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研究生:郭育宓
論文名稱:國小學童平面基本圖形視覺期迷思概念之研究-以高雄縣壽齡國小為例
指導教授:葉啟村葉啟村引用關係
學位類別:碩士
校院名稱:臺南師範學院
系所名稱:教師在職進修數學碩士學位班
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:123
中文關鍵詞:迷思概念隱藏式圖形
外文關鍵詞:prerecognitive level
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本研究旨在探討高雄縣壽齡國小一至六年級學童,對於平面幾何圖形概念之發展,以及三角形角度張開大於135度時,是否會產生迷失概念。為探討壽齡國小與高雄縣其他各地區的國小學童,對幾何圖形的辨識能力是否有差異。因此以高雄縣新甲、橋頭、興達、等國小一至六年級學童,共計488人為一般組型,作為壽齡國小與一般組型之比較。首先以Clements等學者(1999)發展的相關研究為主,收集的資料以單因子變異數分析及事後考驗(Scheffe法)進行分析,探討城鄉、年齡、性別之間的差異性。實驗效益分析以壽齡國小為例,壽齡國小的研究樣本一至六年級共282人,分成實驗組與對照組,實驗組於一般教學後,進行本研究之補救教學,對照組除了接觸學校正常課程外,不另外進行教學,進一步比較各年級之間的差異。研究者針對9位學生進行訪談,瞭解學童慣用語彙作為編製晤談結果試卷,在對770位進行測試,以瞭解學童於視覺期對圖形的特徵,思維型態轉變方式,及其對平面幾何圖形的認知概念。
本研究有以下幾點發現:
一、 三角形角度張開超過135度時,角度越大,學生越容易產生迷思現象。惟各學校的五年級學生,在此向度答對率普遍高於其他各年級。顯示年齡並不會影響其圖形答對率高低,而是與學童的成熟度有關,結果顯示城鄉、性別並無顯著差異。
二、 各年級學童對於圓形、長方形與正方形比較容易掌握。年級越高,學生越能掌握圖形的特徵,且城鄉之間達.05顯著差異。三角形部份,各年級學生依不同圖形的變化,答對率會出現不同的現象,各年級答對率反而與年齡無關。
三、 新甲、橋頭、興達等三所國小男、女生於圓形(F= 2.731)、正方形(F=.801)、三角形(F=.3212)、長方形(F=.497)等四種圖形皆無顯著差異(p>.05)。壽齡國小各年級的實驗組、對照組的前測與延後測的男、女生除三年級未達顯著差異(p>.05),其餘各年級的男、女生達.05顯著差異,而且實驗組成績優於對照組。
四、 壽齡國小在隱藏式圖形部分實驗組一升二年級學童,實施補救教學前後之各答對率分別為18.33與23.60達.05顯著差異,顯示協助學童澄清圖形的概念、分類與性質,有助增進學習效能。對照組二升三年級學生答對率才由15.90提高至22.96,達到實驗組一升二年級的水準,顯示比實驗組慢一年,此與van Hiele教學理論相印證。
This research was to investigate how the students of Shou-Ling Elementary School, Kaohsiung Hsien, developed their concept about geometric shapes and whether they would feel confused when the angle of a triangle was larger than 135 degrees. In order to find out if there was a significant difference in the ability to recognize geometric shapes among the students of Shou-Ling Elementary Schools and those from other elementary schools in Kaohsiung Hsien, the subjects of this research included the first graders to the sixth graders of Hsin-Chia, Chiao-Tou, and Hsing-Ta Elementary Schools, Kaohsiung Hsien, totally 488 students forming the general group in contrast with the students of Shou-Ling Elementary School. First, the relevant research made by Clements, et al. (1999) was taken for reference. Then, the data gathered were analyzed by means of the single-factor variant analysis and subsequent testing (Scheffe method) so as to investigate the differences between the city and country, age, and sex. The experimental efficiency analysis was based on the students of Shou-Ling Elementary School. Totally 282 students from the first grade to the sixth grade of Shou-Ling Elementary School were divided into two groups — experimental group and control group. Make-up teaching of this study was given to the experimental group after normal curricular activities, whereas no extra teaching was offered to the control group aside from normal school courses. Later, a further comparison was made to see the differences between each grade. 9 students were interviewed by the researcher so as to understand the commonly used words among students, and the result was made into the test paper. Then, a test was given to 770 students to get a better knowledge about the students’ thinking pattern about the characteristics of shapes at the visual level, and their cognition about geometric shapes.
