Research On Elliptical Concepts Teaching In High School Based On APOS Theory

With the implementation of the new round of curriculum reform,cultivating students’ core literacy in mathematics is a need for educational development.In this context,students are not only required to master knowledge,but more importantly,to develop their ability of independent inquiry and problem solving.Dubinsky’s APOS theory is a constructivist-based theory of concept learning,which divides the learning of mathematical concepts into four stages: operation,process,object,and schema,guiding students to actively construct concepts and master the essence of concepts.Based on APOS theory,this paper investigates the deficiencies in teaching elliptic concepts.The main research questions include:(1)How much do high school students understand and master elliptic concepts?(2)What are the problems in the teaching and learning process of elliptic concepts? What are the reasons for the existence of these problems?(3)How to propose teaching strategies for elliptic concepts based on APOS theory?This paper summarizes the current status of research on APOS theory and elliptic concept teaching by reviewing the literature,based on the current status of research,206 students in the sophomore and junior grades of X High School in Linyi City were taken as the research objects,preparing standardized and reasonable test papers,combining questionnaires and teacher interviews to investigate the current situation of teaching and learning of elliptic concept in high school,and after analyzing and summarizing,we got the problems in the process of elliptic teaching and learning,responding to The problems of teaching and learning ellipse are summarized in the following four aspects:(1)reliance on teachers’ lectures to generate ellipse concepts;(2)low mastery of the graphical language of ellipse;(3)low ability in mathematical operations;(4)inability to use the concepts flexibly to solve problems.The reasons for the above problems include:(1)students’ low awareness of conceptual inquiry;(2)teachers’ low attention to the process of creating situations and problems;(3)students’ unclear cognition of elliptic concepts;(4)low application of teaching aids;(5)students’ poor arithmetic habits;(6)students’ fear of elliptic problems;(7)students’ failure to form knowledge structures;(8)students’ inability to summarizing and reflecting.Under the guidance of APOS theory and curriculum standards,the corresponding teaching strategies in the four stages of ellipse concept teaching are formulated as follows:(1)Teaching strategies in the operation stage: pay attention to the process of concept generation,create suitable teaching situations;develop intuitive imagination and make full use of teaching software.(2)Teaching strategies in the process stage:deepen the ellipse investigation activities,guide students to explore and think;pay attention to the derivation of elliptic equations and teach the method of solving trajectories.(3)Teaching strategies in the object stage: pay attention to the implementation and consolidation of new knowledge,learn to summarize and generalize concepts;pay attention to the teaching of language transformation,and cultivate students’ mathematical ideas.(4)Teaching strategies of the schema stage:establish the knowledge network of ellipse and improve the mental schema of knowledge;practice open variation questions and cultivate students’ innovative thinking.