以“数”铸“形”，以“形”表“数”——以三角函数的教学为例

Casting Shape with Number, Expressing Number with Shape—Based on Teaching of Trigonometric Functions

摘要: 数形结合思想方法是数学素养的核心成分，在高中阶段应引起高度重视。本文将根据新课标对数形结合思想方法提出的要求，以三角函数的教学为例，进行数形结合思想方法的应用研究。基于双重编码与数学多元表征理论，探究“数”与“形”的转化问题。以“数”铸“形”，渐进渗透非言语信息的价值；以“形”表“数”，关注多元理解的学习过程。以达到逐步搭建支架，强化思维训练，提升创新能力的目的。开拓学生的思维，当学生遇到生活中的数学情景时，能灵活地选择数学思想方法，用数学的眼光有逻辑有条理地解决问题。

Abstract: The thinking method in combination of number and shape is a core component of mathematical literacy, which should be paid more attention in high school education. According to the requirements of the new curriculum standard, this paper takes the teaching of Trigonometric Function as an example to study the application of the thinking method of combining numbers and shapes. Based on the theory of dual coding and mathematical multiple representation, explore the problem in the combination and transformation between number and shape. Cast shape with number, which can permeate the value of nonverbal information gradually; Express number with shape, which should pay more attention to the process of pluralistic understanding, to achieve the aim that can simplify the difficulty of problems, building the support in a gradually way, intensifying the training of mind and promoting the ability of innovation. Broaden student’s mind, when they face to the new problems situation, they can also use the thinking method in combination of number and shape flexibly and solve problem with the vision of mathematical logically and systematically.