The Investigation Of The High School Students' Errors In Solid Geometry Solving

Solid geometry is one of the important learning subjects in senior high school Mathematics.However,few studies focus on the solution errors in solid geometry questions of senior high school students and rare attention has been paid to relevant systematic discussion.In order to instruct teachers' teaching practice more effectively and improve their teaching quality,strengthen students' ability to discern mistakes and optimize their cognitive structure,it is of great importance to conduct an investigation on senior high school students' errors in solid geometry problem-solving process.Targeted at 200 senior high school students in Kunming some Middle School,this research conducts a questionnaire on solution errors in solid geometry questions and distributes solid geometry test papers to 105 of them.In combination with the interview with teachers and students,the purpose of the research is to learn about and summarize the thoughts of senior high school teachers and students about errors in solid geometry questions,major types of errors in students' solid geometry problem-solving process,prime causes of such errors,and how to effectively avoid such errors.In addition,by analyzing the types,features and causes of senior high school students' errors in solid geometry questions,this research refines the principles and teaching suggestions for the correction of such solution errors.Supported by trial-and-error learning theory and constructivism theory,the research refers to the classification of five major error types to carefully examine the solutions of papers in combination with questionnaire and interview results.As proved by final findings,senior high school students primarily make knowledge mistakes and psychological mistakes in solving solid geometry questions,and subsequently make tactic mistakes,few normative mistakes and logic mistakes.In addition,there exists prominent correlation between psychological mistakes and gender.Main causes that result in such mistakes could be ascribed to(1)incomplete mastery of relevant property and theorem,ambiguity,or defective cognitive structure;(2)insufficient understanding about questions and inadequate transformation ability for mathematical symbols;(3)influences from the negative transfer of original knowledge or thinking set;(4)lack of cognitive strategies and integral consciousness;(5)lack of logical reasoning ability and inclination to make false demonstration;(6)lack of spatial imagination ability and graphic perception;(7)influences from students' personal psychological factors;(8)absence of good problem-solving habits.According to above-mentioned features and causes of errors,the research puts forward following teaching suggestions for senior high school Mathematics Teachers,(1)reasonably constructing the teaching flow based on multi-representation learning;(2)focusing on question analysis process and cultivating students' reading ability and analytic ability;(3)valuing problem-solving thinking and forming corresponding strategies;(4)emphasizing non-intelligence factors and continually improving problem-solving ability;(5)normalizing writing process and construction process;(6)reasonably using the error set and reinforcing exercises.The research is expected to arouse the attention of senior high school Mathematics Teachers and students to errors in the process of solid geometry problem-solving,avoid the errors effectively and provide teaching references for teachers.