The findings of this research are shown as follows:
1. When the angle of a triangle was larger than 135 degrees, the larger the angle became, the more confused the students would feel. Generally, the fifth graders obtained the highest percentage in answering correctly than other graders in each school regarding this condition. This suggested that the students’ maturity, not their age, would influence the percentage of answering correctly. And the result showed no significant difference between the city and country, and sex.
2. It was easier for students to recognize the circle, square, and rectangle. The higher grade the students were in, the more easily the students could recognize the characteristics of shapes. And there was a significant difference of .05 between the city and country. As for the triangle, the percentage of answering correctly varied when the shape changed differently. And the percentage of answering correctly had nothing to do with the age of students.
3. No significant difference (p > .05) existed among boy and girl students of Hsin-Chia, Chiao-Tou, and Hsing-Ta Elementary Schools concerning the circle (F = 2.731), square (F = .801), triangle (F = .3212), and rectangle (F = .497). As for the pre-test and post-test given to the experimental group and the control group in each grade of Shou-Ling Elementary School, there was a significant difference of .05 in all grades except for the third grade (p > .05). And the experimental group performed better than the control group in the tests.
4. Regarding the hidden pictures, the first-turn-second graders in the experimental group of Shou-Ling Elementary School had different percentages of answering correctly before and after the make-up teaching was given (18.33 and 23.60, respectively), exhibiting a significant difference of .05. And this suggested that assisting the students to get a better understanding about the shapes and their classification and property would improve the students’ learning efficiency. However, there was an increase from 15.90 to 22.96 in the percentage of answering correctly for the second-turn-third graders in the control group, and that was just the level of the first-turn-second graders in the experimental group, indicating that the control group was one year slower in learning than the experimental group. And this result was the same as shown in the teaching theory of van Hiele.
第一章 緒論
第一節 研究動機 ……………………………………………………. 1
第二節 研究目的 ……………………………………………………. 3
第三節 研究問題 ……………………………………………………. 4
第四節 研究範圍和限制 …………………………………………… 4
第五節 名詞界定 ……………………………………………………. 6
第二章 文獻探討
第一節 兒童圖形概念的發展 ……………………………………… 9
第二節 van Hiele夫婦理論之視覺期 …………………………….. 18
第三節 prerecognitive level…………………………………………. 20
第三章 研究方法
第一節 研究流程 …………………………………………………… 25
第二節 研究對象 …………………………………………………… 27
第三節 研究工具 …………………………………………………… 30
第四節 資料處理與分析 …………………………………………... 32
第五節 幾何圖形補救教學之設計 ……………………………….. 35
第四章 研究結果與討論
第一節 不同年級學童於三角形角度變化的迷失 ………………. 43
第二節 平面基本圖形於城鄉學習成效的差異 …………………. 55
第三節 學童在視覺期對圖形迷失概念之探討 …………………. 68
第四節 各年級學生對隱藏式圖形的認知概念 …………………. 72
第五章 結論與建議
第一節 結論 …………………………………………………………. 83
第二節 建議 …………………………………………………………. 87
參考書目
一、 中文部分 ……………………………………………………… 89
二、 西文部分 ……………………………………………………… 90
附錄A ……………………………………………………………………… 99
附錄B ………………………………………………………………………102
附錄C ………………………………………………………………………108
附錄D ………………………………………………………………………113
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