科技大學的數學教師在教學上皆以專家的知識結構方式授課，而學生常不以直接的方式來表達對此知識學習上的困擾，往往遲至面臨試題後才呈現出學習障礙的情況。因此，本研究根據Bart與Krus（1973）的次序理論，建構一個關於科技大學師生在授課與學習者之間的了解機制。本研究分析南開科技大學工程科系一年級學生，在微積分課程中多項式積分的學習單元，依據教師的專業背景建立學習這一單元所需具備的解題能力，再以紙筆測驗的方式測試，根據學生在試題的反應而建立衡量係數矩陣；依據衡量係數矩陣，就族群題目方式進行分析，藉以回饋任課教師有關於學習者在多項式積分的單元中，除了解經過學習後所得到的解題能力之外，同時進一步提供對學習者在學習前應採取的補救教學內容，以銜接在高職（中）數學課程上學習之不足。

This research acts according to Bart and Krus (1973) “ordering theory”， constructs a organization between teachers and the student in the technology university， the formers instruct their teaching with expert knowledge structure， while the latter present his study confusions not directly， but always from the test response. In this approach we analyzed， the freshmen major in engineering of Nan Kai Technology University， about teaching and learning at the integration of polynomial in the Calculus. Based on the expert of the teachers， we build up the necessary problem solving abilities in this unit， through the Paper-and-Pencil-Based Testing of these freshmen， and according the data of item response from them， the coefficient of impact matrix is hence built. The tribal items based on the coefficient of impact matrix are done. These conclusions are then fed back to the teachers， so as to have the judgments of how many abilities that the learners have gotten from this course， or should adopt the recovery teaching to link up the quality in mathematics before they enter university.