Research On The Guidance Of Basic Elementary Functional Method Under The Core Quality Of Mathematical Abstraction

Based on the mathematics textbook of senior one,this paper studies the learning situation of the basic elementary functions of senior students.The main research directions are exponential function,logarithmic function and trigonometric function.On this basis,it studies the development degree of students' abstract core literacy of mathematics.Around this theme,the main body of this paper is divided into five parts: problem posing,research status and theoretical basis,empirical analysis,case study,summary and outlook.When raising questions,this paper explains the necessity and feasibility of the research from two aspects of teaching content and the development of teachers and students,and defines the purpose,content,method and related concepts of the research.In addition,on the basis of in-depth understanding of the research status and reading a large number of relevant articles,relying on the relevant education theory,using questionnaire survey,interview,communication and other research methods,the paper collect data to analyze students' learning of different basic elementary functions.This survey is mainly conducted from two aspects: the index function and the trigonometric function.Through the investigation of the learning of the index function,we can get the following conclusions: first,the learning interest of senior one students in the survey group for the exponential function and the logarithmic function is related to their gender.The learning interest of male students is significantly higher than that of female students at the same level,which is also related to the students The development of mathematical abstraction;secondly,due to the individual differences of students' development level,the understanding deviation occurs in the learning of exponential and logarithmic functions,which leads to the generation of wrong concepts and affects the development of mathematical abstraction ability;thirdly,students' emphasis on mathematical culture and information technology and learning methods are related to teachers' teaching attitude and methods on this plate.The investigation on the learning of trigonometric functions shows that: first,when students contact the arc system initially,they often have the unequal transformation of the angle system and the arc system and the mixed useof the two;second,trigonometric functions involve many formulas,the students do not remember accurately or understand enough,and the symbols are wrong when they are applied;third,they cannot find out the potential conditions of the topic,or they cannot say that the conditions of the topic are equivalent It is transformed into mathematical symbolic language.According to the data analysis,teaching suggestions and learning guidance suggestions are put forward,and through three different lesson examples,respectively,index function,trigonometric function and logarithmic function are studied in concept teaching,problem solving teaching and function property teaching.In the case study,the concept teaching is summed up into six parts: comparison,observation,generalization,analysis,analysis,and analysis.Through analogy,observation,generalization,analysis,the six teaching processes guide students to learn abstract function concepts and improve their mathematical abstract ability.The problem-solving teaching is summed up into six activity links: examination,thinking,doing,speaking,changing and practicing,so as to fully mobilize students In the process of solving problems,students' ability of solving problems and the development of the core quality of mathematical abstraction are cultivated.The teaching of the nature of abstract functions is divided into five stages:introduction,exploration,discovery,induction and consolidation.In the process of exploration,computer technology should be properly applied to present students with intuitive,dynamic and accurate concrete images.From concrete to abstract,through mathematical thinking methods,the abstract nature of basic elementary functions can be concluded and consolidated.On the basis of the application of teaching theory in educational practice,at the end of the article,it summarizes and looks forward to the application of the research after the author really goes to work,guides the students to master the learning methods,and cultivates the abstract core quality of mathematics.