本研究之主要目的在於探討大學聯考數學成績與大一微積分學習成就之相關；並 比較大一理工學系學生學習一年微積分課程之後，其思考能力與計算能力有否顯著差異；以 及比較分別畢業於公私立高中之大一理工學系學生在學習一年微積分課程之後，其思考能力 與計算能力有否顯著差異。 研究對象為三所國立大學五個理工學系 146 位一年級學生， 研究工具為自行編製之微積分成 就測驗、思考能力測驗與計算能力測驗，統計資料系上述三項測驗前後測驗成績與大學聯考 數學成績。 研究資料根據研究目的與假設， 分別使用皮爾遜積差相關、t- 檢定、共變數分析、迴歸分析 等統計方式處理。主要研究發現如下： 1. 大學聯考數學科成績和大一微積分學習成就測驗成績有顯著相關，相關係數為 0.2969。 2. 大學聯考數學科命題內容涵蓋數學思考能力與計算能力的評量。 3. 大學理工學系大一微積分課程， 對於大一理工學系學生的數學思考與計算能力，有所助 益。 4. 畢業於不同性質（公、私立）高中的大學理工學系學生， 經過一年大一微積分的學習後 ，其計算與思考能力均有進步，公私立高中畢業學生之間沒有顯著差異。唯，單就私立高中 畢業生而言，其計算能力並無明顯的進步現象。 根據上述主要研究發現，本研究提出兩項建議，一為研究大學聯考命題內容與大學甄選辦法 的改進；二為針對大一微積分課程的教材內容或教學方法等加以探討，以了解如何提昇學生 之思考與計算的數學能力。另外，提出進一步研究建議兩項：一為探討大學聯考數學科成績 與大學理工學系各年級數學課程學習成就的關係；以及進一步探討公、私立高中數學科教材 教法與學生數學科成就、數學能力的相關性。

　　　　　Scores of College Entrance Examination and that of Achievement Test of First-year College Calculus Students. The study was aimed to:(1) explore the correlation of Mathematics scores on the college Entrance Examination (CEE) and the freshmen Caculus achievements; (2) examine if there are any significant differences on math thinking and computation ability after they learned the Caculus course for one year; (3) distinguish the Math thinking and computation ability of those graduated from the public senior high schools from those graduated from the private ones. The subjects were 146 freshmen from Science & Engineeing Colleges at three national universities in Taiwan. The study instruments were the measurement of Caculus, the test of Math thinking ability and the test of Math computation ability. The statistic methods used to examine the hypothesises were: Pearson-productive correlation, T-test, ANCOVA, and regression correlation. The findings were the following: (1) The correlation on the Math scores of CEE and the Caculus achievements is significant. The coefficece is 0.2969. (2) The main content in the Math test of the CEE covered the evaluation of Math thinking and computation ability. (3) After learning the Caculas course for one year, the Math thinking and computation ability of the subjects have been improved. (4) There is no significant difference on Math thinknig and computation ability between those who graduated from the public and private high schools. However, within the private students group, there is not very much progress on their computation ability. Some implications of the findings and suggestions for further research were presented: (1) To improve the test contents of the CEE and the procedures to select college students. (2) To select suitable subject matters for college freshmen Calculus and to explore more effective teaching methods.