函数单调性认知阶段及相应数学核心素养发展水平

On the Cognitive Stage of Monotonicity of Functions and the Development Level of Corresponding Mathematical Core Literacy

关于函数单调性的认识,贯穿于小学、初中和高中整个基础教育数学学习之中,需要经历经验感知、定性描述与定量刻画三个认知阶段.每个认知阶段,函数单调性有着独特的知识层次、表征形式与认知水平,集中体现在刻画函数单调性的三种认知模型——算式性质模型、图像特征模型与符号量化模型上.在每个认知阶段的学习过程中,需要不同水平的数学核心素养,并且可促进不同水平的数学核心素养的发展.

The understanding of the monotonicity of function needs to be experienced three cognitive stages of experience perception,qualitative description and quantitative characterization,which under go run through the mathematics study of the whole basic education of elementary school,junior high and high school.In each cognitive stage,the monotonicity of the function is given a unique form of knowledge level,representation and cognitive level,which is concentrated on the three cognitive models of characterizing the monotonicity of the function.These three models are called computational property models,image feature models and symbolic quantization models.In the learning process of each cognitive stage,different levels of mathematics core literacy are required,which can also promote the development of different levels of mathematics core literacy.