On High School Mathematical Problem-solving Errors Remedial Teaching Based On "Three Abilities"

"Mathematics Curriculum Standards for Ordinary Senior High Schools(2017 edition,revised in 2020)"proposes that"mathematics education should guide students to observe the world with mathematical eyes,think about the world with mathematical thinking,and express the world with mathematical language".How to help students improve their problem-solving ability more effectively has become the focus of high school mathematics teaching.Based on the realization of the goal of "Three Abilities",it is necessary to examine the ability of solving math problems in senior high school,the acquisition and presentation of correct methods to solve problems,and the discovery and avoidance of possible errors to solve problems.However,the latter is often ignored in the current teaching of high school mathematics problem solving,which undoubtedly directly affects the improvement of problem solving ability.Under the background of"learning for application" and "literacy development",based on the goal of "Three Abilities",it is undoubtedly of obvious significance and value to explore the teaching of correcting errors in solving mathematics problems in senior high schools,so as to help improve students’ level of solving mathematics problems.Therefore,how to help students find,correct and avoid the determination of several problem solving errors based on the goal of "Three Abilities" is the research purpose of this paper.With the knowledge unit of "equality relation and inequality relation" as the research carrier,literature analysis is adopted to analyze the goal of"Three Abilities" and mathematical problem solving errors.As well as "equality relation and inequality relation" knowledge unit of problem solving errors in the three aspects of the existing research results are summarized and further analyzed,and at the same time,the theoretical basis of the two research porria mathematical problem solving theory and constructivism theory are sorted out.Respectively with the method of questionnaire investigation and test analysis for high school math teacher and high school students to investigate and test,a comprehensive understanding of the goal of"Three Abilities" in the high school mathematics problem-solving error-correction teaching the application of the status quo,through the investigation and analysis of test results,organize students are prone to errors when the problem solving performance and fault reasons,Then the three manifestations and corresponding attributions of the errors of "equality relation and inequality relation" based on the goal of "Three Abilities" are summarized,and the cases are illustrated.On this basis,three teaching strategies for error correction are proposed,and the teaching cases of"equality relation and inequality relation" are designed.The implementation effect of the cases is analyzed,and the effectiveness and operability of the teaching strategies are tested.