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(一) 在中学数学教学中,函数相依的概念占着极其重要的地位。这是因为:(1)函数相依关系是客观世界中的各种現象演变过程的数学反映。例如当我們在研究指数函数的时候,就应该让学生注意到这个函数是反映生物的繁殖、热物体的冷却、放射性元素的分解等等;(2)函数相依关系还体現了近代数学辯証思維的特点,因为在研究自然現象与技术改革的过程中告訴我們:对于一个在变化过程中的量,不能够割裂地彼此孤立地来研究它們,而要研究它們的运动,研究它們之間的依存性和制約性;(3)函数相依的概念是整个中学数学的基本概念,在目前,初等数学已含育了部分高等数学的內容的情况下,它也是从初等数学进入高等数学的基本枢紐。在教函数相依的关系时,教师应該特别注意引导
(a) In mathematics teaching in middle schools, the concept of function dependency plays an extremely important role. This is because: (1) Function dependency is a mathematical reflection of the evolution of various phenomena in the objective world. For example, when we are studying the exponential function, we should let the students notice that this function reflects the breeding of creatures, the cooling of hot objects, the decomposition of radioactive elements, etc.; (2) The function dependency also reflects the modern mathematical dialectical thinking. Characteristics, because in the process of studying natural phenomena and technological reforms tell us: For an amount in the process of change, we cannot study them in isolation from each other in isolation, and we must study their movements and study their interdependence. (3) The concept of function dependency is the basic concept of the whole middle school mathematics. At present, when elementary mathematics contains the contents of some advanced mathematics, it is also the basic hub for entering advanced mathematics from elementary mathematics. When teaching function dependent relationships, teachers should pay special attention to guidance