“量的大小比较”广泛见于科学研究及现实需要,也是高考中常见的基本考查内容,在一些试题分析中常见利用泰勒公式或者麦克劳林公式等高等数学知识解决比较大小的问题,这一导向一方面不符合双减政策要求,更重要的是没有把握新高考中重视“基础性考查”的要求。本文首先通过三个“比较大小”的高考试题分析了其中蕴含的基础性考查,在此基础上就相应的教学模式进行了简单讨论。比较大小试题考查的本质是函数的单调性,高中教学中首先要抓住“函数”这一基础性视角,把基础知识、基本技能、基本的思想方法,以及基本态度价值观融为一体,整体性培养学生,而不是单纯考虑“一题多解”,更不能让一些新、奇、特,或者是所谓的高端方法喧宾夺主。“Comparison of size” is widely seen in scientific research and practical needs, and is also a common basic examination content in the college entrance examination. In some test analysis, it is common to use advanced mathematical knowledge such as Taylor’s formula or McLaughlin’s formula to solve the problem of comparison of size. This orientation does not meet the requirements of the double reduction policy on the one hand, and more importantly, it does not grasp the requirements of the new college entrance examination to attach importance to “basic examination”. This paper first analyzes the basic examination contained in three “comparison of size” college entrance examination questions, and on this basis, a brief discussion is made on the corresponding teaching model. The essence of the comparison of size questions is the monotonicity of the function. In high school teaching, we must first grasp the basic perspective of “function”, integrate basic knowledge, basic skills, basic thinking methods, and basic attitudes and values, and cultivate students holistically, rather than simply considering “multiple solutions to one problem”, and
