Mathematics Deep Learning Based On Distributed Cognition Theory

With the advent of Industrial Revolution 4.0 era,the development of modern science and technology cannot be separated from the support of mathematics.Since citizens’ mathematical literacy affects the development level of society,how to learn mathematics efficiently has become an important issue in the current society.As the second generation of cognitive science,distributed cognition theory is a cross theory integrating artificial intelligence,neuroscience and other disciplines.It is a framework to examine the existing cognitive laws.In the field of artificial intelligence,deep learning has made breakthrough research achievements based on distributed cognition theory.This dissertation is based on the internal demand of mathematics education for mathematics deep learning,draws lessons from the development experience of deep learning in the field of artificial intelligence,seeks the guidance of cognitive science to the development of modern learning theory,and proposes the research topic.From the perspective of research framework,the research of this dissertation is divided into three stages:Literature analysis stage.This paper reviews relevant researches on deep learning,including deep learning in artificial intelligence and deep learning in education and teaching.Theoretical construction stage.Combined with distributed cognition theory,deep learning theory and learning progression theory,mathematics deep learning theory based on distributed cognition is constructed.Specific contents include: clear definition and connotation characteristics(distribution,hierarchy,strategy and instrumentality)of mathematicas deep learning.Theoretical application stage.First of all,combined with the mathematics courses and classes of ordinary high schools,the theoretical basis for the practice of mathematics deep learning based on distributed cognition is gradually constructed.Then,through the teaching strategy cases and classroom teaching cases of mathematics deep learning,the concrete practice process of mathematics deep learning based on distributed cognition theory is presented.Based on the distributed cognitive theory and combined with the deep learning theory,this dissertation re-examines and understands the cognitive process of mathematical deep learning activities,forms the mathematics deep learning theory based on the distributed cognitive theory,and applies it.The main research content of this paper is to solve five specific problems:1.How to understand mathematics deep learning based on distributed cognition theory.2.How to judge whether deep learning activities in mathematics occur.3.How to determine the "depth" of mathematics deep learning.4.How to carry out mathematics deep learning in class.5.How to carry out the classroom teaching practice of mathematics deep learning.This dissertation research conclusion is as follows:1.Mathematics deep learning is the deep learning relying on mathematics subject,which is manifested as the transmission and conversion process of mathematical knowledge through different media representation phenomena.Mathematics deep learning has four connotation characteristics: distribution,hierarchy,strategy and tool.The cognitive activity of mathematical deep learning is a process of understanding the core concepts of mathematics through a certain learning function,which can be represented by the combination of different learning functions to form a chain structure of mathematical deep learning.2."Distribution" should be taken as a significant symbol to determine whether mathematics deep learning is carried out.In other words,the participants of mathematics deep learning activities show the distribution of mathematical knowledge representation in a specific form.3.The "depth" connotation of mathematics deep learning,for a core concept of learning mathematics,is represented quantitatively through the number of chains(or layers).This study constructs two tools to quantitatively express the goal of mathematics deep learning.On one hand,based on the curriculum content of ordinary high school mathematics,the three-dimensional evaluation tool of mathematics core literacy is constructed to measure the "depth" of deep learning of high school mathematics.On the other hand,according to the characteristics of mathematics knowledge learning,the basic hierarchy of mathematics deep learning is analyzed,and the hierarchy is used to measure the "depth" of mathematics deep learning in high school.4.Mathematics deep learning in the classroom is a collective cognitive activities with the participation of mathematics teachers.It is a process of solving mathematical tasks collectively and forming a collective representation of mathematics cognition.The representation system of mathematics deep learning activities is used to express the collective learning activities in the classroom.5.Mathematics deep learning activities are carried out through mathematics deep teaching activities in the classroom.To construct a mathematics deep teaching system based on distributed cognition,and form a hierarchical learning environment for the classroom teaching practice of deep mathematics learning.The innovation of this dissertation: From the perspective of distributed cognition theory,and drawing on the research of deep learning in the field of AI,the mathematics deep learning theory is reconstructed.It emphasizes the explicit characteristics of mathematics deep learning activities,and puts forward that mathematics deep learning activities are observable and the "depth" is measurable.It emphasizes the systematicness of mathematics deep learning activities,and proposes that the mathematics deep learning activities in the classroom constitute a distributed cognitive system.There are many deficiencies in the classroom practice research of mathematics deep learning based on distributed cognitive theory.In the future,looking forward to the change of mathematics deep learning model and the integration of mathematics deep learning content,it can promote the combination of theory and practice.