高雄市小五學生因數與倍數單元錯誤類型與成因之探討

The Study on Misconceptions of Factor and Multiple for Fifth Grade Students in Kaohsiung City

劉伊祝(Yi-chu Liu)

指導教授 ： 鍾鳳嬌 博士

國立屏東科技大學/人文暨社會科學院/技術及職業教育研究所/碩士(2008年)

https://doi.org/10.6346/NPUST.2008.00141

摘要

摘 要
本研究旨在瞭解國小五年級學生在因數與倍數單元常見的錯誤類型，並探討其成因。研究方法為問卷調查法，並以研究者自編之「二階段式因數與倍數基本概?測驗」為研究工具，以多階段分層比例叢集抽樣抽出20校，每校1班合計623位學生進行施測，有效樣本比例達93％。以SPSS 12進行相關統計分析，並獲得以下結論：
一、 錯誤類型
1、遺漏的錯誤。
2、概念連結的錯誤。
3、計算的錯誤。
4、文字轉譯的錯誤。
5、不完全的計算過程。
6、看不懂題目，隨便回答。
二、 錯誤成因
1、對專有名詞概念認知不清或混淆。
2、因在尋找因數與倍數的過程就發生遺漏或多找，進而導致在公因數與公倍數的尋找上也會發生遺漏或多找。
3、忽略1和本身均為因數。
4、忽略本身也是倍數，卻誤認1也是本身倍數。
5、誤解短除法運算結果在公因數與公倍數計算上解讀
6、運用關鍵字解題。
7、因題意認知不清、缺乏文字轉譯能力、計算粗心或忽略題目條
件限制，導致在文字應用題上使用錯誤解題策略。
三、 個人背景變項之差異比較
1、在性別變項方面，?同性別的小五學生在因數與倍?基本概?測驗的得分上沒有顯著的差?。
2、在就?學校?型變項方面，?同?型學校的小五學生在因數與倍?基本概?測驗的得分上有顯著的差?，且平均分?的高低依序為：37?59班＞60班以上＞36班以下。
3、在學業成就方面，不同數學學期成績等第、國語學期成績等第、總學期成績等第上的小五學生在因數與倍?基本概?測驗的得分上有顯著的差?，其中等第愈高，得分愈高，錯誤情形愈少。
4、在家庭社經地位方面，?同家庭社經地位的小五學生在因數與倍?基本概?測驗的得分上有顯著的差?，且平均分?的高低依序為：高社經地位＞中社經地位＞低社經地位家庭的學生。

關鍵字：因數與倍數、二階段測驗、迷思概念

關鍵字

因數與倍數 ； 二階段測驗 ； 迷思概念

並列摘要

Abstract
The purpose of this study not only attempts to understand the types of factor and multiple commonly confused, but also investigates their reasons. “Two-tier Basic Test for Factor and Multiple” was employed as a questionnaire instrument. By stratified-cluster sampling in terms of 623 students in one class of each school (including 20 schools) were invited to participate in the present study. Relevant statistics were analyzed with SPSS 12, and the findings were described as followings.
I. The main wrong types of factor and multiple learning
1. Mistake omitted.
2. Mistake that the concept links.
3. Mistake calculated.
4. Mistake that the characters translate.
5. The computational process is non- completely.
6. Can't understand the question, and answer it at will.
II. The main wrong reason of factor and multiple learning
1. Unclear concept of recognition or confusion on terms.
2. Omission or excessive determination when seeking factors and multiple to further occur in common factors and common multiple.
3. 1 and the number itself omitted as factors.
4. The number omitted itself as multiple, misunderstanding 1 itself as multiple.
5. Misunderstanding the operations of short division for the calculation of common factor and common multiple.
6. Use the key word to solve a problem.
7. Lack of prerequisite knowledge for multiplication and division, question not clearly recognized, careless calculation or omission of conditions to cause the wrong method used to solve question.
III.The difference of misconception for factor and multiple leaning based on personal background variable
1. There was no significant difference for testing score between male and female students.
2. There were significant differences for testing score based on school type variable. The rank order of average score for school was: class 37 to 59 > more than 60 classes > Under class 36.
3. There were significant differences for testing score based on the grades of mathematics achievement, Chinese achievement and total achievement scores. Students who had a higher rank and score of achievement had fewer mistakes.
4. There were significant differences for testing score based on social economic status. The rank order of average score for students was: high social economic status > middle social economic status > low social economic status.

Keywords：factor and multiple, two-tier test, misconception

並列關鍵字

factor and multiple ； two-tier test ； misconception

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