本研究的研究對象為國立中央大學 96 學年度入學的大一新生，樣本資料包含：入學前的學科能力測驗成績、入學後的微積分聯合教學成績與大一英文分班資料。研究使用的軟體主要為 Matlab 及 Microsoft Excel，利用其中的 k-means 分群法，以及統計上的相關係數、t 檢定與回歸等方法分析資料。 研究者嘗試將訊號分析 (signal analysis) 與機器學習 (machine learning) 領域中，經常使用的 k-means 分群法以及做分布圖觀察的方法，運用在教育資料上，討論其效益。以上述之樣本資料為例，經分群與作圖後，可支持研究者探討「入學前的學科能力測驗成績」與「入學後的微積分學習表現」之間的關係。 研究的結果有二。第一，在技術上，k-means 分群法在教育意義上有實用價值，可幫助研究者從眾多資料中觀察現象。第二，在教育上，學科能力測驗成績變異數較大的分群與英文級分偏低的分群，在大一微積分的學習表現上是較危險的，值得我們特別關注。 The subjects of study are the freshmen of the National Central University in 2007. The samples of study include the scores of the Scholastic Aptitude Test (SAT) by the College Entrance Examination Center, the achievements of the United Classes of Calculus (UCC), and the classes of the Freshman English Course. The main software of study is Matlab and Microsoft Excel. The data is analyzed by the methods of k-means and coefficients of correlation, t-test and regression in statistics. The researcher tries to use the k-means and the graph of distribution, which are commonly used in the signal analysis and the machine learning, in education and discusses the benefit of the result. After classifying and graphing, the correlation between “the scores of SAT” and “the achievements of UCC” is discussed. There are two conclusions in this research. Technologically, the k-means is useful in education and helpful for researchers to observe the data. Educationally, the groups of higher variance or lower English score in SAT have a higher risk of failure in UCC. We should pay more attention to these groups of students.
