動態幾何系統GeoGebra對數學學習成效與認知診斷影響之研究-以簡易二次函數圖形為例

A Study on the Effect of GeoGebra on Math Learning Achievement and Cognitive Diagnosis – a Case of Simple Quadratic Functions Graph

黃楷智

指導教授 ： 李榮耀

國立交通大學/理學院/理學院科技與數位學習學程/碩士(2011年)

https://doi.org/10.6842/NCTU.2011.00179

摘要

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。

關鍵字

動態幾何 ； GeoGebra ； 認知診斷評量 ； 二次函數

並列摘要

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.

並列關鍵字

dynamic geometry ； GeoGebra ； cognitively diagnostic assessment ； quadratic function

參考文獻

胡瑞明(2001)。用CAL探討五專生學習與二次函數相關數學概念之研究。科學教育學刊，9(4)，401-416 頁。

蔡志仁(2000)。動態連結多重表徵視窗環境下橢圓學習之研究。國立臺灣師範大學數學所碩士論文。

Brian, R. (1998). Computer-Intensive Algebra and Students` Conceptual Knowledge of Functions. Journal for Research in Mathematics Education, 29(1), 21-40.

Chandler, P. & Sweller, J. (1991). “Cognitive Load Theory and The Format of Instruction,” Cognitive and Instruction, 8, 293-332.

Clark, R. C. & Mayer, R. E. (2008). E-Learning and the science of instruction: proven guidelines for consumers and designers of multimedia learning (2nd ed.). San Francisco: Pfeiffer.