探討動態幾何軟體對國小四年級學生平行四邊形面積概念之研究

A study of fourth graders’ concepts of area of parallelograms through interacting with dynamic geometry software

姜淑菁(Shu-Ching Chiang)

指導教授 ： 許慧玉

國立清華大學/竹師教育學院/數理教育研究所/碩士(2017年)

摘要

本研究目的是在探討動態幾何軟體對國小四年級學生平行四邊形面積概念之研究。基於上述的研究目的，本研究欲探討的研究問題有二：一、各動態幾何軟體教學活動中三組學生之學習表現為何？二、個別學生於動態幾何軟體教學活動之學習表現為何？本研究採方便取樣，主要研究對象為桃園巿某國小四年級學生高分組三名、中分組三名、低分組三名，共九名。本研究採用的研究方法為個案研究法和訪談研究法，進行資料之蒐集與質量並重之分析。本研究的研究工具主要有：半結構訪談、動態幾何軟體GeoGebra設計的教材和學習單。
本研究結果結論如下：
1.能歸納出平行四邊形的變化。
2.能發現底、高、面積之間規律關係。
3.能了解底和面積成倍數關係。
4.能了解高和面積成倍數關係。
5.能釐清同底等高平行四邊形面積相等的原因。
6.能理解長方形面積公式。
7.能覺察長方形的「長、寬」與平行四邊形的「底、高」的對應關聯。
8.能在GGB下，產生心像切割拼湊的思考，由長方形面積轉換出平行四邊形面積公式。

關鍵字

動態幾何軟體 ； 平行四邊形 ； 面積

並列摘要

The purpose of the study is to explore the study of fourth graders’ concepts of area of parallelograms through interacting with dynamic geometry software. Based on the purpose above , there are two problems treated in the research. Firstly, what are the learning effects of the students of the three levels in the teaching activities of the dynamic geometry software? Secondly, what are the learning effects of each student in the teaching activities of the dynamic geometry software? This study adopts convenience sampling; it’s target studying students are the three students who are ranked with high level, the three students who are ranked with medium level, and the three students who are ranked with low level. This study adopts case study and interview method to collect data with both qualitative data analysis and quantitative data analysis. This study’s research tools are mainly semi-structured interview and exercises and worksheets designed by using the dynamic geometry software GeoGebra.
According to the research, the researcher obtains the conclusions of this study as following:
1. Students can induce the variances of parallelograms.
2. Students can find the regular relations among bases, heights, and areas.
3. Students can understand that bases and heights are under multiple relations.
4. Students can understand that heights and areas are under multiple relations.
5. Students can tell the causes why areas of parallelograms are equivalent with same bases and equal heights.
6. Students can understand the formula of area of rectangles.
7. Students can be aware of the relative relations between lengths and widths of rectangles and bases and heights of parallelograms.
8. Students can generate thoughts of cutting and patching of mental imagery under GGB which can transform the formula of area of rectangles to that of area of parallelograms.

並列關鍵字

dynamic geometry software ； GeoGebra ； parallelograms ； area

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