數學極限概念之動態表徵設計

The Dynamic Visualized Computer Design for Learning the Limit Concept

本研究主要目的是利用GSP軟體來融入APOS理論後，設計動態且可允許操作的電腦輔助教材並探究個案學生是否因而對函數的極限概念能理解之過程。研究發現，APOS理論的電腦設計，讓學生可以操作視覺物件，建立正確的函數的極限概念，並且具備代數符號及圖形間的連結能力，藉由圖形學習極限概念及性質，讓學生覺得有意義，形成基模以後，個案學生可以解決極限的問題，更進一步瞭解微分的雛形。

The purpose of this study is infusing the APOS theories with the GSP software to design the dynamic digit materials for students to learn the limit concept, and report the progressive of their understanding. We found in such dynamic APOS environment, the case of students can manipulate the object, visualize the process of change caused by the action therefore can understand the concepts of limit in a concrete way. The participants can connect the meaning between the symbolic and graphic representation. They can also generate the limit scheme and apply them to solve the application problems.