Investigation And Research On Errors In Mathematical Problem Solving Of High School Student

Problem is the heart of mathematics,It runs through each link of mathematics teaching activity.Because mathematical problem solving is a creative activity,Because mathematical problem solving is a creative activity,Problem solving error is a normal phenomenon in the process of mathematical cognition,and it is inevitable.Correct mistakes and help students form a correct knowledge bas.Dissolve mistakes and melt "mistakes" into indispensable teaching resources.This is a problem that every math teacher must face.Based on the research of many scholars on the error of solving general mathematical problems,This study takes the content of "solving triangles" as the carrier,Combine general studies of student problem solving errors with specific chapters on high school mathematics,Through the establishment of the exercise "knowledge package" to analyze the causes of the formation of errors,make error correction strategies.In the research process,first of all,through a large number of literature reading,learning the existing research results,deepen the understanding of mathematical problem solving error research;Then,240 high school students and 40 teachers were investigated by means of student test and written interviews with teachers.On the one hand,students' mistakes in solving triangles are analyzed and classified in the test paper;On the other hand,from the written interview materials of teachers,extensive collection of teachers' error correction methods.Through the constructed knowledge package,the knowledge level where the errors occurred was evaluated,and the corresponding levels of teachers' error correction strategies were analyzed.Finally,some teaching suggestions on error correction are given.Student test paper survey results:(1)The errors of knowledge,strategy and logic also exist in solving trigonometric problems.There are also errors due to attitude towards solving problems.(2)The students who make mistakes can hardly or can only substitute the knowledge points in the knowledge package into the problem solving;The correct student also failed to cover all the points in the knowledge pack.It can be seen from written interviews with teachers:(1)Novice teachers and skilled teachers are also in different levels of knowledge packages.Compared with novice teachers,skilled teachers are better at mastering and understanding question methods.(2)It is the main strategy for in-service teachers who participate in written interview to correct errors by strengthening students'understanding of concepts and variation training in teaching.Comprehensive research,systematic analysis of mistakes is very important,for students'mistakes,teachers should change students' fear psychology and strict attitude into bear psychology and tolerance attitude.The following suggestions are put forward:(1)Stimulate students' interest and sense of inquiry,so that students can build a simple knowledge package and form a relatively perfect knowledge structure on the basis of their own cognition.(2)Pay attention to the cultivation of students' ideological methods,cultivate the stage consciousness of problem solving through problem solving reflection,and deepen in the variant training.(3)Guide students to use the mind mapping tool,realize the image thinking to help abstract thinking,improve logical reasoning ability.(4)Help students correctly face their own problem solving mistakes,know mistakes,recognize mistakes,resolve mistakes,let students like mathematics.