九十四學年度高一學生三角函數之學習狀況研究

The Study on the Result of the Senior High School Students in Learning Trigonmetric Function in Academic Year 2006

黃鈺芸(Yu-Yun Huang)

指導教授 ： 單維彰

國立中央大學/理學院/數學系/碩士(2007年)

摘要

本論文研究目的在於：針對三角函數之研究課題，了解九年一貫實施前後學生的差異性，以及在高中所必須要修讀的三角函數內容，希望透過此研究，可以作為九年一貫暫行綱要實施之後的成效探討，並對九十八學年度高中課程綱要修訂有所助益。
本文研究對象為九十四學年度北台灣的高一學生二十個班級共829人、20位高中教師、164位大學教授的問卷，以及微積分、統計與線性代數三個領域五冊大學用書。依據資料的蒐集分析，歸納出九年一貫實施後的錯誤類型、高中教師的教學心得、大學教授的意見，以及根據大學用書歸納出高中需修讀的三角函數課題。
研究結果建議：（1）拉長三角函數的授課時數（2）將三角函數拆成兩部分（3）延後教授複數的極式（4）杜絕過於複雜或技巧性的題目。期盼本研究對我國未來三角函數之數學課程以及數學綱要的修訂提供有益的參考。

關鍵字

九年一貫 ； 三角函數 ； 錯誤類型

並列摘要

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.

並列關鍵字

the General Guidelines of Grade 1-9 Curriculum o ； Trigonometric function ； specific questions

參考文獻

國立中正大學數學系（2005）。九年一貫數學學習領域九十四學年度銜接高中課程教材。

簡芳怡（2000）。台北地區國二學生的因式分解錯誤類型之研究。國立台灣師範大學數學研究所碩士論文。全國博碩士論文資訊網，088NTNU0479010。

張景媛（1994）。國中生數學學習歷程統整模式的驗證及應用：學生建構數學概念的分析及數學文字題教學策略的研究。國立台灣師範大學教育心裡學系博士論文。全國博碩士論文資訊網，082NTNU3328002。

吳佳起（2003）。函數單元學習前後的概念成長探討。國立台灣師範大學數學研究所碩士論文。全國博碩士論文資訊網，091NTNU0479017。

陳聖雄（2006）。高一學生解一元二次不等式的主要錯誤類型及其補救教學之研究。國立台灣師範大學數學系在職進修碩士班碩士論文。全國博碩士論文資訊網，094NTNU5479002。