動態連結多重表徵視窗環境下橢圓學習之研究

A Study of Learning Ellipse with Dynamic Linked Multiple Representations Windows

蔡志仁(Jyh-Ren Tsay)

指導教授 ： 左台益

國立臺灣師範大學/理學院/數學系/碩士(1999年)

摘要

本研究探討中學生橢圓概念表徵結構的學習歷程，並依據此結果設計動態連結多重表徵之視窗學習環境。學生在此學習環境中，能同時注意到橢圓的不同表徵及其間的連結。
整個研究主要分成兩個階段。第一階段的研究以九名高二學生為樣本，進行診斷性教學，研究結果發現：橢圓概念的外顯表徵主要有語意表徵、圖形表徵、軌跡表徵、方程表徵、以及結構表徵，學生在建構橢圓概念歷程中，依其先備知識的品質，會有不同的發展方向。而圖形表徵是成功解題的重要關鍵，當學生能將題意表徵與其他表徵整合到圖形表徵當中，達成多重表徵間的緊密連結，則較能成功解題。第二階段以高中二年級兩班學生為樣本，進行動態連結多重表徵視窗學習環境實驗教學，研究結果顯示在學習成就前、後測驗上，學生呈現顯著進步效果，實驗組進步分數優於控制組，但未達統計檢定的顯著水準。從解題時的表徵運用情形來看，實驗組學生傾向以圖形表徵作主為表徵，並整合其他表徵於圖形中。
此研究所討論之中學生橢圓概念多重表徵建構歷程，以及動態幾何視窗學習環境之設計概念，可提供中學實務教學之參考。

關鍵字

數學教育 ； 橢圓 ； 多重表徵 ； 電腦教學

並列摘要

This study initially investigated the learning processes of high-school students and how they represent elliptical concepts and interlink them. The results were used to develop computer based instructional tools. The way in which these tools affected the student’s representations was then studied.
The research was in two parts: Initially nine student volunteers participated in the study; each was given diagnostic teaching. It was found that the main external representations of elliptical concepts are verbal, graphical, structural, formulaic, and locus representation. Students were found to have different ways to develop their elliptical concepts, according to their initial knowledge. When students could represent the problem and their related ideas in terms of graphical representation, then they could develop links between different representations, and could thus solve problems more easily.
In the second part of the research two high school classes were compared. A computer-based dynamic linked multiple representation Windows learning environment was used to teach one class. The results showed that students could make significant progress when taught in this way. The progress scores of the experimental group were higher than the control group, but this was not statistically significant. It was found that the experimental group tended to employ graphical representation as their main representation and use it to integrate the other representations.
This paper analyses high school instruction for teaching elliptical concepts, looking in particular at the process by which students construct multiple elliptical representations. It also gives insights into the design of computer-based dynamic linked multiple representation Windows learning environments

並列關鍵字

Mathematical Education ； Ellipse ； Multiple Representations ； Computer-based Instruction

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