论文部分内容阅读
陈国正老师《关于点向式方程的改进意见》一文是对进行改革的新教材的认真钻研 ,这种精神值得鼓励 .国家规划教材《数学 (基础版 )第二册》(高教社出版 )对于直线的点向式方程的推导 ,只需要用到向量的加法和数量乘法两种运算 ,因此所得的点向式方程不仅对于直角坐标系成立 ,而且对于仿射坐标系也成立 .如果采用向量的积来推导 ,由于向量的内积在直角坐标系中才有简洁的计算公式 ,因此所得到的直线方程只对于直角坐标系成立 .此外 ,用内积来推导 ,计算比较繁 .至于新教材在推导直线的点向式方程中 ,“约定当式中某一个分式的分母为零时就表示分子也为零” ,这种约定的合理性 ,可以参看本期发表的《高中和中等职业学校数学教学内容体系的一些改革》一文的第三段
Professor Chen Guozheng’s article “Improvement Opinions on the Point-Directional Equations” is a serious study of new textbooks for reforms. This spirit is worth encouraging. The national planning textbook “Mathematics (Basic Edition) Book 2” (published by Higher Education Press) is The derivation of linear point-wise equations requires only the addition of vectors and the multiplication of quantities. Therefore, the resulting pointwise equations are not only valid for Cartesian coordinate systems but also for affine coordinate systems. If vectorial The product is derived, because the inner product of the vector has a simple calculation formula in the rectangular coordinate system, so the obtained linear equation is only valid for the rectangular coordinate system. In addition, the inner product is used for derivation, and the calculation is more complicated. As for the new textbook In the equation of the point equation for deriving a straight line, “When the denominator of a certain formula in a formula is zero, it means that the numerator is also zero.” The rationality of this agreement can be found in the “High School and Secondary Vocational Schools” published in this issue. The third paragraph of some reforms in the mathematics teaching content system