with fourteen problems select from one of three categories:number sense problems, logic sense problems, and pattern recognition problems. They were given calculators and simple tools such as blocks, and were asked to "think out loud" as they solved the problems, in order to allow a qualitative assessment of their thought processes. The most dramatic difference was observed in problems dealing with logic. The differences between the other two categories of problems were pretty even. The two groups of students varied pretty obvious in their rates of success in all three categories of problems (the differences of success rates were 140%, 28.3% and 16.5%, respectively). They also showed their dramatic differences in the processes of problem solving. The differences of the rates of A's solving quality in all three categories of problems were 20%, 42% and 24%, respectively. Therefore, analysis of the problem solving approaches used by the two groups of students supports the hypothesis that the thought processes of mathematically advanced students are qualitatively distinct form those of their peers. In all three categories of problems, the mathematically advanced students demonstrated an ability about 70% to maintain a broad perspective of the overall conditions of the problem and to execute a systematic, progressive evaluation. They were able to combine all the conditions (information) of the problem and to approach the problem heuristically. Average subjects, on the other hand, tended to deal with problems using limited or partial information over 50%. They made premature connections between conditions and often pursued only one of the conditions of the problem. Because their evaluation of the conditions of a given problem was often inadequate, average students typically made numberous wrong attempts and obtained incorrect or incomplete answers.