Common Mistakes And Causes Of High School Students’ Mathematical Problem Solving——Take "Sequence" As An Example

As an important part of the teaching content of high school mathematics,the number sequence is often widely related to the knowledge of functions,inequalities,equations,etc.,and is an important part of the annual college entrance examination.At the same time,the process of learning the sequence will involve observation,conjecture,analysis,induction and other methods,which can effectively improve students’ ability to find problems,analyze problems and solve problems.Sequence-based learning involves a lot of concepts,formulas,properties,and calculations,so that students often expose many problem-solving errors when solving sequence problems.Therefore,this paper conducts an in-depth investigation of the common error types that occur when students solve the problem of the sequence,analyzes the common error types of students in the solution of the number series,dissects them to find the cause of the error,and takes the "number series" as an example to explore the methods and countermeasures to reduce the errors of the students,so as to further enhance the students’ awareness of error prevention.This paper uses the digital series knowledge test paper for testing,and uses the test paper analysis method to study the common types of errors made by students in solving the number series problem;through the questionnaire "Everyone’s Views on Mathematical Problem Solving Errors",the questionnaire survey method is used to understand the psychological activities and attitudes of students in the face of mathematical problem solving errors;and the causes of common errors in students’ mathematical solutions are further studied through student interviews and teacher interviews.Through research,we have come to the following conclusions:First of all,the common types of errors that students make in solving sequence problems are intellectual errors,methodological errors,calculation errors,and psychological errors.Intellectual errors are manifested as conceptual errors,errors in the use of formulas,errors in understanding properties,and errors in the application of summation and synthesis;methodological errors are manifested as insufficient problem processing ability and improper selection of methods;errors in operation are manifested as errors in shifting to errors,symbol errors,errors in fractional operations,errors in coefficientization to 1,etc.;psychological errors are manifested as errors in solving problems caused by non-intellectual factors such as copying wrong questions,making correct choices,not simplifying results,and not making final conclusions.Secondly,through the study of students and teachers’ cognition of problem-solving errors,it is obtained: students do not pay enough attention to the mistakes that occur in the usual time,which is manifested as the low use rate of the wrong question book,and the attitude towards the wrong questions in the examination and practice is very different;the psychological pressure in the face of the wrong questions is too great,and the performance is that the teacher is worried about the teacher’s criticism of the wrong questions,feeling sorry for the parents,worried about the ridicule of the classmates;the lack of challenge spirit,manifested in the fact that very few students encounter the wrong questions and choose to study and find the wrong causes first,and many students choose to look at the reference answers.Teachers are mostly angry when they encounter students’ problem-solving mistakes,have a relatively negative attitude,and overemphasize the correct answers when explaining.Finally,combined with the common types of errors when students solve the number series problem and the teacher’s and students’ cognition of the problem solving errors,the reasons for the errors in solving mathematical problems are summarized from the three aspects of knowledge,student learning,and teacher teaching.Knowledge: High school mathematics is systematic and involves many knowledge points in the number sequence,and it is relatively difficult to comprehensively investigate.In terms of students’ learning: the knowledge mastery is not solid,the application is not accurate;the learning habits and learning methods are improper;the computing ability is poor;and the right and wrong questions are not paid enough attention.Teachers’ teaching: the attitude towards students’ problem-solving mistakes is relatively negative;the correction of errors is improper.According to the conclusions of the study,the following suggestions are made for teacher teaching and student learning from both the teacher and student levels:(1)Teacher level:Look at the mistakes in students’ problem solving with the right mentality,and make full use of the value of the wrong questions in teaching;Guide students to correct mistakes with a positive attitude,independently and efficiently;Pay attention to the concept generation process,so that students can grasp the essence of concepts and apply them correctly;Cultivate students’ mathematical logical thinking and summarize problem-solving methods;According to the students’ grasp of the situation,timely adjust the difficulties of the classroom;Adjust the classroom atmosphere and cultivate students’ interest in learning.(2)Student level:Correctly view mistakes and avoid repetitive mistakes;Pay attention to habit formation and summarize problem solving experience;Improve mathematical thinking and learn to build knowledge systems.