• 作者： 黃志賢
• 作者服務機構： 明志科技大學電機工程系
• 中文摘要： 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。
• 英文摘要： The present study began as an attempt to explore engineering students’ understanding of the concept of derivative. Based on the initial description of how the concept of derivative may be learned (genetic decomposition) an attempt was made to interpret the data using the Action-Process-Object theoretical framework. The insufficiency of this framework alone, led to extending it to the Action-Process-Object- Schema (APOS) epistemological framework which includes a theory of schema development based on ideas of Piaget and Garcia. The Piagetian Triad is suggested as a mechanism for describing schema development in general, and the derivative is used as an example. The Triad of the Intra, Inter and Trans stages of schema development provides the structure for interpreting students’ understanding of the derivative and classifying their responses to interview questions about the derivative. The results of this data analysis allowed for a proposed revised epistemological analysis of the derivative. Finally, several suggestions and questions for future study are presented.
• 中文關鍵字： 工程學生、行動─過程─物件─基模(APOS)、表徵、導數
• 英文關鍵字： Engineering Students, Action-Process-Object-Schema (APOS), Representation, Derivative