國小五年級學生四邊形概念與作圖之研究

A study of fifth-grade Students' concepts and drawings of quadrilaterals

范力分(Li-Fen. Fan)

指導教授 ： 許慧玉

國立清華大學/竹師教育學院/數理教育研究所碩士在職專班/碩士(2017年)

摘要

本研究旨在探討國小五年級學生四邊形概念與作圖之研究，以問卷對新竹市一所國小五年級學生進行調查，回收一百四十九份有效問卷，依據蒐集到的問卷，分成文字表徵和圖形表徵進行分類，之後進行第二階段的個案研究，半結構式訪談的方式，研究六位學生四邊形概念與作圖情形。
研究結果
一、特殊四邊形的定義表現情形：
正方形定義以「四個邊等長」和「四個角直角」為主要文字表徵，提及「四個邊等長」比「四個角直角」多出24%。長方形定義以「對邊一樣長」和「四個角直角」為主要文字表徵，「邊長」的性質描包含：長一樣長和寬一樣長、兩組一樣長、上下一樣長和左右一樣長、兩邊長和兩邊短。菱形定義以「四個邊等長」為主要文字表徵，描述「對角」關係情形包含：對角一樣大、四個角都(不)是直角、角不一樣大，故學生會出現角度上的迷思。平行四邊形定義以「對邊平行」、「對邊一樣長」或「對角一樣大」為主要文字表徵，部分學生容易只看到上下平行或上下等長，卻未注意到左右邊也是平行且等長的概念。
二、特殊四邊形的繪圖表現情形：
正方形圖形主要特徵：「一雙對邊呈水平」和「一雙對邊呈鉛直」，能畫出大小不同的典型正方形圖形占83%，但將圖形做方位上的變化只17%。長方形圖形主要特徵：「一雙對邊呈水平」和「一雙對邊呈鉛直」，其中「水平的對邊比鉛直的對邊長」占87%，長寬比值範圍介在1~3.9，所占比例為66%。菱形圖形主要特徵：「對角線一條呈鉛直，另一條呈水平」，其中僅畫出典型菱形圖形，即「上下對角為銳角」占50%，銳角角度以六十度正負十度居多，占68%。平行四邊形圖形主要特徵：「有一雙對邊呈水平」、「左右對邊呈現從右上斜至左下」，長寬比值範圍介在1~2.2之間占77%，銳角範圍介在50度~70度之間占59%。
三、手繪與用尺的作圖表現
學生在正方形部分最容易畫出典型圖形，畫圖的順序是以順時針或是逆時針方向；若學生以手繪的情形下畫出典型圖形，則使用工具時，學生也較容易只畫出典型圖形；典型圖形的畫圖順序上，大多是以順時針或是逆時針方向畫出，若學生畫出有方位變化的圖形，大多在畫圖的順序上有不一樣的畫法，其中又以能畫出對邊的情形更容易做圖形上方位的轉換。

關鍵詞：四邊形、文字表徵、作圖

關鍵字

四邊形 ； 文字表徵 ； 作圖

並列摘要

The purpose of this study is to explore fifth-grade Students' concepts and drawings of quadrilaterals. A questionnaire survey was conducted on the fifth grade students in Hsinchu City and 149 valid questionnaires were collected. According to the collected questionnaire, it is divided into character representation and graphical representation. Followed by the second study, explore six fifth-grade Students' drawings of quadrilaterals without a drawing tool and drawings of quadrilaterals with ruler.

Research result
1. The definition of quadrilateral situation
The definition of square is characterized by "four sides are equal " and "four corners are right angles" as the main characters. Referring to " four sides are equal " is 24% more than "four corners of the right angle". The definition of rectangle is characterized by " opposite sides are the same" and "four corners are right angles". The description of the "side length" includes long sides are the same and short sides are the same, two long sides and two short sides, opposite sides are the same. The definition of diamond is characterized by " four sides are equal " as the main characters. The description of the "diagonal" includes the diagonal is the same big, four corners are right angles, four corners are not right angles, corners are not the same . The definition of parallelogram is characterized by "parallelism", " opposite sides are the same " or "diagonals are the same". Some students only see the upper and lower parallel but do not notice that the left and right sides are parallel.

2. The graphics of quadrilateral situation
The main features of the square graphics are "a pair is horizontal " and "a pair is vertical". 83% students can draw different size of the typical square graphics. But only 17% can draw the changes in the orientation of the graphics. The main features of the rectangle are "a pair is horizontal" and "a pair is vertical". 87% of students draw "the opposite side of the horizontal sides is longer than the vertical sides. 66% ratio of the graphics range is from 1 to 3.9. The main features of the diamond pattern are "the diagonal one was vertical, the other was horizontal". Only draw a typical diamond-shaped figure, that is "up and down diagonal for acute angle" accounted for 50%. 68% of the acute angle is from 50 degrees to 70 degrees. The main features of the parallelogram are " A pair is horizontal ", " the left and right sides are diagonally from the upper right to the lower left ". 77% ratio range is between 1 ~ 2.2. 59% acute angle range is between 50 degrees to 70 degrees.

3. drawings of quadrilaterals without a drawing tool and with ruler
Students are most likely to draw typical graphics in the square. The drawing order of typical graphics are in a clockwise or counterclockwise direction. If the student draws a typical pattern in the case of hand drawings, then it is easier for the student to draw a typical graphic with the ruler. If the students draw a pattern of azimuth changes, most of the order in the drawing has a different drawing way. If students can draw graphics on the other side is easier to do graphics orientation conversion.

Keywords: quadrilateral, character representation, drawing

並列關鍵字

quadrilateral ； character representation ； drawing

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