國小四年級在動態幾何環境下學習三角不等式之個案研究

Case study of fourth graders’learning of triangle inequality in dynamic geometry environment

林思汝(Szu-Ju. Lin)

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在職專班/碩士(2016年)

摘要

本研究旨在探討國小四年級個案學童在動態幾何環境下如何學習三角形任意兩邊和大於第三邊，研究目的有二，分別為：一、探討在動態幾何環境下學習三角形任意兩邊和大於第三邊各活動中學童的學習表現。二、探討在動態幾何環境下學習三角形任意兩邊和大於第三邊個別學童於教學活動之學習表現。
本研究採質性個案研究法，以研究者所任教的新竹市某國小之四年級6名學童為研究對象，教學時所使用的動態幾何軟體為GeoGebra。研究工具包含以動態幾何軟體GeoGebra所設計之教材、學習單及半結構式訪談大綱。研究過程蒐集的資料包括以攝影機記錄學童於電腦介面上的拖曳情形、以錄音機記錄個案學童的訪談實錄及學童於操作動態幾何軟體下所完成之學習單，後續將針對以上資料進行分析。
本研究結論顯示，活動與學童的學習表現之分析統整如下：
1.學童較易看出「等於」關係
2.表格有助於學習
3.各學童於活動中的學習路徑與發展層次有所差異
而動態幾何軟體GeoGebra可以協助學童在學習本概念時：
1.產生更多樣化的三角形非典型例
2.藉由操作動態幾何圖形，主動發現邊長關係
3.輔以表格的使用，與動態幾何圖形相互對照出邊長關係
4.練習例題時，能重新回到動態幾何圖形上操作檢驗。

關鍵字

動態幾何軟體 ； 三角形 ； 邊長關係 ； 任意兩邊和大於第三邊 ； 三角不等式

並列摘要

The research is to explore how to learn the triangle inequality in dynamic geometry environment of the fourth graders. The purpose of the research are as follows: 1. To explore the learning performance of students in each teaching activitiy in the research of "learning triangle inequality in dynamic geometry environment" . 2. To explore the learning performance of individual student in the teaching activities in the research of "learning triangle inequality in dynamic geometry environment" .
This research is qualitative and case research.In this research, the geologic software used in the study was based on GeoGebra, which was used by the researcher to study six fourth graders of certain elementary school in Hsinchu City. The research tools include teaching materials which were based on GeoGebra, working sheets, and semi-structured interview. The information collected in the course of the research included the records of how the fourth graders interacted with GeoGebra, the interview records of the fourth graders and the working sheets completed by the students in the operation of the dynamic geometric software. These information will be analyzed in the follow step.
The findings of this research show that the analysis of activities and learning performance of students is summarized as follows:
(1) The students are more likely to see "equal" relationship.
(2) Forms help students to learn.
(3) The learning path and development level of each student in the activities are differnent.
GeoGebra, a dynamic geometric software, can help the fourth graders learn this concept by the strategies as follows:
(1) Produce more diverse triangular atypical cases.
(2) Discover side relationship by operating dynamic geometry.
(3) Students can conjecture the relationship of sides by forms.
(4) When practicing working examples, students can examine whether their answers are correct or not by using dynamic geometry.

並列關鍵字

dynamic geometry software ； GeoGebra ； triangle ； side length relationship ； triangle inequality

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