不同幾何思考層次的國中生判別正立方體透視圖邊長關係之研究

Study to Identify Length Relationships of a Cube in Perspective by Junior High School Students with Different Levels of Geometric Thinking

本研究主要在探討國中學生面對一個正立方體以平面表徵呈現時，其判別圖形中邊長關係的解題表現，及學生的解題表現是否與Van Hiele幾何思考層次有關。本研究以新北市某所國中146名二年級學生為研究對象，其中男生有78人，女生有68人，施以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。具體的研究發現有二：國中學生在視覺線索與答案一致的問題表現優於視覺線索與答案不一致的問題；Van Hiele幾何思考層次2及層次3的學生在測驗結果的表現顯著優於層次0及層次1的學生，特別是在視覺線索與答案不一致的問題上。針對研究結果，本研究提出未來教學及研究上的建議。 This study explored students' performance in solving questions related to a cube represented in a plane and discussing its relationship to Van Hiele geometric thinking levels. In total, 146 eighth graders (78 boys and 68 girls) of a junior high school in New Taipei City were studied. A Van Hiele geometric thinking level test and three-dimensional graphic component relationship judgment test were administered to all students. The conclusions were as follows. (1) Junior high school students performed better in three-dimensional graphic component relationship judgment test problems in which visual cues and answers are consistent than in those in which they are inconsistent; (2) students with Van Hiele geometric thinking levels of 2 and 3 performed better at three-dimensional graphic component relationship judgment test than those with levels of 0 and 1. The differences were apparent in questions in which visual cues and answers were inconsistent. Based on the research results, suggestions for teaching and future study are provided.