微积分的内核裂变与“后微积分范式”的数学教育价值  

Kernel Fission of Calculus and the Significance of Mathematics Education of"Post-Calculus Paradigm"

作　　者：黄秦安[1] HUANG Qin-an(School of Mathematics and Statistics,Shaanxi Normal University,Shaanxi Xi'an 710119,China)

机构地区：[1]陕西师范大学数学与统计学院,陕西西安710119

出　　处：《数学教育学报》2022年第1期13-18,共6页Journal of Mathematics Education

基　　金：中央高校基本科研业务费专项资金资助--数学定理背后的发现细节及心理学解析(GK202105007)。

摘　　要：微积分理论作为人类历史上伟大的知识创造之一,自诞生之后在相当长一段时期内被奉为描绘宇宙与自然运行强有力的数学语言与模型.20世纪以来,作为具有典型革命性意义的知识创新,诞生了分形几何学、混沌理论和复杂性科学等多种新兴学科.这些重要的数学知识创造构成了后微积分时代的主流数学知识形态并凝聚成为一种新的数学范式——“后微积分范式”.作为微积分范式的一种内核裂变,它实现了对原有范式的颠覆、突破和迁越,具有非确定性、混沌性和复杂性等显著的当代科学革命特征.“后微积分范式”已经构成了大学数学课程的重要组成部分和必要内容,也必将成为未来高中甚至义务教育数学课程的基本内容.因此,“后微积分范式”的数学教育意义以及如何开展教学的话题需要予以充分的论证和关注.Calculus theory, as one of the great knowledge creations in human history, has been regarded as a powerful mathematical language and model to describe the universe and natural operation for a long period of time since its birth. Since the20 th century, as a typical revolutionary knowledge innovation, a variety of emerging disciplines such as fractal geometry, chaos theory and complexity science have emerged. These important mathematical branches constituted the mainstream of mathematics knowledge form in the post-calculus era and condense into a new paradigm-“post-calculus paradigm”. As a kernel fission of the calculus paradigm, it realizes the subversion, breakthrough and transition of the original paradigm, and has the remarkable characteristics of contemporary scientific revolution such as uncertainty, chaos and complexity. “Post-calculus paradigm” has already constituted an important part and necessary content of college mathematics curriculum, and it will also become the basic content of mathematics curriculum in high school and even compulsory education in the future. Therefore, the significance of“post calculus paradigm” in mathematics education and the topic of how to use the post calculus paradigm to carry out teaching need to be fully demonstrated and paid attention to.

关 键 词：微积分 内核裂变 后微积分范式 混沌理论 复杂性科学 数学课程 

分 类 号：G640[文化科学—高等教育学]