不同幾何思考層次的國中生判別平面呈現立體圖形組成要素關係之研究

A Study of Differentiating the Relationships of 3D Figure Elements by Junior High School Students with Different Levels of Geometric Thinking

李佳竹(Chia-Tsu li)

指導教授 ： 袁媛

中原大學/人文與教育學院/教育研究所/碩士(2017年)

https://doi.org/10.6840/cycu201700355

摘要

本研究主要在探討國中學生對於立體圖形在平面上呈現時，其判別組成要素間關係的情形及其解題表現是否與 Van Hiele 幾何思考層次有關，並進一步探討立體圖形旋轉因素是否對學生判別組成要素關係的表現造成影響。研究者採用混合研究法，以新北市某所國中146名八年級學生為研究對象，其中男生有78人，女生有68人，於2017年4月期間，對全體樣本正式施測 Van Hiele 幾何思考層次測驗及立體圖形組成要素關係判別測驗，並根據 Van Hiele 幾何思考層次測驗的施測結果，抽取12名學生作為訪談對象，針對立體圖形組成要素關係判別測驗的解題情形，進行一對一半結構式訪談。蒐集學生訪談資料後，進行資料的整理與分析，並得出結論如下：
一、國中學生在視覺線索與答案一致的問題表現優於與答案不一致的問題。
二、不同 Van Hiele 幾何思考層次的國中學生在視覺線索與答案不一致的問題出現表現上的差異。
三、不同 Van Hiele 幾何思考層次的國中學生對於平面中呈現立體圖形組成要素關係的判別策略是不同的。
四、國中學生判別立體圖形組成要素的表現不受圖形旋轉因素的影響。
針對研究結果，本研究提出未來教學及研究上的建議。

關鍵字

Van Hiele ； 國中 ； 立體圖形 ； 幾何

並列摘要

This study aims at exploring students’ performance of solving questions related to three-dimensional graphics which were represented in a plane, discussing its relationship to Van Hiele geometric thinking levels, and further exploring if the rotation of the three-dimensional graphics is a factor that affects the performance of students to determine the relationship between the elements in a three-dimensional graphic.
The researchers used a mixed research method to study 146 eighth graders of a junior high school in New Taipei City. Among them, there were 78 boys and 68 girls. During April 2017, Van Hiele Geometric Thinking Level Test and Three Dimensional Graphic Component Relationship Judgment Test were applied to all samples. According to the results of Van Hiele Geometric Thinking Level Test, 12 students were selected as the interview objects, and were given semi-structured interviews to explore their problem-solving strategies. Data are collected and analyzed, and the conclusions are as follows:
1.Junior high school students perform better in problems which the visual cues and answers are consistent than those are inconsistent.
2.Students with different Van Hiele geometric thinking levels perform differently in questions which the visual cue and the answer are inconsistent.
3.Students with different Van Hiele geometric thinking levels apply different strategies in solving problems related to three-dimensional graphics which were represented in a plane.
4.The rotation of the graphics is not a factor that affects students’ performance.
Based on the research results, suggestions for teaching and future study are provided.

並列關鍵字

Van Hiele ； Junior High School ； Three-dimensional Graphics ； Geometry

參考文獻

洪明顯（2014）。互動式3D電腦輔助教學應用於正投影視圖（未出版之碩士論文）。私立臺中科技大學，臺中市。

陳毓梅（2011）。不同教具教學環境對國小一年級學生學習立方體積木堆疊計數的影響（未出版之碩士論文）。私立中原大學，桃園市。

王學武、蔡佳穎、陳宜均、賴蕙慈（2011）。應用 Van Hiele 幾何思考層次理論於國小學童體積概念數位教材開發之研究。國民教育，51（6），90-99。

王毓婕、陳光勳（2016）。運用幾何軟體 Cabri 3D 與實體積木教具教學對國小二年級學童學習空間旋轉概念之影響。臺灣數學教育期刊，3（4），19-54。

教育部（2003）。國民中小學九年一貫數學學習領域課程綱要。臺北市：教育部。