基于PCK视角的数学原理的教学设计——以勾股定理为例
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摘要
数学教学设计是数学课堂实施的基础和关键。学科教学知识(PCK)是《中学教师专业标准》中专业知识维度的核心要素。以勾股定理的教学设计为例,基于PCK的"3W+3H"视角,从创设疑难情境提出问题,理性探究与直观感知相结合,分解拼补图形论证勾股定理,回到问题情境,解决实际问题,巩固强化把握数学原理的本质,形成系统化的知识结构网络六方面解析了数学原理的教学设计思路,以期为教师优化数学教学设计提供参考。
Mathematics teaching design is the basis and key of the subject in classroom teaching. PedagogicalContent Knowledge(PCK in short) is the core elements of professional knowledge dimension in"professional stan-dards for middle school teachers". Taking the teaching design of Pythagorean Theorem as an example, this paperputs forward some questions based on the"3 w+3 h"model of PCK theory according to the creation of difficult situa-tions. The combination of rational inquiry and intuitive perception induces and verifies conjecture. Somethingmust be done, such as combining rational inquiry with intuitive perception, disassembling patchwork figure to dem-onstrate Pythagorean Theorem, returning to problem situation and solving practical problems, strengthening andgrasping the essence of mathematical principle and forming the systematical knowledge map. Through the six as-pects of analysis, the mathematical teaching design will be the reference for teachers' further study.
Mathematics teaching design is the basis and key of the subject in classroom teaching. PedagogicalContent Knowledge(PCK in short) is the core elements of professional knowledge dimension in"professional stan-dards for middle school teachers". Taking the teaching design of Pythagorean Theorem as an example, this paperputs forward some questions based on the"3 w+3 h"model of PCK theory according to the creation of difficult situa-tions. The combination of rational inquiry and intuitive perception induces and verifies conjecture. Somethingmust be done, such as combining rational inquiry with intuitive perception, disassembling patchwork figure to dem-onstrate Pythagorean Theorem, returning to problem situation and solving practical problems, strengthening andgrasping the essence of mathematical principle and forming the systematical knowledge map. Through the six as-pects of analysis, the mathematical teaching design will be the reference for teachers' further study.
引文
[1]韩龙淑,屈俊,李晓芬,等.基于启发式数学教学思想的命题教学设计——以“一元一次方程的求根公式”为例[J].教学与管理,2012(11).
[2]杨小丽.勾股定理的PCK内涵解析[J].数学通报,2011(3).
[3]苏耀忠,石颐园.从PCK内涵的角度解析函数概念的教学[J].教育理论与实践,2015(20).
[4]教育部.义务教育数学课程标准(2011年版)[M].北京:北京师范大学出版集团,2012.
[2]杨小丽.勾股定理的PCK内涵解析[J].数学通报,2011(3).
[3]苏耀忠,石颐园.从PCK内涵的角度解析函数概念的教学[J].教育理论与实践,2015(20).
[4]教育部.义务教育数学课程标准(2011年版)[M].北京:北京师范大学出版集团,2012.