從事數學教學歷程，需尋找各教學單元中每一概念內容項目的關聯性，其方法以施行測驗來尋找最為便捷。日本學者竹谷博士受Krus, Bart, Airasian等學者研究資序理論的啟示，提供一個有別於次序理論的新方法，稱為試題關聯結構分析法，簡稱IRS分析法。此種方法對於吏用測驗，建立課程教材內容的學生結構圖，以為診斷及進行補救措施，大有裨益。本研究的主要目的是在分析帶刀數加法的學生學習結構圖，以獲得學生的學習結果訊息。因此選擇彰化縣城市學校的一個班級以及鄉村學校的一個班級共 98人，施行紙筆測驗，所得的資料，以目行設計的IRS PC軟體，進行製作結構圖。最後經由分析，可知言辭表徵的理解遠比運算過程為困難等等性質的結果，從而據此提出具體改善教學品質的建議意見。

In order to correctly sequence blocks of instruction, it is necessary to discover the relationship between components of the instructional unit. Test can be used to discover this relationship. The Japanese scholar Dr. Takeya, starting from the logic of Krus, Bart, and Airasian, haspresented a different method of ordering theory called IRS Analysis（Item Relational Structure Analysis）. The advantage of using IRS is that it enables us to construct test for diagnostic purpose with built─in remedial tasks. The purpose of this study was to construct the item relationship by suing the method of IRS in addition problems of mixed numbers. 98 fourth graders（two classes）chosen from elementary schools in Chung─Hwa county, Taiwan, R.O.C., took a paper─and ─pencil test. After their responses gathered, by use of IRS PC software, the structure of students’ learning can be demonstrated. The final results have shown that the properties such as the verbal representation of students is more difficult than the skills of computation. Based upon this study findings, we also offered some suggestions for practical teaching and some opinions for future research.