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数学中函数相关概念是客观民办量与量之间相依关系的抽象形式的反映。在各种函数关系中所体现的事物相互联系规律和发展规律是极其丰富的。恩格斯在自然辩证法一书中指出“笛卡儿的变数是数学中的转折点,运动和辩证法便进入数学。”由此可知,函数概念在数学教学中是一个十分重要的内容。在中学各年级数学教学中加强函数概念的教学,逐步扩大和加深学生的函数观念,自觉地掌握函数图象是培养学生辩证唯物主义世界观的具体内容,也是当前积极提高数学教学质量重要课题之一。1956—1957学年度中学数学教学大纲(修订草案)(以下简称大纲)的说明部分对函数概念和它的图象的教学要求明确规定:“在数学教学中应当特别注意使学生自觉地掌握数学中的概念、观念和方法,尤其是函数的观念和它的图象。”也充
The related concept of function in mathematics is the reflection of the abstract form of the relationship between the objective and the quantity of the people. The interrelated laws and development laws of things embodied in various functional relationships are extremely rich. Engels pointed out in his book Natural Dialectics that “Descartes’s variable is a turning point in mathematics, and movement and dialectics enter mathematics.” From this we can see that the concept of function is a very important content in mathematics teaching. To strengthen the teaching of function concepts in mathematics teaching in all grades of middle school, gradually expand and deepen students’ concept of function, and consciously grasp function images is to cultivate the concrete content of students’ dialectical materialist world view, and it is also one of the important topics to actively improve the quality of mathematics teaching. . The instructional part of the Middle School Mathematics Syllabus (Revised Draft) (hereinafter referred to as the Outline) for the 1956-1957 academic year clearly states that the functional concept and its image teaching requirements: “In mathematics teaching, special attention should be paid to consciously mastering mathematics. Concepts, concepts and methods, especially the concept of functions and their images."