数学抽象的认知与脑机制

Cognitive and Brain Mechanism of Mathematical Abstraction

抽象是数学的本质特征.对数学抽象本质的争论,伴随着数学发展的历史.从认知神经学的视角分析数学抽象的本质后发现：（1）数学抽象本质争论中的不同观点实质上都有其合理性,它们各自在不同认识水平上反映了数学抽象的某些侧面;（2）抽象过程的本质是大脑神经细胞集群对数量和空间信息的选择性、简约化激活反应;（3）抽象活动的基本步骤为：分离属性与建构模型——概括与一般化——定义与符号化——系统化.

Abstract was the essential characteristic of mathematics, The debate on the essence of mathematical abstraction runs through the development history of mathematics. By analyzing the process of Mathematical abstraction using the perspective of cognitive neuroscience, obtained following conclusions：（1） in the debate about the essence of mathematical abstraction, all of the different viewpoints essentially had its rationality, each of which reflects a certain side of mathematical abstraction at different level of understanding;（2） The essence of mathematical abstraction was the Neural cell cluster＇s selective and abstract reaction about the information of quantity and spatial;（3） the basic activities step of mathematical abstraction were： separating property and Constructing model, generalizing and universalizing, defining and Symbolization, Systematization.