• 作者： 左台益；蔡志仁
• 作者服務機構： 國立台灣師範大學數學系；台北市麗山國民中學
• 中文摘要： 本研究的目的在探討高中生橢圓概念多重表徵之認知特性，進而分析學生在表徵運用上的表現。研究學生對一數學概念多重表徵之認知結構，有助於瞭解學生概念建構歷程以提供教學活動的設計。此研究是以九位不同層次高中二年級學生學習橢圓概念作為研究主題，以探討學生內在思維心理歷程及其外顯多重表徵結構。研究方法採取診斷式面談活動，以質性分析，詮釋學生橢圓概念多重表徵建構歷程與結構。研究工具包括先備知識測驗以及診斷性面談教學活動。研究結果發現：橢圓概念的外顯表徵主要有語意表徵、圖形表徵、軌跡表徵、方程表徵、以及結構表徵，學生在建構橢圓概念歷程中，依其先備知識的品質，在不同層次學生中會有不同的發展方向。
• 英文摘要： The purpose of this study was to investigate the cognitive characteristics of senior high school students in constructing multiple representations of an ellipse, and to analyze the application of representations in problem solving. It is useful to our understanding the process of concept construction and designing of learning activities to study the cognitive structures of multiple representations of mathematics concepts. The sample consisted of 9 eleventh-grade, mixed ability students enrolled at six senior high schools in the Taipei area. The investigations employed diagnostic interviews and qualitative method to interpret the construction processes of multiple representations of elliptical concepts. It was found that the main external representations of elliptical concepts are verbal, graphical, structural, formulaic, and locus representation. The results of this study revealed that students have different ways to develop their elliptical concepts based on their initial knowledge.
• 中文關鍵字： 多重表徵；認知特性；橢圓概念
• 英文關鍵字： multiple representations, cognitive characteristics, elliptical concepts