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題名:國小學童面積概念轉化文本之設計及其教學效果之實驗研究
作者:陳嘉皇 引用關係
作者(外文):Chen Jia Huang
校院名稱:國立高雄師範大學
系所名稱:教育學系
指導教授:陳密桃
梁淑坤
學位類別:博士
出版日期:2004
主題關鍵詞:面積概念轉化文本圖形與面積解題能力一般文本面積教學模式設計Conception transfer of area learning text.The general area learning text.The capabilities on figures and area problem solving.The models design of area conception teaching.
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Clements認為,影響學生幾何概念發展良窳的主要因素,在於課程的設計與教學引導兩大機制,數學教育若能克服此層面的困難,將有助於提升學生幾何概念發展的層次。因此,本研究參考了Outhred與Mitchelmore之「面積概念公式理解發展模式」、Clements與Battista之「面積覆蓋能力發展層次」的探討、Pirie與Kieren之「數學概念理解動態發展模式」及相關理論,先設計國小五年級學生學習之「面積概念轉化文本」,再進行教學實驗,最後與接受教科書「一般文本」教學之控制組學生在「圖形與面積解題成就測驗」上之表現,進行效果比較。研究者更探討實驗組學生在「圖形與面積解題實作與訪談問卷」上有關「圖形與面積視覺比對與表徵」、「方瓦排列覆蓋」、「面積圖形重構」、「公式理解與運用」等策略表現與方法使用情形,進而建構面積概念教學模式,並獲得主要的研究結論如下:
一、面積概念轉化效果方面:「概念轉化文本」教學活動設計融合幾何「數」、「量」、「形」的知識與技巧,可幫助學生轉化獲得較完整之面積概念體系。
二、面積解題能力表現方面:接受「面積概念轉化文本」教學的學生其面積解題成就表現或概念保留皆較控制組學生為佳。
三、面積解題策略應用方面:「面積概念轉化文本」教學活動設計的測量、比對、操作可促進學生對公式意義的明瞭及轉化運用。
四、圖形辨識與表徵方面:接受「面積概念轉化文本」教學後,學生具備完善的圖形視知覺能力,正確抽離圖形要素,可提昇面積解題成就。
五、認知概念保留方面:接受「面積概念轉化文本」教學活動可強化圖形重構策略,提升「等積異形」面積保留概念。
六、情意與信念方面:「面積概念轉化文本」教學連結學生面積概念重要活動與機制,可激發學生幾何學習的動機和興趣,提升幾何能力的發展。
七、教室學習風氣方面:「面積概念轉化文本」教學設計促進教室討論風氣的養成,可提升學生幾何知識溝通及表達能力。
本研究除驗證研究者設計之「面積概念轉化文本」具有優越的成效外,另在學童實作與訪談作業表現上,發現學童表現出豐富、多樣的解題策略及方法,可提供教師掌握學生認知發展之參考,並協助模塑合適之教學模式,以提升學生面積概念學習之成就。
Clements has proposed that the area measurement conception development might better be considered more broadly as curriculum designed and teaching methods guide. If mathematical education can overcome these difficulties, it can aid teacher in promoting student’s geometry conception development levels. Thus, this research refers first to Outhred & Mitchelmore’s research on young children’s intuitive understanding of rectangular area measurement, Clements & Battista’s research on geometry and spatial reasoning, and Pirie & Kieren’s “The dynamical theory for the growth of mathematical understanding” for designing the conception transfer of area learning text to elementary fifth grade students, and secondly, proceed with teaching experiment. Thirdly, researcher explore the performance achievement and strategies of problem solving on “ figure and area contrast and representation by vision,”” grids array and cover,”” figure’s reconstruct on area,” and ” understanding and applying on area’s formula,” and, finally, construct the model of area conception development. The author attained some conclusions as follows:
1.Effect aspect. Because the conception transfer of area learning text has integrated mathematical knowledge of “numbers,” ”quantities” and ”shapes,” it can help students to acquire the whole area conception.
2.Problem solving aspect. The achievement performance of area problem solving or the conception retention in the experimented group accepted teaching on the conception transfer of area learning text is better than the controlled group accepted teaching on the general text of area.
3.Strategies applied aspect. Conception transfer of area learning text can help students to promote their understanding and applying on area formula.
4.Figures identification and characteristics aspect. Students accepted conception transfer of area learning text can acquire the perception on vision. By abstracting the elements of figure correctly, it can promote the achievement performance on area problem solving.
5.Conception retention on cognitive aspect. Students accepted conception transfer of area learning text can reinforce the reconstruct strategies of area figures, and promote the conception of area retention on “identical area but different shapes”.
6.Affection and belief aspect. Conception transfer of area learning text combining the activities and mechanism of student’s area conception can encourage student’s learning motivation and interesting and promote the capabilities on geometry concepts development.
7.Learning climate aspect. Conception transfer of area learning text can encourage the discussing climate in classroom and promote the capabilities on communication and expression.
By students’ interview and their actual performances, this research also find that students have demonstrated their various strategies and methods of area problem solving, so that it can provide suggestions for teachers and help them to design and select appropriate teaching models.
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