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 本研究目的是藉由自編的「平均數問題工作單」進行調查研究，以探討某高職271位學生在平均數問題的解題類型和所佔的比例，並分析其中3位個案學生的解題表現。研究結果如下： 高職學生面對熟悉的問題的解題類型，大多以「總和/個數」求解(75%)；錯誤類型，則多數未考慮權值(9%)與欠缺程序性知識(11%)。面對不熟悉的平均速率問題，多數以假設兩地距離方式求解(4%)；在解「有相同增量」的問題，多數以「調整前、後總分」求解(3%)。面對等差數列的平均數問題，可能因欠缺等差數列的平均數即是中位數的先備知識，導致解題發生困難。面對「由各數與最小數差的總和求資料個數」的平均數問題，多以「直觀」列式求解。 個案學生的解題表現：小維解熟悉且抽象問題時，以嘗試錯誤法解題，但因未「控制」所代入數字，以致解題失敗。小琪解不熟悉且具體的問題時，因欠缺對答案的「控制」，誤以為答案需再加1，以致解題失敗。小政解各資料均以相同增量調整的不熟悉且抽象問題時，欠缺多餘訊息的解題經驗，即「資源」不足，而解題失敗。
 This study aimed to investigate 271 vocational high school students’ ability of solving average problem and the percentage of the types of problem solving by using a self-designed “Average Problem Worksheet”. According to the analysis of resources, heuristics, and control of 3 case students’ performance of problem solving, the research findings could be found. Problem solving could be divided into three types when the students dealt with the familiar average problems: 75% students chose to use “total sum divided by the number”; students of using error type were 9% due to the lack of considering “weighted”; 11% students did not have procedural knowledge. When facing unfamiliar questions of average speed, most students solved the problems by the assumption of the distance in between two locations (4%); when facing “restoration average problems”, most students used the method of “work backward” (3%). In terms of the average problems of arithmetic progression, students had difficult solving it possibly because they did not have prior knowledge of arithmetic progression’s median. Referring to the averaging problems of “seeking the total sum of each number and the minimum number of the sum of the difference”, the students tended to use ‘intuitive method’. Regarding the performance of the case students who failed to solve the average problems, Hsiao-Wei solved familiar and abstract problems by using the method of error type. The results were close or far from the average problems because he did not control the used numbers. Next, Hsiao-Chi solved unfamiliar and concrete problems due to the lack of control towards the answer. Finally, Hsiao-Cheng solved unfamiliar and abstract problems such as “restoration average” because he had insufficient resources and did not identify the extra message.
 中文摘要 i英文摘要 ⅱ目次 ⅲ表次 ⅴ圖次 ⅵ第一章 緒論第一節 研究背景與動機 1第二節 研究目的與研究問題 3第三節 名詞釋義 4第四節 研究範圍與研究限制 5第二章 文獻探討第一節 問題解決 7第二節 數學解題 12第三節 平均數問題 22第四節 學生在平均數問題的認知概念與解題表現 32第三章 研究方法第一節 研究方法與研究架構 39第二節 研究對象 42第三節 研究工具 44第四節 研究實施 49第五節 資料蒐集、整理與分析 50第四章 研究結果與討論第一節 高職一年級學生解平均數問題的解題類型和所占的比例 52第二節 個案學生在平均數問題的解題表現 79第五章 結論與建議第一節 結論 95第二節 建議 100參考文獻中文部分 102英文部分 104附錄附錄一 平均數問題工作單 108
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 1 個案資優生對平均數問題解題表現之研究 2 國中七年級資優生在非例行性平均數問題的解題表現 3 國小六年級學童百分率問題之解題表現與歷程 4 高職一年級學生線型函數應用問題之解題表現與歷程 5 國小六年級資優生在比例問題之解題表現

 1 歐用生 (1995) 。國民小學新課程標準的精神與特色。台北市：台灣省國民學校教師研習會。 2 蔡子雲、劉祥通(2007)。資優生在想什麼？－速率篇。資優教育研究，7(1)，29-47。 3 喻平 (2002) 。論數學解題教學的現代理論基礎。數學傳播，26(4)，60-68。 4 黃敏晃 (1991) 。淺談數學解題。教與學，23，2-15。 5 林碧珍 (2001) 。教師如何培養學生形成數學問題的能力。國教世紀，198，5-14。

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