國小六年級數學分數除法錯誤類型與成因分析
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2019
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Abstract
本研究旨在探討國小六年級的學生在分數除法的學習表現、可能產生的錯誤類型及其成因，希望能提供教師在分數除法教學上及補救教學策略的參考。
研究工具為研究者自編分數除法測驗。預試以新北市板橋區某國小一百零六學年度六年級五個班學生，共163人為預試對象，預試結果此份測驗難度為簡單、鑑別度良好、效度高、內部一致性信度高。
正式施測，以一百零七學年度六年級十個班，共324人為研究對象。
研究結果為：
一、新北市板橋區某國小六年級學生在分數除法前備知識學習表現良好。
二、新北市板橋區某國小六年級學生在分數除法之學習表現，程序執行優於思考解題；分數除法錯誤類型有八種：受分數加法的影響、受分數乘法的影響、受整數除法的影響、分數除法運算法則不清的誤用、分配律的誤用、不瞭解文字題題意、無法分辨基準量與比較量、分數除法餘數部份發生錯誤。
三、新北市板橋區某國小六年級學生在分數除法之錯誤形成原因：1.受先前學習經驗影響，做過度類推，導致誤用；2.受新近學習經驗影響，倒攝抑制；3.機械記憶運算規則，未確實理解；4.不瞭解文字題題意；5.缺乏分數概念，不明白分數的意義；6.基準量、比較量概念不清。
研究者就研究結果提出對於分數除法未來教學上及未來研究建議。
The main purpose of this research is to discuss the learning performance, possible error types, and causes regarding six-grade elementary school students on fraction division, which would provide other teachers with a reference for teaching design and remedial teaching strategy on the subject. The research tool is a set of self-compiled assessment on fraction division by the researcher. The pilot test of the research was conducted on 163 students from five six-grade classes at an elementary school in Banqiao District, New Taipei City in 2017. The result of the pilot test shows that the difficulty index is easy with good discrimination index, high validity, and excellent internal consistency. Afterward, the formal examination was conducted on 324 students from ten six-grade classes in 2018. The research results show: I.The students’ learning performance regarding the prior knowledge of fraction division was good. II.Concerning the learning performance of fraction division, procedural knowledge surpasses problem solving. There are eight error types of fraction division: influence by fraction addition, influence by fraction multiplication, influence by integer division, misuse of the rules of arithmetic, misuse of distributive law, unable to understand the intention of the questions, unable to distinguish reference quantity and comparison quantity, and occur mistakes while handling the remainders of fraction division. III.The causes of fraction division errors are 1. Influence by previous learning experience and misuse due to over-analogy; 2. Influence by recent learning experience; 3. Rote memorizing the rules of arithmetic without a comprehensive understanding of it; 4. Unable to understand the intention of the questions; 5. Lacks the knowledge of fractions; and 6. Unclear concepts of reference quantity and comparison quantity. Based on the research results, this study further offers suggestions of fraction division for future teaching and research.
The main purpose of this research is to discuss the learning performance, possible error types, and causes regarding six-grade elementary school students on fraction division, which would provide other teachers with a reference for teaching design and remedial teaching strategy on the subject. The research tool is a set of self-compiled assessment on fraction division by the researcher. The pilot test of the research was conducted on 163 students from five six-grade classes at an elementary school in Banqiao District, New Taipei City in 2017. The result of the pilot test shows that the difficulty index is easy with good discrimination index, high validity, and excellent internal consistency. Afterward, the formal examination was conducted on 324 students from ten six-grade classes in 2018. The research results show: I.The students’ learning performance regarding the prior knowledge of fraction division was good. II.Concerning the learning performance of fraction division, procedural knowledge surpasses problem solving. There are eight error types of fraction division: influence by fraction addition, influence by fraction multiplication, influence by integer division, misuse of the rules of arithmetic, misuse of distributive law, unable to understand the intention of the questions, unable to distinguish reference quantity and comparison quantity, and occur mistakes while handling the remainders of fraction division. III.The causes of fraction division errors are 1. Influence by previous learning experience and misuse due to over-analogy; 2. Influence by recent learning experience; 3. Rote memorizing the rules of arithmetic without a comprehensive understanding of it; 4. Unable to understand the intention of the questions; 5. Lacks the knowledge of fractions; and 6. Unclear concepts of reference quantity and comparison quantity. Based on the research results, this study further offers suggestions of fraction division for future teaching and research.
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Keywords
分數除法, 錯誤分析, 錯誤類型, Fraction Division, Error Patterns, Error Types