臺灣博碩士論文加值系統

本研究是屬於「個案研究」，其主要研究目的是在探討三位國小六年級數學科低成就學童，透過Excel電腦輔助軟體設計，進行「分數乘法」的補救教學活動，觀察學童在活動之後，對「分數乘法」概念的改變情形，以便進一步的瞭解並分析在補救教學的實施過程中，「多重表徵」與學童學習的影響，作為其他教師教學的參考。
研究對象是研究者所服務的高雄市某國小六年級學童，根據研究者設計的「多重表徵」教學模式電腦視覺化表徵視窗環境進行補救教學，資料的搜集則採用學童在實施補救教學前和教學後的成就測驗、半結構式訪談與學習日誌等，資料的整理與分析則採行質量並重。依資料分析所得的研究結果有下面幾點：
一. 學童在接受Excel電腦視覺化表徵視窗環境進行補救教學後，建立了「分數乘法」的概念。這些概念包括有：
1. 學童學會五大類型題目的解題策略，並找出符號計算的規則。
2. 學童學會掌握三個不同層次的單位關係。
3. 學童學會建立單位分數的概念，及對單位量的認識。
4. 學童學會分割及再分割的操作技巧。
二. 學童在接受Excel電腦視覺化表徵視窗環境進行補救教學後，學童在運思發展上獲得提升。
三. 學童在接受Excel電腦視覺化表徵視窗環境進行補救教學後，「多重表徵」對學童學習的影響。這些影響包括有：
1. 學童學會不同表徵間的轉譯。
2. 學童能理解表徵內部的轉換。
3. 學童能藉由各種表徵提供的線索進行解題。
四. 學童在接受Excel電腦視覺化表徵視窗環境進行補救教學後，學童在學習態度上不僅有所改變，且也是他們對數學科的學習產生了興趣。
五. 研究者發覺在Excel電腦視覺化表徵視窗環境下，這個電腦軟體在學童學習上具有一些特性，有助於學童的學習。這些特性包括有：
1. 電腦輔助補救教學軟體可以將學習表徵系統保留下操作的軌跡及歷程。
2. 學童可任意變更題目數字，經由反覆練習，讓學童自行察覺到計算的規則。
3. 當學童輸入錯誤時，可以多次嘗試直到答案正確。

Based on three sixth-grader subjects who did not do well in mathematics at school, the purpose of this research is to investigate how the students improve their performance in fraction multiplication after receiving Excel-based remedial instruction. Also, the researcher seeks to further understanding and analyze how the multiple representations materials influence students’ learning and to provide reference for other teachers.

The subjects in the study are from the Kaohsiung elementary school where the researcher is serving. The cases received the remedial instruction with the “multiple representations” teaching mode under visualized computer setting. The data adopted in this study including students’ scores in tests before and after they received the remedial instruction, semi-structured interviews, and study journals. The analysis of the data focuses both quality and quantity. The results of the research can be concluded as follows:

I. After receiving the Excel-based remedial instruction under visualized window setting, the students are proved to have better understanding of fraction multiplication:
1.They have learned how to solve the five major math subjects and the rules of symbolic calculation related the multiplication of fraction.
2.They have learned the unit relation among the three different levels of the multiplication of fraction.
3.They have become familiar with the concept of unit fractions and unit quantity.
4.They have learned the skill of partition.

II. After receiving the Excel-based remedial instruction under visualized window setting, the students have improved their logical thinking.

III. After receiving the Excel-based supplementary education under visualized window setting, related to the multiple representations topics has the following effects on students:
1.They have learned to translate among different representations.
2.They can understand the inner transformation of the representations.
3.They have learned to solve problems by looking for clues in the representations.

IV. After receiving the Excel-based remedial instruction under visualized window setting, they have changed their attitude toward studying and showed more interest in mathematics.

V. The Excel-based remedial instruction under visualized window setting has certain characteristics that can help students to learn:
1.The computer-based supplementary education can record and keep the process of a student’s learning and operation on the representations system.
2.Students can change the numerals given in the questions and do repeated exercises to find out the rules of calculation on their own.
3.When the students put in a wrong answer, the system will allow them to try as many times as possible before they get the right answer.

中文摘要················································Ⅰ
英文摘要················································Ⅱ
誌 謝··················································Ⅳ
目 次··················································Ⅴ
表 次··················································Ⅶ
圖 次··················································Ⅷ
第一章 緒論············································1
第一節 研究動機········································1
第二節 研究目的········································3
第三節 待答問題········································3
第四節 名詞釋義········································3
第五節 研究的範圍與限制································5
第二章 文獻探討········································6
第一節 分數乘法的相關文獻······························6
第二節 分數的多重表徵··································11
第三節 電腦輔助教學的理論······························15
第三章 研究方法········································19
第一節 個案研究之理由··································19
第二節 研究架構········································19
第三節 研究設計········································20
第四節 研究對象········································22
第五節 研究工具········································23
第六節 實施程序········································28
第七節 資料處理········································29
第四章 研究結果與討論··································31
第一節 在動態視覺補救教學前的評量結果及錯誤類型········31
第二節 在動態視覺補救教學情境中呈現的學習情形··········42
第三節 在動態視覺補救教學後的概念及解題表現···········102
第五章 結論與建議 ····································110
第一節 結論···········································110
第二節 建議···········································113
參考書目···············································115
附錄一·················································118
附錄二·················································120

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