在数学教学中从质点几何学出发创新理解向量  

Innovative Understanding of Vectorin Mathematics Teaching from Theory of Particle Geometry

作　　者：胡乙[1] HU Yi(Jiangsu Vocational College of Commerce,Nanjing 211168,China)

机构地区：[1]江苏经贸职业技术学院,南京211168

出　　处：《北京工业职业技术学院学报》2023年第2期86-90,共5页Journal of Beijing Polytechnic College

基　　金：2022年江苏经贸职业技术学院科研项目(JSJM2022041)。

摘　　要：为全面深入地理解向量概念及其运算的数学内涵,从质点几何学出发,通过质点倍法、加法推理得到质点减法,进而重新定义了向量。将向量视为两质点之差,对向量长度、向量路径、向量封闭回路之间的关系进行了研究;构造点差形式的一组平行向量,利用质点系统质心位置公式,引导学生掌握交线比例计算方法;利用点差形式的向量坐标,将向量代数运算转化为质点代数运算,并推导出向量模长计算公式、向量三角不等式,解释了向量的平行移动过程等。To comprehensively and deeply understand the mathematical connotation of vector concept and its operation,starting from particle geometry,particle subtraction is obtained by particle multiplication and addition reasoning,and then vector is redefined.The relationship among vector length,vector path and vector closed loop is studied by regarding vector as the difference between two paricles.A set of parllel vectors in the form of point diference is constructed,and the formula of centroid position of particle system is used to guide students to master the calculation method of intersection ratio.By using the vector coordinates in the form of point diference,the vector algebra operation is transformed into the particle algebra operation.The calculation formula of vector module length and vector triangle inequality are derived,and the parallel moving process of vector is explained.

关 键 词：质点几何 向量概念 平行向量 向量代数 向量不等式 

分 类 号：G642.0[文化科学—高等教育学]