Research on the Interplay between Diagram and Geometric Properties Formulated by Ruler-and-Compass Construction

• Main Authors: LI,YI-XUAN, 李怡萱
• Other Authors: Hui-Yu Hsu
• Format: Others
• Language: zh-TW
• Published: 2015
• Online Access: http://ndltd.ncl.edu.tw/handle/96465520721840794588

碩士 === 國立新竹教育大學 === 數理教育研究所 === 103 === This research was conducted to investigate the property of equidistant lengths from any point on a certain arc to the center, while drawing an arc by a certain measure generated by compasses construction. In this study, we examined students’ abilities to recognize the property mentioned above and the possible factors leading to their apprehensions. In this study, we defined the essential factors of compasses construction to be center, radius and arc; the manipulated variable to be single or more than two essential factors of compasses construction embedded in a certain diagram. We also further discussed whether the ways we presented the factors of compasses construction in a certain geometric diagram could also be one determining factor to explain how students perceive the idea of equidistant lengths from any point on a certain arc to the center as we mentioned in the very beginning part. In this study, we designed all the testing questions based on the following four ways of presenting the factors of compasses contructions to discuss students’ performances; the different ways are connected-unconnected radius, whole-partial arc,solid-dashed line arc, and drawing an arc with a line as a center or with an arc as a center respectively. The object of this research are junior high school students from four schools located in Hsinchu county and country, including 311 8th grade students and 308 9th grade students. Still, the findings were quantitative analyed as to provide some suggestions for teaching compass and straightedge constructions.Analyses of students’ responses on survey items show that concerning control variables such as single-multi radius, solid-dashed line arc ,and drawing an arc with a line as a center or with an arc as a center respectively, students’ performance showed statistical significance. Still, the findings showed that two diverse arcs even drew with the same radius couldn’t be understood by students. That is to say, studetns couldn’t tell the property of equidistant lengths from any point on a certain arc to the center, while drawing an arc by a certain measure generated by compasses construction. Based on the findings, this study provided suggestions and comments for teachers’ teaching and advanced the future research directions.