Abstract: 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.