Research On Teaching The Concept Of "Cognition Of Graphics" In Elementary School Mathematics From The Perspective Of APOS Theory

"Cognition of graphics" focuses on the concept of graphs and their characteristics.It is an important prerequisite for students to develop spatial concepts,geometric intuition and reasoning ability.According to the requirements of mathematics curriculum standards and the realistic needs of teaching the concept of graphs in elementary school,the pedagogical concepts of APOS theory can provide teachers with ideas on how to teach the concept,which can help teachers understand students' learning situation in time,master the classroom instruction efficiently,and promote the development of students' abstract thinking.Based on the perspective of APOS theory,this paper adopts the interview survey method and the case study method.Firstly,we analyze the applicability of APOS theory to the teaching of concepts in the area of "Cognition of graphics" in elementary school;secondly,we analyze the content of teaching concepts in the area of "Cognition of graphics" from three aspects,namely,the requirements of curriculum standards,the distribution of textbook contents and the analysis of learning situations,by combining the interviews with teachers.Finally,we collected the teaching examples of famous teachers in the field of "Cognition of graphics",such as "preliminary knowledge of angles","knowledge of triangles","knowledge of parallelograms and trapezoids" and "knowledge of circles",and converted some teaching fragments into textual recordings according to the characteristics of the four stages of APOS theory: activity,process,object and schema.The APOS theory is used to analyze the cases in each stage and to interview front-line teachers for teaching interpretation,presenting the ways and methods of teaching the concept of "Cognition of graphics" and the teaching concerns of teachers from the perspective of APOS theory.Based on the insights obtained from the above analysis,we propose suggestions for teaching the concept of "Cognition of graphics" in elementary school under the guidance of APOS theory.In the action stage,we need to build real situations,design problems precisely,and operate in various ways;in the process stage,we need to insist on students' main body,focus on reflective thinking,and pay attention to all interactions;in the object stage,we need to focus on exercise design,guide reasoning and analysis,and focus on core literacy;in the schema stage,we need to focus on conceptual connection,break the knowledge barrier,and pay attention to knowledge sorting.