高中向量問題之研究

本研究宗旨在探討、研究高中向量問題的題型即解題技巧，了解學生在平面向量、空間向量中的迷思，整理高中兩向量單元的重點，及彙整近年大考題目，及高中教師徵選之試題，使教師更了解近年考題趨勢，及考題之間的觀念連結，並給予協助及教學上之建議。研究向量問題與試題分析後獲得結果列點如下： 1. 平面與空間差異 2. 解題方法歸納能啟發學生多元思考的精神，以下為歸納向量問題在平面及空間中之解題技巧 I. 求向量、長度 II. 求兩向量、兩直線、兩平面之夾角 III. 求面積、體積 IV. 求極大值、極小值問題透過本研究的結論，提出建議教師教學及未來研究參考列點如下： 1. 教師可以明確為學生整理幾何意義轉化為符號及計算式的過程 2. 向量中運用到許多圖形表示法，在教學時建議教學者能使用數位繪圖教學軟體 3. 對於未來研究建議可以以在球體圖形為主 4. 建議將計算及繪圖功能之軟體也融入其研究

關鍵字

向量問題

並列摘要

The purpose of this research is to explore and study the problem-solving skills of high school vector problems. Understand the students' myths in vectors and space vectors. Organize the focus of the two vector units in high school, collecting the questions in recent years, and the questions selected by high school teachers, let teachers more aware of the trend of recent exam questions, and the link between the questions, to give advice on assistance and teaching. The research vector problem and the test result are obtained as follows. 1. Differences between Vector and Vector Space. 2. The method of solving problems can inspire the spirit of multiple thinking of students, the following is the problem of solving the inductive vector problem in plane and space: I. Find the vector and length II. Find the angle between two vectors, two lines, and two planes III. Find area and volume IV. Finding the maximum and minimum values Through the conclusions of this study, the recommended reference for teachers' teaching and future research is as follows: 1. Teachers can clearly define the process of transforming geometric meaning into symbols and calculations for students. 2. The use of many graphical representations in vectors suggests that the teaching staff can use digital drawing teaching software during teaching. 3. Suggestions for future research can be based on sphere graphics. 4. It is recommended to incorporate the software of calculation and mapping functions into its research.