“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
2024年教材是落实核心素养的最新教材,新教材在实施课程上有哪些变化是一个值得关注的问题。比较人教版和苏科版新旧教材有理数主题在定义、习题设置及课外阅读材料方面的变化,发现人教版在有理数定义上从归纳分类模式变成了形式定义,而苏科版恰恰相反;在习题配置上,人教版强化了有理数的分类和集合意识的渗透;在阅读材料上,新版人教版教材从中国历史中对负数的认识,进一步扩充至人类对负数的认识历程。苏科版新教材删除了“循环小数可以化为分数”的课外阅读内容,保留了有理数在日常应用的阅读材料。建议在具体教学中教师应该参考多个版本的教材,取长补短,适当淡化形式,加强应用和整数、小数化分数的练习。The 2024 textbook is the latest textbook for implementing core competencies. What changes will be made in the new textbook in the curriculum implementation is a question worthy of attention. This study compares the changes in the rational number content of the old and new editions of the People’s Education Edition and the Jiangsu Science and Technology Edition, focusing on definitions, exercise arrangements, and extracurricular reading materials. The findings reveal that the People’s Education Edition has transitioned from an inductive classification model to a formal definition in terms of the definition of rational numbers, whereas the Jiangsu Science and Technology Edition has taken the opposite approach. In terms of exercise configuration, the People’s Education Edition strengthened the classification of rational numbers and the infiltration of collective consciousness. Regarding reading materials, the new People’s Education Edition has expanded the historical context of negative numbers from a focus on Chinese history to a broader exploration of their development in human civilization. Meanwhile, the new Jiangsu Science and Technology Edition has removed the extracurricular reading
