Research On The Analysis And Visualization Of Mathematical Problem Solving Process

Modern education not only focuses on learners' learning outcomes,but focuses more on the learner's learning process.Researchers have studied the cognitive modes,strategies and influential factors in solving mathematical problems.The analysis research about learners' specific operation and solving process to solve mathematical problems can make learners' learning process concrete,master the learner's knowledge level,and provide reference onions to teachers for instruct students solve problem.Based on Cognitive Learning Theory,Constructivism Learning Theory,Information Processing Theory and Bloom's educational target classification theory,this research adopts the research methods of literature analysis,content analysis,structure analysis,comparative research and case study,to study on the learner's process of solving mathematical problems.First of all,the paper constructs a mathematical problem solving process model.Secondly,it designs a analysis table of mathematical problem solving process and methodology of analyzing the process to solve the mathematical problem.Finally,it chooses learners' mathematical problem solving process to conducts a case study.The research work of this article has the following points:(1)Build the mathematical problem solving process model.On the basis of integrating existing mathematics problem solving models and combining relevant theories,a mathematical problem solving process mode is constructed that emphasizes knowledge level and problem solving process,which provides a theoretical basis for analyzing learners' solving mathematical problems.(2)Explore mathematical problem solving process analysis methods.Design mathematical problem solving process analysis table to regulate the specific problem solving process;design knowledge level coding table of mathematical problem solving process to analyze the content of the process;combining with the structure analysis method,explore the visualized analysis method to visualize the process of problem solving,which are constituting the mathematical problem solving process analysis method.(3)Analysis and research on the process of solving mathematical problems as one case.Select typical learner homework exercises as sample for case analysis,standardize standard and learner's solution process,analyze learner's problem-solving process knowledge level,visualize standard response and learner's solution process which forms sequence hierarchy relationship diagram,and use comparative research method to analyze the difference of standard response and learner's process.At the same time,do an interview to mathematics teachers,which aimed to be an auxiliary analysis material.This paper selects the written problem solving process as the research object,and it is still difficult to restore and analyze the process of problem solving.This paper proposes the mathematical problem solving process model,designs the mathematical problem solving process analysis table and knowledge level coding table,and explores the visualization method of the mathematical problem solving process.The specific implementation of the analysis method is given as a case study.The results of the case study verify the feasibility and effectiveness of the mathematical problem solving process analysis method.Finally,it has some expectation for follow-up research.