| The mathematics thinking of grade 8 students is undergoing a transition from image thinking to formal thinking,and the learning in this stage will have a great influence on the subsequent learning of geometry knowledge.However,after students entered the eighth grade,their math scores became more and more polarized,especially the triangle knowledge in three consecutive chapters,which became more and more difficult,and students made many mistakes in solving problems.If we can analyze students’ problem solving errors,explore the root of the existence of errors and seek effective corrective measures,it is of great benefit not only to the cultivation of students’ thinking logic but also to the subsequent learning of knowledge.Therefore,this study puts forward three questions :(1)The investigation and research on the influencing factors of eighth grade students’ solving triangle problems.(2)A study on the errors and attribution of eighth grade students in solving triangle problems.(3)What are the strategies to reduce or avoid mistakes in solving triangle problems for grade 8 students?For the study of the above problems,combining with the reference and the related materials,adapted to the existing questionnaire,the formation of the eighth grade students solving triangle problem error influencing factors questionnaire ",through the two schools of nine classes,363 students of questionnaire investigation and analysis,to determine the grade eight students solving triangle problem error factors,and variance analysis.And composed on the basis of the problem solving situation of the students at ordinary times grade eight students to solve the triangle test,and make the interview outline,based on 196 students of two schools five class testing related topics and revise,interview students of some typical mistakes,make the students proposed to solve the problem existing in the triangle error verified,at the same time,summarize the error types and analyze the factors that cause the eighth grade students to solve the triangle problem wrong.Finally,combined with relevant literature and interview records of front-line teachers,effective countermeasures are put forward to help students reduce the occurrence of mistakes and provide reference for teachers and students.Based on the above research,it is concluded that the factors leading to the error of solving triangle question can be divided into knowledge factors,logical factors,psychological factors and strategic factors.The knowledge factor is embodied in the fuzzy concept;confusion of similar concepts;unable to grasp the meaning of the question accurately;ignore the conditions under which a theorem exists.The logical factors include changing the topic;circular argument;the argument is not rigorous.Psychological factors are embodied in ignoring implicit conditions;short-term memory problems;stayable errors(that is,set thinking).Strategic factors are reflected in calculation errors;formatting errors;pattern recognition error;three language conversion errors.Students’ mistakes in solving triangle problems include: vague concepts and properties,ignoring the use conditions and scope of theorems;Failure to explore the implicit conditions in the title;Numbers,letters and other transcription errors;Circular argument;To replace the general with the special,to replace the logical reasoning with intuitive judgment,resulting in the error of changing the topic;False arguments or reasoning processes are not supported by evidence;No ancillary wire added or ancillary wire added error The writing of reasoning process is disordered and formatting is wrong;Calculation error.From the Angle of attribution analysis,it can be attributed to: intellectual error,psychological error,logical error,strategic error.In view of students’ mistakes in solving triangle problems,the following teaching strategies are proposed: Help students deepen their understanding of concept theorems based on constructivism;Improve students’ ability of examining the topic by using The thought of Solving the problem of Bolia;Make good use of "analysis chart" to eliminate students’ logic errors;Use "self question method" to help students seek the way to solve the problem;Guide students to understand the relationship between "general" and "special";Strengthen one more solution,break through the thinking pattern;Strengthen variant training and diverge students’ thinking;Improving computing power;Clarify the writing requirements of the solution format;Practice adding strings. |
