A Research On Understanding Level Of Logarithm And Logarithmic Operation Of Senior High School Students

Greater demands are being placed on comprehension study by developing student's six key competencies and mathematical key competencies.As the basic concept in senior high school mathematical curriculum,logarithm is the foundation to learn mathematics further.It is not difficult to learn,but many students have problem with it.To describe the senior one student's understanding level of logarithm and logarithmic operation is this paper's main subject.The research work unfolded mainly through three parts.The first is to build understanding model on logarithm and logarithmic operation of the senior one student by literature analysis : the understanding model can be divided into aware-understanding ?reasoning-understanding and essential-understanding.The aware-understanding contains aware of definition and properties,aware of operation rules,aware of the base changing formula for logarithms.The reasoning-understanding contains interpretation of definition,proof of properties and formula,generalization of properties and formula.The essential-understanding contains history of invention history and mathematical thinking method.And aware of definition and properties is not relevant to the invention history,the others have a positive correlation with each other.The second is to make a questionnaire according to the model,and research senior one students in WuHu Twelfth High School.The Cronbach's Alpha of questionnaire is 0.806,the Spearman-Brown split-half reliability coefficient is 0.813,by analyzing data through SPSS20.0,so the questionnaire is reliable.The third is to compare the difference among students that with different sex and different mathematical skills on understanding logarithm and its operation.The conclusion is that boys and girls have no different in aware-understanding and essential understanding,but boys do better than girls in reasoning-understanding.Specifically,boys do better than girls in proofing and generalizing the operation properties and formula,worse than girls in interpreting the definition of logarithm.Top students?medium students and weak students show obvious different in understanding logarithm and logarithmic operation,and the better student's mathematical performance is,the better he does in understanding logarithm.But the medium students and weak students' understanding level have no different in knowing definition and properties,the top students and medium students' understanding level have no different in knowing the base changing formula for logarithms.It reflect a fact that some student learn logarithm with a rote memory.