遞迴是電腦科學的基本概念之一，瞭解遞迴概念將有助於學習複雜的
資料結構和程式控制。然而電腦科學教育學者多認為，遞迴對於學生來說
是一個難以學習的概念；對老師而言，也是一個難以傳授的主題。同時，
由於遞迴對大部份學生而言是新奇的，日常生活中又缺乏可以類比的事物
，因此學生喜歡從程式設計本身尋找相類似的概念來類比。然而，在很多
的情況下，初學者往往由於經驗不足，以及不夠了解問題之間的差異性，
而造成過度簡化的類比、產生錯誤的答案；甚至於自己發展出不適當的心
智模式(mental model)，影響往後的學習。 為了幫助學生課後遞迴的
學習，我們運用完成策略去發展一個有效的學習環境，以指引學生使用適
當的心智模式，讓學生能夠循序且系統化地去建構、思考遞迴的問題。所
謂完成策略是就現有設計良好的程式(即專家已規畫好的範例程式)，讓學
生去進行完成、修改及擴充的工作。 在研究中，我們探討了遞迴概念
的學習、遞迴的心智模式和目前遞迴教學系統的特質，然後提出我們的系
統架構。我們選用教育界較常用的PASCAL語言練習遞迴，在Window環境下
發展這套系統。 為了驗證系統的學習效果，我們以台北工專的學生做
了實測，其結果肯定了這套學習系統的成效。我們希望遞迴程式設計學習
系統確實對想要學習遞迴程式設計的人有一番助益。

Recursion is a fundamental concept in computer science. Computer science educators have found that recursion is a very difficult concept for students tolearn and students generally avoid using recursion. Since the recursive conceptis usually completely novel for novice student and there are very few analogs that exists, students like to find the analogies come from programming itself. In many cases, however, they were not experienced enough to deeply understand all dissimilarities of different tasks. They often simplified the analog mappingprocess and generated an erroneous solution, even tended spontaneously to develop an inappropriate mental model of recursion influencing the further studying. To help novice students to learn recursion and to construct an adequate mental model of recursion, we develop a recursive programming learning systemusing completion strategy. Let students can generate and think the recursive idea systematically. The so called Completion Strategy is to use the well-designed program (a program designed by export) to allow students to makecompletion, modification and extension. The system has been evaluated as effective by a practical educationalexperiment. The results show that this system is of great help for the peoplewho want to learn the recursive programming skill.