科技大學工程學生導數概念理解之研究

An Investigation of Engineering Students' Conceptual Understanding of Derivative

10.6173/CJSE.2011.1906.01

黃志賢(Chih-Hsien Huang)

工程學生 ； 行動─過程─物件─基模（APOS） ； 表徵 ； 導數 ； Engineering Students ； Action-Process-Object-Schema (APOS) ； Representation ； Derivative

科學教育學刊

19卷6期（2011 / 12 / 01）

483 - 506

繁體中文

本研究以APOS （Action-Process-Object-Schema）理論與表徵理論為理論架構，目的在於探討科技大學大一工程學生的導數概念基模，以做為導數概念教學設計之參考。研究對象為21位接受傳統微積分教學的科技大學大一工程學生，研究方法包括問卷調查及半結構式一對一訪談，以Piaget與Garcia的三合一機制（triad mechanism）做為描述導數基模的模型。從理論的觀點，APOS理論與表徵理論的理論架構是有用的且是互補的，讓研究者可以從兩個不同但互補的觀點檢視同一現象。一方面，APOS理論可以用來確定學生能夠在表徵系統內和表徵系統間進行表徵轉換所必要的構思；另一方面，藉由學生在表徵系統的轉換方式的分析，提供學生已經建立的導數基模的成分間的關係。研究結果顯示，學生學習導數概念及其導數基模發展所遭遇的困難分別是數量導數的過程概念及圖形導數的過程概念，這兩個過程概念居導數基模的樞紐位置。

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