Research On The Concept Teaching Of Basic Elementary Function(Ⅰ)in High School Based On APOS Theory

Mathematics concepts are the foundation of mathematics learning.At present,there are many problems in the teaching and learning of mathematics concepts: mathematics teachers have insufficient ability to teach concepts;students have poor autonomy in concept learning.There are many basic concepts in high school mathematics.The basic elementary functions(Ⅰ)are exponential,logarithmic,and power functions,which are the foundation of high school students' function learning.The concept of fingers,pairs,and power functions is abstract,and students may encounter difficulties in learning.APOS theory helps to construct mathematical concepts.Therefore,this article focuses on the teaching of combining APOS theory with basic elementary functions(Ⅰ).What is APOS theory? What is the current status of basic elementary function(Ⅰ)concept teaching and learning? What principles should be followed in the teaching of APOS theory? What is the teaching of combining APOS theory with basic elementary functions(Ⅰ)?What is the effect of the basic elementary function(Ⅰ)after the implementation of APOS teaching?The author first introduces the research background and related theories.By consulting domestic and foreign literatures,the origin of APOS theory,the four-stage model,the basic elementary function(Ⅰ),and the teaching status of mathematical concepts are reviewed.The author takes the teachers and students of the first middle school in Dalian Development Zone as the research object,and uses interviews and surveys to understand the current status of the concepts of exponential,logarithm and power function in high school mathematics teaching and learning.Based on the investigation results and theoretical basis,the author summarizes the basic elementary function(Ⅰ)teaching principles under APOS theory.Based on the four-stage model and teaching principles of the APOS theory,the author has formed the teaching design of "The Properties and Images of Exponential Function","Logarithmic Operation" and "Power Function" based on the APOS theory.APOS teaching was conducted in the first grade of middle school and high school,and comparative teaching was carried out in the second grade of high school in the conventional teaching method.The author combined with the implementation content,showed some teaching fragments,analyzed the teaching process,and further reflected and analyzed the implementation effect of the APOS theory.After the implementation,the author tested the students in Class 1 and Class 2 of the first year of high school,and conducted a quantitative study on the results of Class 1 and Class 2 beforeand after the implementation.From the preliminary research,we can see that the basic elementary function(Ⅰ)teaching under the guidance of APOS theory can improve the actual teaching efficiency,help students deeply grasp the essence of concepts,form a knowledge network,and further build knowledge.It is hoped that this research can standardize the teacher's concept teaching,improve the teacher's awareness of students 'concept learning,and further enhance the students' concept learning ability.