本研究的目的是瞭解函數單元教學前國二學生變數概念的成熟度與教學後其函數概念的發展情形，進而探討學生變數概念的成熟度對其函數概念發展的影響。研究方法採量與質並行，對三個台北市國中之六個班級共163位學生進行全面的紙筆測驗與選樣的訪談，以瞭解學生的解題思維與錯誤來源，並將所得的資料進行統計與分析。
本研究主要的結果為：（一）在變數概念的理解上，約有32﹪的學生尚未開始文字符號的真正使用，20﹪的學生將文字符號當作特定的未知數，33﹪者將文字符號當作一般數，15﹪者能察覺文字符號之元素間的高階關係。（二）在函數概念的理解上，約有16.6﹪的學生未能處理代入求值的相關問題，31.3﹪的學生已能代入求值，但未能以符號表示兩變數間、函數與變數間的關係，或無法畫出正確的函數圖形；約有33.7﹪的學生僅有函數的操作性知識，未有概念性知識；18.4﹪的學生已有函數的概念性知識，能在不同表徵上區分出函數的正例與非例。（三）變數概念的成熟度對其函數概念發展是有影響的，但並非變數概念完全成熟後函數概念才會開始發展，除非是對變數概念完全不瞭解者，函數概念才可能完全空白，而且變數概念層次越高者，其函數概念發展的層次也較高，變數概念層次越低者，其函數概念發展的層次也較低。

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