臺灣博碩士論文加值系統

動態幾何系統GeoGebra結合代數運算與幾何建構兩大系統的雙向軟體，主要特色在以動態互動的方式讓學習者主動操作、觀察數學物件，方便學習者連結真實經驗並建構數學形式，因此可透過適當的教材設計，引導學生注意力，進行認知學習，並達到師生互動。
本研究以簡易二次函數為例，採準實驗研究法，探討GeoGebra動態幾何呈現的教學設計，相較於一般簡報教學與一般傳統教學，是否能達到較好的學習成效，並進一步分析其認知診斷評量訊息。
主要研究結論可以彙整如下：
1、GeoGebra動態幾何呈現的教學設計有助於低、中學業能力的學生在數學上的學習。
2、GeoGebra動態幾何呈現的教學設計明顯有助於學生將數學概念、技能形成新知識並儲存於長期記憶區。
3、GeoGebra動態幾何呈現的教學設計有助於提高學生學習數學技能之精熟度，並增強概念的圖像表徵。

GeoGebra (dynamic geometry system) is an interactive software that combines algebraic calculation and geometric construction. The main feature focuses on students’ own initiatives to operate and observe mathematical objects through interactive methods. It facilitates building mathematical concepts through tangible experiences. With properly designed teaching materials, it can focus students’ attentions, promote cognitive learning and encourage student-teacher interactions.
Using the quasi-experimental method, the study uses simple quadratic function as the particular case to investigate whether GeoGebra’s teaching design can achieve better learning outcomes compared to the typical PowerPoint presentations and the common traditional teachings; and to provide further analysis on cognitive diagnostic assessment.
The main conclusion can be summarized as follows:
1.GeoGebra’s instructional design helps students with low to mid academic abilities to improve their mathematical learning.
2.GeoGebra’s instructional design has the apparent effect in aiding students form mathematical concepts and turn hands-on skills into new knowledge stored in the long-term memory.
3.GeoGebra’s instructional design helps students to increase their proficiencies in acquiring mathematical skills and enhance the concept of pictorial reprentations.

中文摘要…………………………………………………………………… i
英文摘要…………………………………………………………………… ii
誌謝………………………………………………………………………… iii
目錄………………………………………………………………………… iv
表目錄……………………………………………………………………… vi
圖目錄……………………………………………………………………… vii
第一章 緒論……………………………………………………………… 1
第一節 研究背景與動機……………………………………… 1
第二節 研究目的……………………………………………… 2
第三節 研究問題……………………………………………… 4
第四節 名辭解釋……………………………………………… 4
第五節 研究限制……………………………………………… 5
第二章 文獻探討………………………………………………………… 7
第一節 多媒體學習認知理論………………………………… 7
第二節 動態幾何系統GeoGebra……………………………… 13
第三節 認知診斷評量………………………………………… 16
第四節 二次函數相關研究…………………………………… 22
第三章 研究方法………………………………………………………… 25
第一節 研究流程……………………………………………… 25
第二節 研究對象……………………………………………… 26
第三節 研究設計……………………………………………… 28
第四節 研究工具……………………………………………… 32
第五節 資料分析方法………………………………………… 36
第四章 研究結果與討論………………………………………………… 38
第一節 施測樣本的敘述統計資料與檢定分析……………… 38
第二節 認知診斷評量………………………………………… 47
第三節 研究結果摘要………………………………………… 54
第五章 結論與建議……………………………………………………… 55
第一節 研究結論……………………………………………… 55
第二節 研究建議……………………………………………… 56
第三節 未來研究方向………………………………………… 57
參考文獻…………………………………………………………………… 59
附錄………………………………………………………………………… 63
附錄一 課程學習單…………………………………………… 63
附錄二 GeoGebra輔助教學教材內容及分析………………… 67
附錄三 一般簡報教學教材內容及分析……………………… 78
附錄四 函數學習成就測驗後測……………………………… 92

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