一般常使用小學數學電腦輔助教學軟體，通常都有許多共通的缺點，像是無法動態的給予學生適性的教學、學生於單機上的操作系統容易覺得無趣等。本系統是以網際網路架構為背景的一套遊戲系統，將鷹架理論應用於小學數學加法的補救教學上。期望能夠藉由在網際網路上運作，讓學生們感覺到和同學們在一同做題，因此提昇學習動機與樂趣；另一方面，系統使用鷹架理論(Scaffolding)作為補救教學時的基礎，對於真的需要幫助的學生，能夠給予適合的鷹架支持。
本系統針對舊有的加法階層圖，將學生的能力考慮進去，提出一個新的樹狀架構，利用此架構且配合學生的資料與紀錄，當作給予學生適性化學習時，系統選擇類型的依據。
在實驗結果資料分析方面，本篇論文針對【只以結果來做分析】與【參考學生答題紀錄過程做分析】兩種分析法的差異，說明了系統在運作時，紀錄學生答題過程的重要性，並利用學生答題紀錄分析了加法常見的錯誤類型。
以下為本篇論文主要的工作與目的：
1.程度的診斷及適性學習：本系統在遊戲與學習的過程中，依照學生的答題紀錄，來診斷出學生加法程度所在，並且依據每位學生的學習進度，在學習過程中，給予學生適時的引導，並且嘗試藉由鷹架理論的使用，來幫助學生改正錯誤的觀念。
2.收集完整的解題資訊：在學生使用系統的過程中，系統動態地收集學生的解題資訊，包括題目、答案、時間、解題過程等等。利用這些解題資訊，可以作為學習策略的分析，作為引導學生學習的依據，達到因材施教的目的。

There are several drawbacks with current CAI (computer-aided instruction) software for elementary arithmetic. Typically, there are no adaptive instructions. There is also a lack in the use of a more dynamic user interface in providing the instructions. The learner can easily get bored when using such a system.

In this thesis, we propose a system for remedial tutoring of elementary addition. The system works in conjunction with a gaming environment. It implements the ideas of adaptive instruction and computational scaffolding. The existing idea of learning hierarchy is further refined by adding the idea of refinement into it. As a result, students with different abilities can be considered on different levels. Essentially, this just means that each kind of learners has their own learning hierarchy, and there are altogether three kinds of learners : learners with a higher ability, learners with a medium ability, and learners with a lower ability.

In analyzing the results of the experiment, we use two different types of methods in the analysis. In one analysis, we consider only the “macro behaviors” of the learners, namely the answers they give to the problems. In another analysis, we consider not only the macro behaviors but also the “micro behaviors”, i.e., the system usage profiles of the learners.

The main contribution of this thesis is two-fold.

1. Diagnosing the level of the learner and offering corrective instructions :
When a learner uses this system, the system will identify the “status” of the learner according to how well the learner does the given problems. Once the status of a learner is identified, the system then uses the idea of computational scaffolding to help the learner doing problems that lie within the learner’s presumed zone of proximal development.

2. Collecting and using the usage profiles of the learners :
When a learner uses the system, the system collects information about the details of how the learner solves any particular problem. This includes recording specific user actions such as the clicking of a button as well as measuring the time used to solve any particular problem. The collected information is then used to help instructing the learner.

摘要i
Abstractii
目錄iv
圖表目錄vi
第一章緒論1
1-1研究背景1
1-2研究動機1
1-3研究目的2
1-4系統特性2
1-5論文章節介紹3
第二章相關文獻探討4
2-1傳統教學模式與現在教學模式4
2-2鷹架理論6
2-3ITS(Intelligent Tutoring System)7
2-4鷹架理論應用於ITS上8
2-5Cognitive Apprenticeship9
2-6一般CAI系統之分析10
第三章理論介紹12
3-1系統出題機制的流程12
3-2加法題的出題機制13
3-1-1Learning Hierarchy14
3-1-2Learning Tree15
3-3趣味題的出題機制23
第四章系統介紹25
4-1系統架構25
4-1-1系統主架構25
4-1-2執行平台語開發工具26
4-1-3遊戲流程27
4-1-4Client端元件的目的與功能33
4-1-4-1加法元件33
4-1-4-1-1元件的目的33
4-1-4-1-2元件的功能33
4-1-4-2趣味題元件36
4-1-4-2-1元件的目的36
4-1-4-2-2元件的功能36
4-1-5實作細項37
4-1-5-1鷹架理論如何應用在加法元件上37
4-1-5-2產生量身訂做的題目39
4-1-5-3出題機制中，產生題目的方式41
4-1-5-4分組43
4-1-5-5隨機出題的方法45
4-1-5-5-1學生目前在 NO_TRAINING組中45
4-1-5-5-2學生完成後測，或不需要訓練46
4-1-5-6出現訓練題的時機46
4-2系統使用47
4-2-1主角的操控47
4-2-2選擇出戰的神奇寶貝47
4-2-3加法元件的使用48
第五章實驗的設計與結果50
5-1實驗目的50
5-2實驗樣本50
5-3實驗假設50
5-4實驗進行方式51
5-5實驗結果54
第六章評估與討論60
6-1依照學生詳細紀錄的評估60
6-2加法錯誤類型82
6-3結論分析84
6-4減法、乘法、除法的未來初步規劃86
第七章結論及未來展望91
7-1結論91
7-2未來展望91
參考文獻95
附錄A

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