学习进阶视角下导数概念的教学

The Teaching of Derivative Concepts from the Perspective of Learning Progression

在学习进阶视角下进行导数概念教学时,首先分析《标准》要求,明确学生应达到的水平。然后基于学习进阶的理论研究,划分4个导数概念学习进阶水平,并列出相应水平下学生的预期学习表现。最后结合教材,围绕学习进阶展开导数概念的教学。从常见的物理学和几何学中的两个问题,让学生体验“平均变化率向瞬时变化率”的变化,感悟极限思想;引导学生脱离问题背景比较分析两者的共同属性,由低到高逐步进阶,从而抽象出导数的概念并加深理解。

When teaching the concept of derivatives from a learning progression perspective,the first step is to analyze the requirements of the“standards”and clarify the levels students should achieve.Then,based on the theoretical research of learning progressions,divide derivative concepts into four levels of advancement,and list the expected learning performances for students at each level.Finally,in conjunction with the textbook,the teaching of derivative concepts unfolds based on the learning progression.Introducing two problems from common physics and geometry,students experience the transition from“average rate of change to instantaneous rate of change,”thus grasping the concept of limits.Guiding students to analyze the common attributes of the two beyond the context of the problems,progressing step by step from the simple to the complex,abstracting the concept of derivatives,and deepening their understanding.