探討國中資優數學幾何圖形之輔助線

The Study of Gifted Mathematics in The Course of Auxiliary Line Geometry in Junior High School

李怡君(I-Chun Li)

指導教授 ： 王牧民

中原大學/理學院/應用數學研究所/碩士(2014年)

https://doi.org/10.6840/cycu201400169

摘要

本研究主旨在於探討，國中八、九年級學生學習幾何圖形(如何運用輔助線)問題時，可能發生的迷思概念或困難。透過行動研究的研究方法，老師可以在教學時更了解學生的迷思概念所在，並且在適當的時機給予學生輔導與協助，進而達到提升學生的學習動機、培養學生獨立思考解題，以及教師的專業成長，使教學更成熟圓潤。
研究與試題分析後獲致的結果如下：
一、學習困難的主要原因有：
1.未能以正確、完整的數學語言或符號描述圖形或數學專有名詞。
2.未能將所學的知識整理成有系統的概念幫助學習。
3.論證觀念不完整，文字表徵與形式論證的能力不足。
4.缺少相關的解題經驗，沒有主動繪製參照圖的習慣。
5.未熟悉預備知識，缺乏利用已知性質推理的能力。
二、研究整理出的幾何解題概念如下：
1. 建立基本圖形與幾何知識的雙向關聯。
2. 把經常在習題中出現的基本形態作為基本圖形。
3. 把反映重要數學規律的圖形作為基本圖形。
4. 利用基本圖形分析法分析幾何問題的基本教學模式。
5. 分析基本圖形與數學思想方法相融合。
透過本研究的結論，提出以下幾點建議供教師在教導學生學習幾何問題時參考：
1.培養學生解讀題目能力，並澄清迷思概念。
2.「設計有系統的教材進行類比遷移」、「局部推理與模仿」等教學策略能有效的協助學生解決學習困難。
3.使用動態幾何軟體模擬，觀察圖形變換，實證所學之幾何概念。
4. 「類比遷移」、「局部推理與模仿」的教學策略能有效的使學生由形式證明的渾沌狀態趨向明朗化。

關鍵字

國中數學教材 ； 輔助線 ； 幾何

並列摘要

This study aims to explore , junior grade eight , nine students ' misconceptions or difficulties geometry ( how to use the auxiliary line ) problems that may occur. Through action research methods , teachers can better understand when teaching where students ' misconceptions , and at the appropriate time to give students guidance and help , and then to enhance students' motivation to learn , develop independent thinking problem solving , as well as teachers' professional grow, make teaching more mature mellow.
After studying and analyzing the results attainable questions are as follows:
First, learning difficulties main reasons:
1 . Failure to properly complete mathematical description of a graphic or symbolic language or
mathematics proper nouns .
2 . Failed to organize what they have learned into a systematic concept help learning .
3 . Demonstrates the concept of incomplete and inadequate capacity to characterize the form of the text argument .
4. Related to solving the lack of experience, no initiative to draw reference to FIG habits.
5. Not familiar with prior knowledge , lack of ability to use the known properties of reasoning.
Second, the study of geometry problem-solving concepts sorted out as follows :
1. Establish bidirectional association basic graphics and geometric knowledge.
2. The basic form often appear in the exercises as a basic graphics.
3. Graphics to reflect the important mathematical laws as the basic graphics. Analysis of basic
geometric problems teaching mode
4 . Use basic graphical analysis method.
5. Basic graphical analysis and integration of mathematical thinking .
Through the conclusion of this study , made the following recommendations for teachers to teach students in the geometric problems :
1 .Topic students the ability to interpret and clarify misconceptions .
2. "Design a systematic textbook analogy migration ", " local reasoning and imitation " and other teaching strategies can be effective To help students overcome their learning difficulties.
3 .Using dynamic geometry software simulation , graphics transformation observed geometric
concepts , empirical have learned .
4. " Analog Migration ," teaching strategies " local reasoning and imitation " so that students can be effective as evidenced by form Chaotic state tends to become clear .

並列關鍵字

teaching materials of math in junior high school ； geometry ； auxiliary line

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