Research On The Causes Of Learning Disabilities Of Exponential Function And Logarithmic Function In Freshman Of Senior High School Students

Functions are one of the main lines of high school mathematics learning,and the mastery of functions plays a role in students’ follow-up learning.Exponential functions and logarithmic functions are two widely used basic elementary functions,which are closely related to inverse functions.The study of exponential functions and logarithmic functions contains a variety of mathematical ideas such as combination of numbers and forms,equivalent transformation,and classification discussion,etc.,which is of great significance for cultivating students’ core accomplishment of mathematical discipline such as mathematical abstraction,mathematical operations and mathematical modelling.However,for the freshmen in the first year of senior high school,it will be chaotic to learn exponential and logarithmic functions which have some similar conceptual properties,so it is necessary to study the learning obstacles of exponential and logarithmic functions at the same time.Taking students in Harbin NO.9 Middle School as research participants.According to the mathematical curriculum standards,the complied questionnaire consists of five aspects: the concept,image,nature,relationship and comprehensive problems.After answering the questionnaire,the data will be analyzed to research the students’ thinking level of solving the problem according to the SOLO classification evaluation theory.Besides,the result of the questionnaire will be combined with the interview of front-line teachers to find out the main obstacles in learning index logarithmic functions.Here are six main obstacles presented:1.Conceptual aspects: the obstacle of basic conceptual understanding;the obstacle of conceptual confusion;the obstacle of old knowledge transference.2.Image aspects: the obstacle of image rendering;the obstacle of image transformation.3.Properties: the obstacle of comparing exponential function and logarithmic function;the obstacle of monotonicity of composite functions.4.Comprehensive aspects: the obstacle of the integration of knowledge;improper application methods and the obstacle of association ability.5.Mathematical thinking and methods: the lack of combination of numbers and forms,classification discussion,and the lack of transformation thoughts.6.Mathematical operation: low operation accuracy;bad computing habits;operation retreat psychology.The learning obstacles of exponential functions and logarithmic functions in the first year of senior high school students are divided into external and internal reasons.From the external perspective,it is because of the complexity of knowledge content and teacher factors.From the internal view,it can be concluded as students’ weak mathematical thinking ability,weak mastery of basic knowledge,negative learning attitude,and poor learning habits.Finally,combining the types and causes of learning exponential function and logarithmic function senior high school students face and teachers’ interview,some teaching suggestions are given as follows: 1.introduce the realistic background of functions and perceive the process of knowledge generation;2.compare the teaching of exponential functions and logarithmic functions and master the essence of function concepts;3.Clarify the main points of function drawing and be aware of the dynamic transformation process;4.sort out the connection between knowledge and strengthen the general comprehensive problem solving;5.Select open sample exercises to cultivate students’ divergent thinking;6.Optimize classroom teaching design and penetrate mathematical ideas and methods;7.Standardize the process of problem-solving and improve their mathematical computing ability;8.Stimulate interest in mathematics learning and improve mathematical learning attitude;9.Improve methods of previewing and reviewing and cultivate good learning habits.