本研究主要的目的在於探討經由高一上學期，教學對學生函數概念的影響，並找出學生建立函數概念的模式。
研究採調查與面談兩種方法互相配合進行，依據Anna Sfard的概念成長理論，將函數概念分成內化、壓縮、物化三個層次，設計測驗卷。藉由三次紙筆測驗的結果，調查學生的函數概念層次的變化情形，輔以面談的方式深入瞭解學生填寫測驗卷時的想法以及其迷思概念。另外再找一名個案進行長達一學期的訪談，期能藉由教學後的即刻訪談，找出影響學生函數概念的變因，以便探討教學對學生函數概念的影響。本研究以台北地區北區某所公立高中一個班級的高一學生共42名為研究樣本。
本研究的主要結果有：
壹、教學對學生建立函數概念所提供的幫助：
一、直接由函數的定義傳達函數概念。
二、藉由函數圖形的正例與非例，提供學生修正基模的機會。
三、課本提供不同的函數表徵，幫助學生瞭解函數的定義。
四、提供許多不同的函數讓學生逐漸抽象出函數的概念。
貳、經由高一上學期的教學，學生函數概念的層次改變的情形
一、大部分的學生通過內化的階層的要求。
二、自內化到壓縮的幫助最大。
三、只有極少部分的學生達到物化。
最後根據本研究的結果加以討論，並提出若干建議，希望能對教師或教科書的編排提供參考資料。

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