探討高中生平面向量概念學習情況與評量工具之研發
Abstract
本研究之主要目的為探討高中學生學習平面向量概念之學習困難，並試著找出學生學習平面向量之後所應具備的能力為何？根據所探討的平面向量概念，訂定學生平面向量能力的四大向度，並依據訂定之四大向度發展評量工具進行施測，探討學生學習向量課程後是否達到應具有之能力。藉由探討錯誤成因，並依據訪談高中教師任課時之向量教學過程，期望瞭解高中生平面向量概念之學習情況。
本研究之研究對象為臺北市某市立高中之高二自然組學生42位，及嘉義市某公立高中之自然組學生40位，利用研究者自行開發之向量能力紙筆測驗題本為研究工具，包括向量表徵、向量定義與概念、向量運算、向量內積與投影四大向度試題。而探討出學生錯誤成因之後訪談兩位任課教師，探究其學習過程與造成錯誤的原因及學生之學習困難。
本研究之研究結果如下：
1. 學生學習向量課程後所具備之向量能力四大向度分別為瞭解、詮釋及轉換向量表徵；瞭解向量的定義與其性質；能操作、理解向量之運算並瞭解向量之幾何意義；瞭解內積之幾何意義並計算向量之內積。
2. 部分學生會將位移向量與方向向量之意義產生混淆。
3. 在本研究中發現有部分學生將一向量的單位向量視為其本身。
4. 部分學生認為兩向量平行且反向的情況下不存在夾角。
5. 當兩向量的始點未重合的時候，部分學生仍然將兩向量的終點連線進行向量加法。
6. 本研究中發現部分學生認為兩個向量若為平行，則不可做內積。
This thesis aims to explore senior high school students' learning difficulties of vector concepts, and to figure out what ability students' should have learned about vectors after learning vector curriculums. According to the vector concept to explore, this thesis sets four dimensions about students' vector abilities. Based on these four vector ability dimensions, this thesis also developed an assessment tool about students' vector concept. Our research sample involved 82 senior high school students in Taipei City and Chiayi City, Taiwan. A test developed by the author was exploited as investigation tool which including four dimensions as vectors' representation, vectors' definition and properties, vectors' operation, and vectors' inner product and projections. In order to understand the learning difficulties in vector, the author also interviews teachers who teach in senior high school in Taipei and Chiayi. The findings are summarized as follows: 1. Students' who have to equipped these abilities after learning vectors lessons which included four dimensions. These dimensions included vectors' representation, vectors' definition and properties, vectors' operation, and vectors' inner product and projections. 2. Some students confused about the meaning of displacement vector and direction vector. 3. Some students have a misconception about unit vector, which thought a unit vector is a vector which equivalent to itself. 4. Some students think two vectors which are opposite and parallel have no angles. 5. Some students use tail-to-tail method to operate vectors' addition, even if these vectors' starting point are not on the same point. 6.Some students finds that if two vectors are parallel, they have no inner product.
This thesis aims to explore senior high school students' learning difficulties of vector concepts, and to figure out what ability students' should have learned about vectors after learning vector curriculums. According to the vector concept to explore, this thesis sets four dimensions about students' vector abilities. Based on these four vector ability dimensions, this thesis also developed an assessment tool about students' vector concept. Our research sample involved 82 senior high school students in Taipei City and Chiayi City, Taiwan. A test developed by the author was exploited as investigation tool which including four dimensions as vectors' representation, vectors' definition and properties, vectors' operation, and vectors' inner product and projections. In order to understand the learning difficulties in vector, the author also interviews teachers who teach in senior high school in Taipei and Chiayi. The findings are summarized as follows: 1. Students' who have to equipped these abilities after learning vectors lessons which included four dimensions. These dimensions included vectors' representation, vectors' definition and properties, vectors' operation, and vectors' inner product and projections. 2. Some students confused about the meaning of displacement vector and direction vector. 3. Some students have a misconception about unit vector, which thought a unit vector is a vector which equivalent to itself. 4. Some students think two vectors which are opposite and parallel have no angles. 5. Some students use tail-to-tail method to operate vectors' addition, even if these vectors' starting point are not on the same point. 6.Some students finds that if two vectors are parallel, they have no inner product.
Description
Keywords
向量, 表徵, 內積, 學習情況, vector, representation, inner product, learning situation