Investigation On The Understanding Level Of Elementary Geometric Transformation And The Causes Of Errors In Senior High School Students

Geometric transformation has experienced a long development process,and has important applications in production and life.However,students have great difficulties in learning geometric transformation.So based on the theory of mathematical understanding level of Bergeron,using literature analysis,questionnaire investigation and interview method,a survey was conducted on students of eight grade two science classes in a key senior high school in Harbin,Heilongjiang Province.From the translation transformation,rotation transform and axial symmetry transform plane elementary geometry transform three dimensions research students understanding of the situation.SPSS software was used for quantitative analysis of the questionnaire results,and the acquisition of students' intuitive understanding level,procedural understanding level,abstract understanding level and formal understanding level of geometric transformation was studied.And through the interview,analyze the problem solving strategies used by students,the types of errors and the causes of errors.Through the research of this paper,it will provide help for teachers' future teaching and students' learning.It is found that the first level of elementary geometric transformation students' overall understanding is procedural understanding,the second level is intuitive understanding,the third level is abstract understanding,and the fourth level is formal understanding.The four levels of understanding are mutually reinforcing.Boys perform better in the level of intuitive understanding,abstract understanding and formal understanding,and there is no significant difference in the level of procedural understanding between boys and girls.Translation direction,rotation center,rotation Angle,symmetry axis,transformation steps and transformation sequence affect students' understanding level.The common solving strategies are to use formulas,draw diagrams by tracing points,and summarize coordinate relations of corresponding points by examples.At the level of intuitive understanding,the main errors are knowledge errors,at the level of procedural understanding,and at the level of abstract understanding,the main errors are logic errors and strategic errors.Psychological errors also occur.At the level of formal understanding,the errors are mainly logical and strategic.The main reason for the error is that the essence of the concept is not understood and the relation between geometric transformation and algebraic transformation cannot be established.