• 作者： 羅昭強
• 作者服務機構： 中國文化大學應用數學系
• 中文摘要： 函數是一十分複雜的數學概念，如定義域、函數值、變數、一對一、映成、連續、極限等等概念。因可微函數皆連續，故此，在初等微積分課程中，連續概念不應被輕視。再者，讀圖、解圖、描繪函數圖形、以及如何從點而線的繪圖概念皆為我國中等數學教育課程中極為重要的課題。實際上，連續概念的必要性在中間值定理上表露無遺。 雖然很多學者從事有關函數概念的研究，但對連續概念的「圖形定義」和極限定義的研究卻是不多，尤其對此兩種連續定義之關連性的研究更是少之又少。故此，本研究特別針對此兩種連續定義作探討，並且嘗試瞭解學生在不同的數學情境中，交替使用此兩種連續定義次數的情形。再者，本研究的主要目的在於揭露出學生對此兩種連續定義之間學習轉移存有極大的困難。因此，本研究欲透過資料的蒐集，來探索學生對此兩種連續定義之瞭解情況，同時希望能發現學習此兩種連續定義之認知障礙，藉以達到本研究的最終目的。
• 英文摘要： The concept of function is very complex and has a number of concepts associated withit, such as domain, image, variable, one-to-one, onto, continuity, limit and so forth. Sinceall differentiable functions are necessarily continuous, the concept of continuity should notbe overlooked in the teaching of calculus courses. Moreover, reading and interpretinggraphs, sketching graphs of functions, and the transition from the concept of drawing agraph of discrete quantities to that of a continuous quantity are the most fundamental topicsand central themes of the junior and senior high school mathematics curriculum in Taiwan.In practical work, the concept of continuity is important and necessary because it satisfiesa very important property called the intermediate value property. Although many researchers have studied the concept of function, little has been donethat has addressed the connection between the "visual definition" and the limit definitionof continuity. The research reported here was aimed at these two definitions of continuityassociated with how frequently students take the concept from one setting and apply thesame concept in a different setting. It is our intention to demonstrate the fact that studentshave great trouble in establishing appropriate links between these two definitions ofcontinuity. Therefore, the purpose of the study is to collect information about the natureof the students’understanding of these two representations and attempt to reveal anycognitive obstacles which students may have.
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