国 立 中 央 大 学
数 学 研 究 所 硕 士 论 文
九十四学年度高一学生三角函数 之学习状况研究 学习状况研究
研 究 生:黄钰芸 指导教授:单维彰博士
中 华 民 国
九十六 年 五 月
论文摘要
本论文研究目的在於:针对三角函数之研究课题,了解九年一贯实施前后学生 的差异性,以及在高中所必须要修读的三角函数内容,希望透过此研究,可以 作为九年一贯暂行纲要实施之后的成效探讨,并对九十八学年度高中课程纲要 修订有所助益. 本文研究对象为九十四学年度北台湾的高一学生二十个班级共 829 人,20 位高中教师,164 位大学教授的问卷,以及微积分,统计与线性代数三个领域 五册大学用书.依据资料的搜集分析,归纳出九年一贯实施后的错误类型,高 中教师的教学心得,大学教授的意见,以及根据大学用书归纳出高中需修读的 三角函数课题. 研究结果建议: (1)拉长三角函数的授课时数(2)将三角函数拆成两部 分(3)延后教授复数的极式(4)杜绝过於复杂或技巧性的题目.期盼本研究 对我国未来三角函数之数学课程以及数学纲要的修订提供有益的参考.
关键字
九年一贯,三角函数,错误类型.
I
Abstract
This is a thesis which mainly focuses on: (A) The distinction between those students who received "The General guidelines of Grade 1-9 Curriculum of Elementary & Junior High School Education" and those who did not on the difficulty in studying Trigonometric function they've faced in senior high schools; (B) The specific range of Trigonometric function which students should be required to study in senior high schools. Truly hope that this thesis will be some of the assistance to the development of future mathematics education in 2009 in Taiwan. The targets of this research are senior high school students, in northern Taiwan, 829 students in total from different 20 classes, and 20 senior high school teachers, plus 164 university professors. Also, 5 academic books from three different fields are recruited in for the research, which are Calculus, Mathematical Statistics, and Elementary Linear Algebra. According to data analysis, the author pointed out that: (1) Students have much more difficulty in correctly answering some specific questions after receiving the General Guidelines of Grade 1-9 Curriculum of Elementary and Junior High School Education; (2) Teaching experience & thought from senior high school teachers; (3) Professors' opinions; (4) The appropriate range of Trigonometric function for senior high school students to study for further education in universities or colleges. The results of the research suggest that (1) Extended & longer teaching hours for Trigonometric function; (2) Dividing Trigonometric function into two parts for students to learn in separate semesters; (3) Avoid teaching the Polar Form of a Complex Number in the first year of senior high schools; (4) Avoid teaching certain questions that are too difficult. It is our hope that these conclusions and suggestions can make beneficial contributions to the future mathematics education in senior high school in Taiwan. Keywords: the General Guidelines of Grade 1-9 Curriculum of Elementary and Junior High School Education, Trigonometric function, specific questions.

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