CAS 實驗活動的學習環境下極限概念之建構歷程

Abstract

本研究旨在探討 CAS 實驗活動的學習環境下，大學生極限概念之建構歷程及 其迷思情形，並進一步說明在此環境下數值與圖形對極限概念之影響。本研究採質性研究方式，針對國立交通大學微積分實驗班 40 名大一學生進行教室觀察及晤談，並以紙筆測驗和問卷等資料作為分析詮釋之參考。 研究結果發現：極限概念主要的外在表徵有語意表徵、數值表徵、圖形表徵及代數符號表徵，學生在建構極限概念歷程中，先備知識會影響後續形式概念之發展，在此一學習環境下，學生仍具有傳統模式下之迷思概念。概念視覺化有助於學生極限概念的建立，但先決條件是能夠正確地解讀 CAS 所產生的圖形。

The purpose of this study was to investigate the representation structure of college students’limit concept, and their misconceptions under the CAS laboratory learning environment. Especially, how the numerical and graphical aspects of CAS help students to develop their limit concept. Upon analysis of 40 freshmen students’laboratory recording, laboratory reports, questionnaires responses, and interview details, we found that 1. The main external representations of limit concept were verbal, numerical, graphical, and algebraic-symbolic representations. 2. Students’pre-knowledge affected a great deal on the development of their limit concept. 3. Students in the CAS laboratory learning environment still tended to have the same misconceptions as those of students in traditional classrooms. 4. Under the assumption that the graphs generated by CAS are correctly interpreted, visualization does help in students’conceptual understanding.