國中基本學力測驗數學科之性別差異與差別試題功能(DIF)分析

Gender Differences and Differential Item Functioning in Mathematics Basic Competence Test for Junior High School Students

本研究分析90至94年度國民中學學生基本學力測驗數學科之性別差異和差別試題功能（Differential Item Functioning，簡稱DIF），各次測驗資料係隨機從該次全體考生中抽取之5000 名受試的答題反應。在性別差異分析部分，本研究分析全體受試、低成就組（後10%）和高成就組（前10%）之數學總分的性別效果量、女／男標準差比和女／男人數比三項指標，此外，也分析數與量、代數、幾何、統計與機率四項內容，及程序知識與執行、概念理解和問題解決三類認知歷程的性別效果量。整體數學表現的性別差異分析結果顯示：全體受試和低成就組無顯著的性別差距出現，高成就組的男生表現略高於女生；此外，男生分數的變異程度較女生大，低成就組和高成就組的男生人數比例都高於女生，高成就組又比低成就組更高些。分項表現的性別差異分析結果顯示：全體受試的男生在問題解決的表現略高於女生，其餘分項皆無顯著的性別差距出現；高成就組男生在幾何的表現略高於女生，其餘分項皆無顯著的性別差距出現；低成就組在所有的分項皆無顯著的性別差距出現。在性別DIF分析部分，本研究採Mantel-Haenszel 法評估DIF，分析結果顯示：基測數學科性別DIF 出現率為2.5%，DIF 題數量雖不多，但性別DIF 與試題特徵似有關聯，具體而言，代數DIF 題傾向對女生有利，幾何和問題解決DIF 題傾向對男生有利。

This research investigated gender differences and differential item functioning (DIF) on Mathematics parts of the Basic Competence Test for Junior High School Students (BCTEST) from its 2001 to 2005 administrations. Data for each administration were a sample of 5000 examinees randomly drawn from its examinee population. In the study of gender differences， we calculated and compared the effect size， female/male standard deviation ratio and female/male ratio for total-group， low- achieving (bottom 10%) and high-achieving groups (top 10%) across test administrations. Results based on overall performances indicated that there were no visible gender differences among total groups and low-achieving groups. However， males performed slightly better than females amongst high-achieving groups. Results based on performance of math contents and processes indicated that there were no visible gender effect sizes among total， low-achieving and high-achieving groups with only a few exceptions. The exceptions were that males performed slightly better on problem solving among total groups and on geometry among high-achieving groups. In the study of gender DIF， Mantel-Haenszel procedure was used. And results showed that the average percentage of items displaying gender DIF across administrations were low， at about 2.5%. There appeared associations of gender DIF with item characteristics， DIF in favor of females on algebraic items， and DIF in favor of males on geometry and problem solving items.