本研究主要目的是以「線型函數」單元為主題，探討「APOS教學方式」與「傳統教學方式」兩種教學，對學生學習線型函數概念的影響。研究設計是採準實驗研究法。研究對象為台北市某國中七年級學生，分兩組為實驗組與對照組。實驗組進行APOS教學課程，對照組則進行傳統教學課程。
兩組的教學教材，皆為翰林版國民中學數學課本第二冊與習作為主。但APOS教學活動是以Asiala等人(1996)所建立的「概念層次」為架構，將課本與習作重新依概念層次編排而成；傳統教學是依照翰林版國民中學數學課本第二冊所呈現的內容順序進行。
研究依據Dubinsky(1991)所提出的概念發展層次：「動作」、「過程」、「物件」及「基模」，進行上述重組教材實驗教學，並設計線型函數測驗卷（後測及延後測），來安置學生在教學後與經過一段時間後（約莫一個月）的線型函數概念層次，以分析學生概念改變及保留情形。
本研究主要發現如下：
1．經過教學後，實驗組與對照組學生在後測的概念層次上以「百分比同質性檢定」未達顯著水準，但兩組在延後測時則得到 p^(**)＝.041<.05，達到顯著水準。顯示接受APOS教學方式的學生概念保留的程度較傳統教學方式的學生高。
2．實驗組在三次測驗中，學生進階至「物件」層次且維持的人數較對照組多，而退階至「動作」的人數亦較對照組少，顯示APOS教學方式對學生概念提升與理解有所助益。
3．在三次測驗中，兩組在代數表徵與圖像表徵的延後測上，以「百分比同質性檢定」皆達到顯著水準；而表列表徵則在三次測驗中無顯著差異。顯示APOS 教學在函數的「代數表徵」與「圖像表徵」的概念保留上，有明顯助益。

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