本研究旨在探討圓規作圖的半徑等量性質，圓心到弧線上任一點等長度，此長度的定量關係為半徑等量性質，研究中將探討學生辨識半徑等量的能力表現，及其可能影響的因素為何。
圓規作圖的要素為「圓心、半徑、弧線」，將其與操弄變項「單一與相異」設計施測試題，分別為「單一圓心相異圓心」、「單一半徑與相異半徑」、「單一弧線與相異弧線」等，並進一步討論圓規作圖要素在幾何圖形中繪製的方式是否為影響半徑等量辨識的因素之一，再分別以「半徑連接與不連接」、「完整弧線與部分弧線」、「實線弧線與虛線弧線」、「以線段為圓心畫弧與以弧線為圓心畫弧」等設計試題，考驗學生半徑等量的答題表現。
以新竹縣市四所國中為研究對象，共施測八年級311位學生、九年級308位學生，並將施測結果以量化資料分析，做為提供促進尺規作圖教學的成效建議。結果顯示：(1)在控制變項「單一半徑與相異半徑」、「實線弧線與虛線弧線」及「以線段為圓心畫弧與以弧線為圓心畫弧」中學生表現有統計顯著差異；(2)施測結果指出，若將圓規以相同的半徑，繪製兩個相異的弧線，學生易直觀從圖形中直接認定其半徑相異，無法正確判別兩相異弧的半徑等量關係。
本研究之施測結果期能針對教師教學及未來研究方向提出相關建議。

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.

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