本研究目的在以試題反應理論探討國小四、六年級學童數學成就之現況，研究者採用問卷調查法進行研究，情商我國某依縣市作為樣本縣市，對該樣本縣市四、六年級學童進行分層與集群之隨機取樣。研究工具則由研究小組自編符合研究目的之「數學學習成就問卷」，問卷分四年級和六年級兩份，其測驗內容包含選擇題、填充題、計算題、作圖題和應用題。
根據資料分析結果，本研究主要發現如下：（一）在不同學區類型與學校規模下，四、六年級學童平均整體能力皆優於logit；（二）在不同學區類型方面，四、六年級整體表現結果皆為大學區優於中學區，中學區優於小學區；（三）在不同學校規模方面，四、六年級整體表現結果皆為大型學校優於中型學校，中型學校優於小型學校；（四）在學習主軸方面，四年級表現最佳為「代數」，但到六年級卻敬陪末座；（五）依四、六年級在各學習主軸表現，皆可將學童分為優異型、中上型、一般型、不佳型，但其實質內涵有些許差異。（六）發現隨著年齡的提升，學生的類型分布從優異型逐漸往不佳型移動中。（七）在小學區鄉鎮與小型學校中，四、六年級學童類型都產生極大的變化，優異型學童驟減，不佳型學童相對急速遞增。

This study is to analyze the 4th and 6th grade students’ math achievement by item response theory (IRT). Questionnaire survey is used as the study method. A city in Taiwan is selected as a sample area. We randomly selected students from 4th and 6th grade as our study subjects. The study tool is called “questionnaire of math learning and achievement” developed by the study group. Two different questionnaires are designed for 4th and 6th grade students. The content of the test includes multiple choice question, cloze, calculation, geometry, and application.
According to the analysis, this study has the following findings. (1) In different areas and different sizes of school, the average ability of 4th and 6th grade students is better than logit; (2) When comparing different school areas, the average ability of 4th and 6th grade students shows: university school area is better than high school area; high school area is better than elementary school area.(3) When comparing students among different sizes of schools, the average ability of 4th and 6th grade students shows: students in large school are better than medium school; students in medium school are better than small school. (4) When comparing different math subjects, 4th grade students do best on algebra, but it became the worst for 6th grade students. (5) According to the different math subjects, we classify students into “excellent”, “good”, “average”, “poor”, however, the actual level is a little different. (6) The distribution chart of students’ level is moving from “excellent” to “poor” along with the age growing. (7) In elementary school areas and small schools, the performance of 4th and 6th grade students is poorer. The number of “excellent” students is much smaller and the number of “poor” students is extremely high.

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