「高一學習多項式微分」之教案研究;A Study on the Lesson Plan of Polynomial Derivatives for Grade 11 Students

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题名:	「高一學習多項式微分」之教案研究;A Study on the Lesson Plan of Polynomial Derivatives for Grade 11 Students
作者:	龍昌灝;Lung,Chung-hao
贡献者:	數學系
关键词:	綜合除法;泰勒多項式;多項式函數的微分
日期:	2015-06-29
上传时间:	2015-07-31 00:38:48 (UTC+8)
出版者:	國立中央大學
摘要:	本研究旨在探討研究者與指導教授共同設計的「高一學習多項式微分」教案。本教案共設計四堂多項式的微分課程與一份測驗，從泰勒形式帶入多項式的微分觀念，最後能描繪出三次多項式函數與解決應用問題。本研究並根據測驗結果分析且討論不同程度的高一學生學習多項式微分的成效與問題所在。根據研究結果顯示，程度佳的學生對於此教案幾乎能完全學會；而程度中等至中下的學生，對於此教案前面的部分尚能接受，但對於後半部分三次函數的圖形與應用問題的部分，則半數以上學生學習成果較差。若增加後半部分的教學時間，亦能提升學生的學習成效。部分學生對於數學語言無法確實掌握，此問題不僅發生在程度中下的學生，亦出現在程度佳的學生中。最後研究者依據研究結果，對教學情況與教材內容設計及未來相關研究提出建議。 ;This study aims at investigating the lesson plan of polynomial derivatives for grade 11 students. Four lectures and one assessment consist the lesson plan which was designed by the researcher and the advisor. This lesson plan regards the form of Taylor as the cutting point. By the end of the lectures, students can sketch the cubic polynomial function and solve the application problems. Basing on the observation and assessment results, this study analyzes and discusses the effects and problems of learning the polynomial derivatives on different level students of grade 11. On the one hand, the result shows that advanced learners can almost aquire all the lessons. And the medium to challenged learners can learn the former part, but over half of them can not learn well on the latter part: sketch the cubic polynomial function and solve the application problems. If the teaching time of the latter part is increased, the learning effect can be better. On the other hand, some students fail to grasp the mathematical language precisely, which happens not only in medium and challenged learners but also in advanced learners. According to the result, the researcher provides some sugesstions for teaching conditions, lesson plan designs and related studies in the future. Keywords: synthetic division, Taylor polynomials, polynomial derivatives
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