探討國中三年級學生透過摺紙活動進行尺規作圖補救教學之成效

陳宥良(Yu-Liang Chen)

指導教授 ： 譚克平

國立臺灣師範大學/理學院/科學教育研究所/碩士(2009年)

摘要

學生在尺規作圖的學習上常遇到不少困難，本研究希望設計創新的教學法，利用直觀的摺紙經驗幫助學生學習尺規作圖。本研究有二個研究目的，第一為了解國三學生尺規作圖學習表現，第二為探討國三低學習成就學生透過摺紙活動進行尺規作圖補救教學之成效。
本研究設計分成二部分，第一部分採取調查研究法，自編經效化的「尺規作圖試題」工具，挑選台北地區三所國中，共150位學生進行施測；第二部分採用教學實驗法，研究者根據摺紙作圖的數學理論，發展6個摺紙動作，以作為學習尺規作圖的過渡性工具，此6個動作為「摺出通過兩點的直線」、「從直線上一點作垂線」、「從直線外一點作垂線」、「在直線上取等線段長」、「將兩點重合」與「將兩直線重合」，教學對象為台北市某國中3位國三學生，挑選的判準為該生的「尺規作圖試題」總得分為全體受測學生的後四分之一，此3位學生接受4天共計6小時的教學。
本研究的主要研究結果如下：
（一）關於國三學生的尺規作圖學習表現：
1. 學生不清楚尺規作圖的工具使用規定。
2. 學生不熟練基本尺規作圖步驟，不清楚該等作圖步驟與幾何性質之間的關係。
3. 學生在應用尺規作圖解決作圖問題方面有困難。
（二）關於透過摺紙學習尺規作圖的成效：
1. 摺紙能幫助學生熟練基本尺規作圖步驟，理解作圖步驟所應用的對稱性質。
2. 摺紙能幫助學生分析作圖問題，檢驗想法的正確性，找出正確的作圖步驟。
3. 摺紙能提升學生尺規作圖學習興趣。
根據研究結果，本研究建議教師教學時應強調尺規作圖的工具使用方式，可讓學生先利用摺紙解決作圖問題，再將摺紙動作一一轉換成尺規作圖作法。未來研究建議擴大樣本數，進一步探討摺紙對中、高程度學生學習尺規作圖的成效。

關鍵字

尺規作圖 ； 摺紙 ； 補救教學

並列摘要

It is common knowledge that many students encountered difficulties in learning geometric construction. This study develops a creative teaching method to learn construction that makes use of the intuitive origami experience of students. There are two purposes in this study. The first is to survey ninth graders’ learning performances in geometric construction. The second is to explore the effectiveness of ninth grade low achievers in learning geometric construction through origami.
This study is divided into two parts. The first part is a survey research. A total of 150 ninth graders’ in Taipei area filled out a questionnaire on geometric construction. Their performances are then analyzed and reported herein. The second part consists of an innovative teaching experiment. Following the mathematical principles of geometry construction through origami, this author designs six origami operations to serve as the transitional stage to geometric construction. They are organized into four lessons that require six hours of instruction. Their effectiveness is studied by way of a teaching experiment on three ninth grade low achievers in math from the Taipei area.
The following results were obtained:
1. Some students did not know that geometric construction were restricted to the use of only a straightedge and compass.
2. Students were awkward with basic geometric construction, and did not understand the relationship between construction procedures and their underlying geometric properties.
3. Students did not do well in solving geometric construction problems.
4. Origami helped students to be proficient in basic geometric constructions.
5. Origami enabled students to analyze geometric construction problems and to find out the correct construction sequences.
6. Origami enhanced students’ interest in learning geometric construction.
Based on the results of this study, the following suggestions are provided for consideration in future instruction of geometric construction. First, teachers should emphasize on the basic rules of geometric constructions. Second, teachers can motivate students to solve construction problems through origami, and then translate the origami operations back into geometric construction procedures.

並列關鍵字

Geometric construction ； Origami ； Remedial instruction

參考文獻

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