國小四到六年級學生分數迷思概念及其加減運算錯誤類型之研究

The Misconceptions of Fraction and Error Types of Its Addition and Subtraction for Fourth to Sixth Graders

林易慧(Yi-Hui Lin)

指導教授 ： 楊坤原

中原大學/人文與教育學院/教育研究所/碩士(2016年)

https://doi.org/10.6840/cycu201600431

摘要

本研究是探討國小四到六年級學生在分數迷思概念及分數加減運算錯誤類型之研究，研究方法採紙筆測驗及半結構式訪談。探討學生在分數的迷思概念及加減運算的錯誤情形，歸納出各年段錯誤的差異性、學生迷思概念及加減運算的錯誤類型，並找出錯誤發生的原因。研究樣本為桃園市平鎮區一所學校，抽樣24個班，總人數為686人。本研究主要發現如下:
一、國小四到六年級學生在分數概念部分共計有十二種迷思概念
測驗結果發現(一)三個年段錯誤率都高的是真分數的意義、部分/全部/離散量(第5題)、數線概念、文字與分數連結的概念。(二)三個年段錯誤率都低的是部分/全部/離散量(第4題)、部分/全部/連續量、整數相除、平分概念。(三)原則上錯誤率隨年級增高而降低，但仍有特殊情形。(四)四年級和其它年段錯誤落差大的是平分概念、部分/全部/離散量、數線概念、分數比較大小。(五)三個年段間錯誤率差異不大的是部分/全部/連續量、數線概念、文字與分數連結題、平分概念。
二、國小四到六年級學生在分數加減運算部分有九種錯誤類型，錯誤發生的原因如下: 1.解題時無法負荷多個概念。2.受到後來所學知識的影響。3.受到先備知識的影響。4.缺乏對分數的數感。5.粗心、計算錯誤。6.自行建構合理化的的規則。

關鍵字

分數迷思概念 ； 加減運算錯誤類型 ； 迷思概念 ； 錯誤類型

並列摘要

The purpose of this research was to explore the misconceptions of fraction and error types of its addition and subtraction for fourth to sixth graders .Two methods, paper-and-pencil test and semi-structured interview, were adopted in this research. Through paper-and-pencil test, the results of tests revealed the difference of errors in each grade, students’ misconceptions and error types of addition and subtraction. The reasons that make the student errors occurred were found through semi-structured interview. A total of 686 students from fourth to sixth grade in 24 classes in the elementary school in Pingzhen, Taoyuan City participated in this study. The major findings of this research were summarized below:There are twelve patterns of fractional misconceptions for fourth to sixth graders.
1.The results showed that (1) The error rate of concepts was high for fourth to sixth graders, including the meaning of proper fraction, part / all / discrete magnitude (Question 5), the concept of number line, and the links between text and fraction. (2) The error rate of concepts was low for all graders, including part / all / discrete magnitude (Question 4), part / all / continuous magnitude, integer division, and bisection concept. (3) In principle, the error rate was reduced with increasing grades, but there have been still special circumstances. (4) The gap between the error rate of the fourth graders and other graders was large in the concept of bisection, part / all / discrete magnitude, number line, and fraction comparison. (5) There was little difference in the error rate among three graders, such as the concept of part / all / continuous magnitude, number line, the links between text and fraction, and bisection.
2.There are nine error types of fractional addition and subtraction for fourth to sixth graders. The reasons consisted of the following: (1) Students cannot load multiple concepts in problem-solving. (2) Students were affected by learned knowledge. (3) Students were affected by prior knowledge. (4) The errors were due to the lack of the number sense of fraction. (5) The errors were due to students’ careless miscalculation. (6) Students constructed their own rules of rationalization.

並列關鍵字

the misconceptions of fraction ； error types of addition and subtraction ； misconception ； error type

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