“重复”有何奥妙?

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  【摘要】基本数学思想是一节课的灵魂,也是课堂中的隐形线索。课堂中通过现实到数学的抽象,从现实世界到数学内部把研究对象以及对象之间的关系形成概念,使其具有一般性进而发展数学思维。
  【关键词】规律;符号化;数学思想
  《数学课程标准(实验稿)》中提出:一些重要的数学概念与数学思想宜逐步深入。基本数学思想是一节课的灵魂,也是课堂中的隐形线索。一节课往往蕴含多个数学思想,每一节课都离不开抽象、推理、建模这几个最基本的。本课凸显抽象思想派生出来的“符号化”及“变与不变”的数学思想,主要帮助孩子感悟“符号”的简洁及“变与不变”的互相转化。

一、初识规律,妙在“符号化”


  符号,一般是某种事物的代号,采用对应的方式,把一个复杂的事物用简便的形式表现出来。“符号化”思想就是用一种符号代替原物进行表示、交流、运算等活动的思想。数学符号是数学的语言,数学世界是一个符号化的世界,数学是人们进行表示、计算、推理和解决问题的工具。 “符号化”思想是一般化的思想方法,具有普遍的意义。
  (一)【课堂片段一】初步感受符号表示规律
  师:你能把灯笼的规律用自己喜欢的方式表示出来吗?比一比,看谁又快又好!
  (学生独立思考,自主展示作品,分享创作。)

  生1:大小大小大小大小
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