关于矩阵乘法教学设计的一些思考

Some Idea on the Teaching Design for Matrix Multiplication

本文通过发生教学法对矩阵乘法的定义进行了教学设计,根据学生的认知规律,帮助学生了解矩阵乘法的创立过程,理解矩阵乘法的本质.特别地,从矩阵乘法的本质出发,由线性变换的复合顺序不同导致结果不同,说明矩阵乘法不满足交换律的原因.通过比较、举反例,总结出矩阵乘法的运算规律和特点.通过分析线性方程组、矩阵方程与矩阵乘法之间的关系,让学生体会矩阵乘法在矩阵理论中的重要性.最后结合Matlab软件从图像处理方面介绍了矩阵乘法的应用.教学中多次设计了与学生互动的环节,以学生为主体、教师为主导的教学模式增加了学生在发现知识过程中的学习投入和情感投入,激发了学生学习数学的内在动机,培养了学生发现知识的能力,提高了学生分析问题和解决问题的能力.

The article designs the definition of matrix multiplication through the generation teaching method.According to the cognitive laws of students,it helps students to understand the creation process of matrix multiplication and the essence of matrix multiplication.In particular,starting from the essence of matrix multiplication,we notice that different composite orders of linear transformations lead to different results,which shows that matrix multiplication does not satisfy the commutative law.Then,the operation rules and characteristics of matrix multiplication are summarized by comparison and negative examples.By analyzing the relationship between linear equations,matrix equations and matrix multiplication,students can realize the importance of matrix multiplication in matrix theory.Finally,the application of matrix multiplication is introduced from the aspect of image processing combined with Matlab software.The interaction with students has been designed for many times in teaching.Teaching of “Student-centered,teacher-led” increases students’ learning input and emotional input in the process of discovering knowledge,stimulates students’ intrinsic motivation to learn mathematics,cultivates students’ ability to discover knowledge and excellent intelligence,and improves students’ ability to analyze and solve problems.