微積分的教學與動態教材設計

The Instructions and Dynamic Materials for Calculus

在本文中，我們將為微積分的教學，設計出動態畫面的教材，來詮釋較為抽象的數學概念，諸如極限、連續函數的合成、導數的圖解、方向導數、偏導數等有助於提升抽象解題能力之具體示例，請參考第參節。我們將嘗試以全新的表象，來詮釋微積分的定義及定理。本文所展示的結果，將作為在教學上的輔助教材，希望能引導初學者建立正確的概念。我們在第貳節，針對本校在微積分教學上所遇到的困難及因應對策做探討。最後，我們也在第肆節對於學習者與教學者提出建言，期望能達到拋磚引玉的效果來，並企盼先進前輩們能提供後學更多有效的經驗與指正。

In this paper, we construct some dynamic frames in order to interpret some abstract concepts from the Calculus Course such as「limits」、「the compositions of the continuous functions」、「derivatives」、「directional derivatives」、「partial derivatives」and so on. These concrete presentations of the dynamic frames will improvement in learning environment for the freshmen and the beginners and helpful to increasing the interest and the learning achievement in the Course, we refer to Section III. We introduce the definitions and theorems by whole new impressions. These results will applications to the teaching context display and lead the beginners to establish validly conceptions. We also discuss the difficulty in the teaching Calculus Course and their strategies in Section II. Finally, we also propose some constructive suggestions for the beginners and the supervisors in SectionIV. We'll expect to obtain some useful educational suggestions about the Calculus Course from the advanced scholars.