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在高等师范院校数学系的高等数学课程的教学中,加强与中学教学的联系是体现师范性特点的一个方面。在本文中就数学分析课程的教学中,如何尽量贯彻面对中学的精神,谈一点个人的体会。一、关于函数概念。在教育部制订的全日制中学数学教学大纲中指出:“函数知裁十分重要。为了使学生切实地、系统地掌握函数知識,应该在中小学数学教学过程中,有意識地、有步骤地进行教学”。根据这个精神,在数学分析的教学中,无疑必须使学生清楚地、准确地掌握任意集上的函数概念。在函数概念的教学中,明确指出函数概念的两个要素——定义域与对应法则。学生往往不太注意定义域,比如把x~2-1/x-1与x+1看作同一个函数,把2lgx与lgx~2也看作同一函数,他们根据的是中学代数中恆等变换的知識,但忽视了这种变换的条件。而且,学生也常常不能自觉地意識到,中学代数中在解方程时,产生增根和减根的
In the teaching of advanced mathematics courses in the mathematics department of higher normal colleges and universities, strengthening the connection with high school teaching is one aspect that reflects the characteristics of normal education. In this article, in the teaching of mathematics analysis course, how to implement the spirit of secondary school as far as possible, talk about personal experience. First, on the concept of function. In the full-time secondary school mathematics syllabus formulated by the Ministry of Education, it was pointed out: “Functional literacy is very important. In order to enable students to master function knowledge practically and systematically, it should be conducted consciously and step-by-step in the mathematics teaching process of primary and secondary schools. teaching". According to this spirit, in the teaching of mathematical analysis, students must unambiguously and clearly grasp the concept of functions on any set. In the teaching of the concept of functions, the two elements of the concept of function are explicitly specified—the domain of definition and the corresponding laws. Students often do not pay much attention to the definition of the domain, such as x~2-1/x-1 and x+1 as the same function, and 2lgx and lgx~2 as the same function, they are based on the middle school algebra Transformed knowledge, but ignored the conditions of this transformation. Moreover, students often do not consciously realize that when they solve equations in middle school algebra, they produce root-increasing and root-reduction.