國小五年級學童在異分母分數的加減之試題品質分析及性別與題目表徵類型關係之研究

A Study on Item Analysis and the Relationship between Gender and Representation of the Performance on Adding and Subtracting with Unlike Denominators for the Fifth Graders

本研究旨在探討國小五年級學童在異分母分數的加減單元的試題品質分析，並討論不同性別之學童與不同題目表徵類型間的關係。本研究採紙筆測驗，依據國小五年級學童在研究者自編的異分母分數加減的學習成就測驗上的解題表現，蒐集量化資料。研究者取臺南市某一市區內的國民小學五年級學童作為樣本，完成研究者自編的異分母分數的加減學習成就測驗，透過描述性統計、獨立樣本t檢定、成對樣本t檢定及二因子變異數分析等統計方法，將所蒐集到的量化資料去分析國小五年級學童在異分母分數的加減在不同性別或不同題目表徵是否會對解題表現造成差異、不同題目表徵型式與不同性別二者之間是否存在交互作用的關係。研究結果如下： 一、 國小五年級學童在異分母分數的加減學習成就測驗之試題表現分析，結果如下: 1. 整體平均答對率0.66。 2. 整體平均答錯率0.34。 3. 學童作答錯誤類型包含「通分的錯誤」、「擴分的錯誤」、「觀念的錯誤」等。 二、 不同性別之國小五年級學童在異分母分數的加減單元表現沒有顯著差異。 三、 國小五年級學童在異分母分數的加減之不同題目表徵類型沒有顯著差異。 四、 異分母分數的加減之不同題目表徵與不同性別之學童二者間不存在顯著交互作用。

 

The purpose of this study was to analyze the results of the achievement test of adding and subtracting with unlike denominators for the fifth grade students from one elementary school in urban area of Tainan City, and to investigate the relationship between gender and different types of representation. In this study, data was collected through the achievement test designed by the researcher. Statistical methods of Descriptive statistics, Independent Sample t test, Paired Sample t test and Two-way ANOVA were then employed to analyze the performance of the different gender of the fifth grade students, the performance of the fifth grade students on the different types of representations, and whether there were interactions between different gender and different types of representations.The research results were as follows: 1. The results of item analysis on the achievement test of adding and subtracting with unlike denominators for the fifth grade students: (1) The average pass rate for the test is 66%. (2) The average fail rate for the test is 34%. (3) The error patterns include fractional addition errors, Expanded fraction errors, conceptual errors, and etc. 2. There was no significant difference between gender among the fifth grade students in the performance of the achievement test on adding and subtracting with unlike denominators. 3. There were no significant differences among the fifth grade students on the different types of representation of the achievement test on adding and subtracting with unlike denominators. 4. There were no remarkable interaction effects between different types of representations of adding and subtracting with unlike denominators and different gender.