Research On Concept Teaching Of Conic Curve Based On APOS Theory

In recent years,new curriculum reforms in middle schools have been increasingly promoted in various regions.More and more teaching examples show that in the past,in order to pursue the "efficient" of mathematics classrooms,the teaching model of simplifying mathematics concept often has great deficiencies.It does not mean that the knowledge is truly mastered,and the lack of teaching links will have an impact on the richness and comprehensiveness of the conceptual construction of students.Therefore,the importance of teaching mathematics concepts has gradually surfaced.In this process,more and more teaching and experienced educators began to use the relevant theories of psychology to explore the law of conceptual teaching.APOS theory is one of them.APOS theory is a kind of mathematics learning theories based on constructivism and proposed by American scholar Dubinsky.The point of it is to guide students to learn mathematics knowledge in social clues,analyze mathematical problem situations,and construct their own mathematical ideas.Under the guidance of APOS theory,Dubinsky successfully educated students to learn a series of mathematical concepts,such as groups,cosets,and quotient groups of abstract algebra.Therefore,APOS theory is in mathematics.Conceptual teaching has strong feasibility.Conic curve is an important part of high school mathematics.The conical curve of high school math class mainly includes four types:circle,ellipse,hyperbola,parabola,etc.,and each type of conic curve has its own standard equation,eccentricity formula,focal radius formula,and asymptote formula,focus chord formula,guideline formula,etc..Knowledge points of this section are numerous and abstract.If students just learn the definition of conic curve and some important conclusions by rote,and do not pay attention to the understanding of the essential concept,they will find it is hard to get good grades in this section.This study will explore how to use APOS theory to link new knowledge with old knowledge in a organized and logical way,and investigate how to use this theory to assist in the teaching of conic curve concepts.The research is mainly divided into the following aspects:first,the content analysis of the high school conic curve;second,the high school students learn the conic curve survey;third,the learning and analysis of the APOS theory;fourth,the APOS theory applied to the conic curve teaching Feasibility;fifth,Conical teaching design under the guidance of APOS theory;sixth,Analysis and reflection on the teaching results after teaching this theory.The main methods used in this study are literature research method,questionnaire survey method,and case analysis method.The focus of the research is how to design the conic curve under the guidance of APOS theory,apply the APOS theory method to practice,carry out effective teaching activities,and analyze and summarize the effects and follow-up feasibility of this method after teaching.