利用有趣的摺紙活動學習尺規作圖,是使課室活潑化的方式之一,也能幫助學生克服學習尺規作圖的困難。因此,本研究的目的有三,第一,藉由分析國中教材中的尺規作圖,探討陳宥良(2008)提出的六個摺紙動作是否足夠應付國中教材;第二,編製一套透過摺紙學習尺規作圖的教材,並探討此套教材在認知面向對學生的幫助。第三,探討此課程在情意面向對學生的幫助。 本研究的研究設計採質性研究,為著深入探討本實驗課程的成效,分為兩個部分:第一部分是藉由分析現行國中教科書中所有的尺規作圖題,以找出所有尺規作圖的動作,並發展出能應付所有教科書內尺規作圖的摺紙動作。第二部分乃是根據第一部分的結果,參考設計研究法的精神,編製一套透過摺紙學習尺規作圖的教材,並採前實驗研究法進行教學實驗,對象為苗栗縣某國中6名學生。資料分析參考David Middleton提出的D-analysis進行教學過程分析,再加上前後測結果與質性訪談的內容,探討此教材的有效性。 本研究主要的研究結果如下: (1)摺紙能幫助學生記憶基本尺規作圖的繪圖步驟。 (2)摺紙能強化學生對稱的概念,且增強他們等距離的直覺。 (3)摺紙能成為學生驗證作圖正確性的工具之一。 (4)摺紙能提供學生解題的想法,特別在「完成線對稱圖形」與「需利用中垂線性質或角平分線性質」兩種題型上尤其明顯。 (5)學生容易利用摺紙動作聯想、理解並記憶尺規作圖動作,並且此種轉換未對學生造成認知負荷。 (6)參與的學生接受並喜愛利用摺紙學習尺規作圖,並且透過摺紙學習能使學生更有興趣學習尺規作圖。 根據本研究的結果,研究者建議可進一步透過較大樣本的教學實驗驗證其有效性,並在較大的班級中利用分組的方式讓學生進行摺紙活動。本研究也發現「過線外一點作平行線」、「等線段作圖」、「等角作圖」對參與的學生而言有相當程度的困難,因此,研究者建議可進一步研究,探討如何有效的幫助學生學習藉由摺紙進行此三種作圖,並從摺紙作圖轉換到尺規作圖。
Learning geometric construction through origami activities is one way to make mathematics lessons more interesting. Could hands-on activities through origami also help students to overcome their difficulties in learning geometric construction? The answer to this question is explored in the present study, which carries three purposes. The first is to investigate whether the six origami operations delineated in Chen (2008) form an adequate system for use at the junior high school level. The second is to design teaching materials that relate origami activities to straightedge and compass construction. Its effectiveness in the cognitive domain will be explored and relevant issues in this regard will be discussed. The third is to discuss the efficacy of such activities in terms of the affective domain. This study adopted two different process in its research design. The first one involved analyzing the geometric construction contents and problems in Taiwan’s junior high textbooks so as to find out what were covered at the junior high school level. The result from this process was used to develop teaching materials that intended to enhance students learning straightedge and compass construction via origami construction. This is done by way of following principles from design research. A teaching experiment on six participating eighth grade students from the Miao-Li County was conducted according to the pre-experimental design. Data from the teaching experiment were partly analyzed by using D-analysis as proposed by David Middleton, whereas the rest of the results from the pretest, posttest, and interviews were analyzed qualitatively. Major findings of this study are as follows: (1)Origami can help students memorize the procedures when constructing geometric figures. (2)Origami can reinforce students’ conception of symmetry and strengthen their intuition about equivalent length. (3)Origami can be a useful tool for students to check the validity of a construction procedure. (4)Origami can provide students with heuristics to solve construction problems, particularly in relation to two formats of problem, namely, those related to completing figures with symmetrical features, and those that involve the construction of perpendicular bisectors or angle bisectors. (5)It is relatively easy for students to think of, understand, and remember origami construction procedures. They can then relate these procedures to the corresponding straightedge and compass construction procedures. Moreover, such transitions do not impose an extensive amount of cognitive load on the participating students. (6)The participating students expressed positive acceptance and enjoyment in learning geometric construction through origami activities. Such activities enhanced the students’ interest while they learned geometric construction. According to the results of this study, it is suggested that the effectiveness of the teaching materials can be tested out in a larger scale study, with the materials introduced to larger classes using small group teaching method. This study found that such tasks as “construct parallel lines through a given point,” “construct a segment of equal length to a given segment,” and “construct an angle of equal magnitude to a given angle” posed a certain degree of difficulty on the participants. Hence it is suggested that more research is necessary regarding how to teach effectively the above mentioned procedures, both in terms of construction by origami as well as transition from origami construction to straightedge and compass construction.
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