[ 摘要 ]

本研究的目的，在探討國小五年級學童的分數概念，分別瞭解屏東縣原住民和非原住民學童在分數概念的答題表現、常犯錯誤以及產生這些錯誤的可能原因。

本研究以自編「國小五年級分數概念學習表現測驗」為工具，以屏東縣閩南、客家、排灣及魯凱族群地區之六所國小292位五年級學童為研究對象，配合半結構式訪談進行資料蒐集。資料分析採質、量分析，量的分析以T考驗、單因子變異數分析等方式來分析各族群之分數概念學習表現；質的分析用以歸納並比較多元族群學童在分數概念易犯錯誤的類型及成因之分析。

綜合紙筆測驗及個別晤談結果，本研究的結論如下：

一、男女性別對分數概念的學習表現沒有顯著差異。

二、非原住民與原住民學童在分數概念的學習表現上有顯著差異。

三、閩南、客家和原住民(排灣加魯凱族)族群的學童在分數概念的學習表現上有顯著差異，其中以閩南族群的學童表現最優，客家族群次之，原住民族群的學童相對而言表現較差。

四、就全體樣本而論，本研究發現學童在分數概念常犯的錯誤類型有：「缺乏『等分』概念」、「誤認為『等分』就是除了面積相等以外，形狀也必須相同」、「忽略給定的單位量或對基準量的指認有困難」、「將數線上的點表示分數時，未能考慮分數間的相對位置」、「在『商』模式中，對於哪一個數該放在分子或分母的概念尚不清楚」、「數感及估測能力欠佳」、「相對關係型概念較弱」、「在處理分數的大小比較及等價分數時，僅以分子或分母作為判斷的依據」及「作答文字題時不瞭解題意，對於單位的疏忽或缺乏判別多餘數字的經驗或能力」。

五、就個別來說，在多元族群中，以閩南族群的學童表現較優，他們不僅在學習表現上得到較高的分數，在易犯錯誤類型部分也較其他族群來得少且較集中；客家族群的學童普遍較缺乏「分數是數」的概念，另外在文字題的表現稍弱；相對而言，原住民族群的學童對於「等分」概念較缺乏、對單位量的指認有困難，在文字題的表現也尚待加強。

根據研究結果和結論，提出若干建議作為改進教學與未來研究的參考。



[ 英文摘要 ]

The purpose of this study was to explore the fraction concept of fifth graders in elementary schools in Pingtung country and determine the differences between aboriginal and non-aboriginal students in their problems solving performance and the possible causes of mistakes they made.

This study used a self-designed quiz , “The learning performance test in fraction concept for fifth graders”, as a tool and selected 292 fifth grade students as samples. The students came from six elementary schools in Pingtung County which included HoRou（閩南）, HaKa（客家）, PaiWan（排灣） and RuKai（魯凱） tribes. Also this study took semi-structural interview to conduct data collection. As for data analysis process, this study took both qualitative and quantitative methods, the latter included reliability test, validatity test, T-test, and One-way ANOVA analysis. The qualitative method included analysis and comparison of multi-cultural students on their frequently made mistakes related to fraction.

Base upon the written test and individual interview, the conclusions of this study were listed below:

1. There was no significant difference in students’ genders on their learning performance toward fraction.

2. There was a great difference between non-aboriginal and aboriginal students on their learning performance toward fraction.

3. From the samples they showed students in different tribes had different learning performance on the concept of fraction. In general, HoRou students (閩南族群) were better than HaKa’s (客家族群). And the aboriginal students had a lower achievement on fraction concept among all.

4. The general and typical mistakes on fraction concept for multi-cultural students were identified and detailed.

5. Among multi-cultural tribes, HoRou students not only got better scores but also had less typical mistakes. Most HaKa students lacked the notion that faction is number and had difficulty with word problems. Aboriginal students, by contrast, were deficient in equality, determining of unit, and word problems upon fraction concept.

According to the findings, this study proposed several suggestions for the reference of future teaching and research.