The Application Of Factorization In High School Mathematics "Problem Solving"

"Problem solving" is one of the core links in mathematics teaching.Since the1980 s,"problem solving" has gradually gained attention and has become a popular research object in mathematics education.Many scholars have researched "problem solving" one after another.It is very effective in problem solving mode,influencing factors of problem solving,and problem solving teaching.As a favorable tool for dealing with algebraic deformation,factorization is mostly reflected in high school mathematics problem solving.Therefore,the study of factorization in the application of high school mathematics problem solving has certain significance and value to the teaching and learning of teachers and students.This paper combines quantitative research with qualitative research,through literature review,questionnaire survey,diagnostic test,data statistical analysis,and case analysis,focusing on the factorization level,problem-solving ability,and factors of the second-year high school students in the High School Affiliated to Hefei University of Technology The research on the application of factorization mainly includes the following five aspects:(1)The current situation of the ability of high school students to solve mathematical problems using factorization.(2)The factoring level of high school students and the current situation of their ability to solve specific mathematical problems using factoring methods.(3)Attribution analysis of the current situation of high school students' problems.(4)Analyze the factorization cases involved in the college entrance examination and design the teaching process on how to solve them.(5)Do a good job in cultivating factoring ability in problem solving.Through the analysis of questionnaires,test papers,and case studies,this paper obtains the following research results:(1)The current situation of the ability of high school students to solve mathematical problems by factoring is not ideal,and the overall level is lower than average,mainly affected by the attitude of solving problems,The way of solving the problem and the quality of solving the problem has three influences.(2)The overall level of factorization of senior two students is relatively low,which is manifested as forgetting the concept of factorization,lack of factorization methods,inability to use factorization flexibly,weak computing ability,etc.These potential factors all affect factorization.Application of decomposition in problem solving.(3)Taking college entrance examination questions as examples,analyzing the application of cross multiplication,grouping decomposition method,splitting and adding item method and related ideas in problem solving,and realize supplementary teaching of factoring method in problem solving teaching,to improve students' factors.while developing the problem-solving ability of students.(4)Based on students' learning situation,the current situation of problems,and college entrance examination cases,put forward the teaching strategies of factorization in problem solving,such as promoting the connection of factorization in junior and senior high schools,expanding the factorization method,and appropriately supplementing the remainder theorem The promotion and training of mining students' factoring thought.