Research On Senior High School Students' Understanding Level Of Conic Concept Based On APOS Theory

As an introductory chapter of analytic geometry,conic curve is the focus of mathematics teaching in senior high school.From the dynamic concept formation process to the static research object,students have different levels of understanding.APOS theory is an important theory about students' learning mathematical concepts,which plays an important role in guiding concept teaching.Taking the questionnaire survey as the main research method and APOS theory as the benchmark,this paper formulates the analysis framework of conic concept understanding level,designs the test paper according to this framework,and carries out the conic concept teaching experiment based on APOS theory.Through the implementation of different teaching designs in the experimental class and the control class,and the experimental test after completing the concept teaching,this paper evaluates the level of students' understanding of the concept of conic curve,and reflects and explains the specific role of APOS theory in students' understanding of conic curve.The experimental results show that most of the students in the two classes can meet the requirements of the action stage and the process stage.The number of students who meet the learning requirements of the object stage accounts for only 30.7%,and the number of students in the schema stage accounts for only 6.93%.Specifically,the proportion of the experimental class meeting the learning requirements in the four stages of APOS theory increased by 8.08%,8.28%,21.18% and 9.17% respectively compared with the control class.This shows that the concept understanding level of students in the experimental class is better than that in the control class.The teaching under the guidance of APOS theory plays an important role in promoting the concept understanding level of conic curve.In order to help teachers better combine APOS theory in teaching practice,this paper puts forward the following three targeted teaching suggestions:(1)Teachers can use APOS theory to guide the teaching of conic concept.(2)Pay attention to students' understanding and mastery of the essence of the formation of mathematical concepts,and learn from doing.(3)Construct the structural network of mathematical objects to achieve a comprehensive understanding of the concept of conic.The above suggestions hope to provide some teaching enlightenment for primary and secondary school teachers.