本研究為二年期研究的第二部分－四年級部分，第一部份（五年級）已於去年完 成。本研究主旨在探討小學數學資優生及普通生（定義採教師認定，寬鬆適合多數學生傾向 ）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，所使用的思考方式及答題比率作為探討的重點，採質式為主 ，量式為輔的研究方向。本研究以三大類非例行性問題的解題來進行，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式，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。 第二年研究與第一年研究不同之處除了年級不同（四年級代替五年級）外，尚加入城鄉比較 ，同時對城市國小（臺南師院附小）與鄉村國小（高雄縣岡山某國小）做解題歷程之比較， 以便使此研究更具普遍性，可信性。 實驗結果發現： 在城市國小以及鄉村國小，兩類學童同時在解數概念題時差異最大，邏輯概念題次之，題組 及創意題差距最小。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 次序城市國小依次為 41.7%、 28.5% 以及 15.9%； 鄉村國小依次為 43.8%、 28.3% 以及 29.9%。 他們在顯示解題策略，解題行為以及所用的思考方式的解題層次上的差異城市國小 依次為 32%、45.4% 以及 22%；鄉村國小依次為 43.6%、31.5% 以及 29.9% （此差為 A+、 A 類層次比率之差）。此結果顯示不論城鄉數學資優生不僅在答題率上優於普通生，在思考 品質層次上亦大幅優於普通生。 在國小兩類學童的解題方面， 城市數學資優生有一半左右（ 54.3% ），鄉村數學資優生也 有近一半（ 46.9% ）比較能掌握題目的全面性， 以系統的、有計畫的方式來設計策略解決 問題（即 A+、A 層次）。 他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。在 普通生方面， 普通生中則四分之三以上（城市普通生有 75.1%，鄉村普通生有 78.3% ）以 局限的、部分條件作為思考、解題的依據（即 B、C、D 層次）。 他們通常不能有效地整合 題中各類條件，如此不周全的思考模式常常導致錯誤或者部分答案產生。在所有三類題型中 ，普通生的解題行為也均有一致性。 在城鄉的比較方面，數學資優生中城市國小學童以總答題率差距 12.8% （ 75.4% 比 62.6% ）優於鄉村國小學童。 在解題層次上則以 7.4% （ A+、A 類層次差）略有差異（城市國小 比較優）。 數學普通生中則差異較大， 城市普通生以總答題率 19.5% （ 48.3% 比 28.8% ）之差優於鄉村國小學童。在解題層次上城市普通生則以 13.2% （ A+、A 類層次差）之差 優於鄉村普通生。

　　　　　This study explores the differences between the thought processes of mathematically advanced fourth grade students with the thought processes of average students of the same level, when solving a variety of mathematics problems. This is a series of two years study. The first years study focused on the student's problem solving processes of the fifth grade. Now the study focuses on the students' problem solving processes of the fourth grade. Students were presented with fifteen problems selected from one of three categories: number sense problems, and pattern recognition, creative 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 major in qualitative assessment of their thought process. For fourth grade the most dramatic difference was observed in number sense problems. The differences between logic sense problem was on the second place. So the least differences happened in pattern recognition problems. The two groups of students varied pretty obvious in their rates of success in all three categories of problems. The differences of success rates for city stydentswere41.7%, 28.5%, and 15.9% for three categories of problems respectively. As for urban students, the differences of success rates were 43.8%, 28.3% and 27.8% for three categories of problems, respectively. They also showed their dramatic differences in the processes of problem solving. The differences of the rates of A+'s or A's solving quality in all three categories of problems were 32%, 45.4% and 22% for city students, and 43.6%, 31.5% and 29.9% for urban students, respectively. Therefore analysis of the problem solving approaches used by the two groups of students of two schools supports the hypothesis that the thought processes of mathematically advanced students are qualitatively distinct from those of their peers. In all three categories of problems, the mathematically advanced students demonstrate an ability about 54.3% for city students 46.9% for urban students 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 75% (75.1% for city students, 78.3% for urban students). They made premature connections between conditions of the problem. Because their evaluation of the condition of a given problem was often inadequate, average students typically made numerous wrong attempts and obtained incorrect or incomplete answers.