本研究想探究國小中年級學生如何理解多邊形的概念以及多邊形之間的關係，是以學生對多邊形的識別、找出多邊形的共同屬性，將多邊形進行歸類、畫出指定屬性的多邊形，根據學生的解題表現差異，探究學生對多邊形的概念，為主要研究方向。
透過問卷調查法，採方便取樣的方式，進行多邊形問卷的施測。施測對象為研究者任教的學校附近，橫跨新竹縣市共四間學校的中年級學童，每校三年級兩班、四年級兩班，一共八個班級，有424學童。施測結果的統計方法為獨立樣本T檢定，對研究結果進行分析與研究。
研究結果顯示，中年級學童對多邊形的認知情形為：
一、 多邊形的要素中「圖形的封閉性」、「邊應該是直的」、「兩條線段不交叉」對中年級而言，「圖形的封閉性」、「邊應該是直的」已經相當穩固，而給學童實例進行判斷或修改時，四年級學童的表現優於三年級。尤其在「邊應該是直的」，三年級學童在進行給圖例判斷時可以清楚辨認其為非多邊形，但進行圖形修改時，卻無法正確修改這個要素。
二、 透過給定分堆的結果，請三、四年級學童找出性質分類屬性相當困難，不管是三年級或四年級均表現不佳。學童必須透過論述將自己心中的理解，再轉化成圖形和文字，對未曾接受這樣教學方式的學童而言有實際上的困難。在「凹凸多邊形」、「邊數」、「對稱」三個子題中，三年級學童和四年級「邊數」的表現均佳，顯示學生對邊的覺察較為敏銳。而「凹凸多邊形」則三年級明顯和四年級有落差。
三、 屬於關係的認知上，學生正確放入分堆的表現有一定程度，但在說明理由上仍然有困難。而在這個題組下，給定文字和情境讓學生進行屬於關係的判斷，難度大於給圖形進行判斷，此部分四年級優於三年級
四、 由給定屬性畫出多邊形的認知情形，四年級在學過四邊形的完整性質後，對於畫圖工具的使用意義更加鞏固，會追求圖形的準確性，能利用已有的知識畫出一雙對邊或兩雙對邊相互平行的四邊形。。

最後根據研究結論，分別針對欲進行國小中年級學生多邊形之相關研究者，提出具體的建議以供參考。

關鍵字：多邊形的識別、多邊形概念

This research aims to explore how middle primary school students understand the concept of polygons and the relationship between polygons. The main research direction is to explore the students' concept of polygons based on the differences in students' problem-solving performance in identifying polygons, finding their common attributes, classifying polygons, and drawing polygons with specified attributes.
The study adopted the questionnaire survey method. The questionnaire was administered in a convenient sampling method. The subjects were middle-grade students in four schools in Hsinchu County and City near the school where the researcher taught. Each school has two classes in the third grade and two classes in the fourth grade, a total of eight classes with 424 students. The statistical method of the test results is the independent sample T-test, and the research results are analyzed and studied.
The results of the study show that the cognitive situation of middle-grade school children about polygons is as follows:
1. Among the elements of polygons, "the closedness of the figure," "the sides should be straight," and "the two-line segments do not intersect," the middle-grade students have a very stable understanding of the first two elements. However, the fourth-grade students outperformed third-grade students when identifying or modifying polygons in the survey. In particular, third-grade students can use the concept "the sides should be straight" to identify non-polygon figures but cannot correct this element when modifying the figures.
2. Through the results of the given piles, it is quite difficult for students in third- and fourth-grade students to find out the principles of classifying polygons. Both third- and fourth-grade students did not perform well. Students must convert their understanding through discussion, then transform their understanding into figures and words, which is practically difficult for school children who have not accepted such a teaching approach. In the three sub-topics of "concave-convex polygon," "the number of sides," and "symmetry," the third- and fourth-grade students performed well in "the number of sides," which indicates that students are more sensitive to "sides." However, the third and fourth grades have a clear performance gap on the "concave-convex polygon" topic.
3. In terms of the cognition of belonging relationships, students are capable of putting the polygon figures into the correct categories but still showed difficulties in explaining reasons. In this set of questions, given words and situations for students to make judgments about belonging relationships is more difficult than making judgments when given polygon figures. Fourth-graders have better performance than third-graders in this part.
4. For the cognitive situation of drawing polygons from given attributes, students have a more consolidated understanding of the meaning of using drawing tools after learning the whole properties of quadrilaterals in fourth grade. They also pursue the accuracy of figures and can use existing knowledge to draw a quadrilateral with a pair or two pairs of opposite parallel sides.
Finally, according to the research conclusions, specific suggestions are put forward for reference for the relevant researchers who want to conduct research on polygons in middle primary grade students.

Keywords: polygon identification, polygon concepts

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