Research On The Theory And Practice Of Mathematics Concept Teaching In Junior Middle School From The Perspective Of APOS Theory

Concept is the cell of thinking,and mathematics is the gymnastics of thinking.As the basis of mathematical knowledge,mathematical concepts are of great significance to students’ knowledge learning and ability development.However,in actual teaching,some teachers still ignore the importance of concept teaching,and there is the phenomenon of "emphasizing results,neglecting process;emphasizing teaching materials,neglecting practice",which makes students’ understanding of mathematical concepts stay in mechanical memory and shallow understanding,and can not understand the essence of mathematical concepts in depth.APOS theory is a mathematical learning theory based on constructivism.It combines it with concept teaching,and undergoes four different stages of operation,process,object and schema.At each stage,students are gradually constructed mentally,allowing students to experience the process of perception,abstraction and formation of concepts,and comprehend the essence of mathematical concepts.On the basis of consulting a large number of documents and materials,this study systematically introduced the current research situation of APOS theory and mathematical concept teaching,explained the connotation and characteristics of APOS theory,briefly analyzed the specific content,characteristics,learning methods and teaching characteristics of junior high school mathematical concepts,and established a systematic cognition of APOS theory and mathematical concept teaching.In order to better understand the current situation of mathematics concept teaching in junior high school,students and teachers were investigated in the form of questionnaires and interviews to thoroughly understand the problems in concept teaching and teachers’ cognition and application of APOS theory.Based on the results of the survey,the various stages of APOS theory were analyzed,and specific concept teaching design principles were proposed:(1)the integrity principle of teaching process;(2)The principle of combining student-oriented and teacher-oriented;(3)Adhering to the exploratory principle of teaching content,the concept teaching design process from the perspective of APOS theory is constructed:(1)operation stage: student-oriented construction of situational activities,perception of concepts;(2)Process stage: reflect on the operation setting,explore the problem,abstract the concept;(3)Object stage:layering exercise,skillful use of variant differentiation and internalization of concepts;(4)Schema stage: sort out the concept of knowledge structure connection and incorporate it into the system.Based on the above principles and processes,select more typical concepts in the fields of number and algebra,graphics and geometry modules for teaching design,further implement the concept teaching case "Plane Cartesian Coordinate System" from the perspective of APOS theory,and compare it with traditional concept teaching to verify and clarify the advantages of APOS theory guiding concept teaching,Finally,according to the four stages of teaching experiment process and theory,specific teaching strategies are proposed to better use APOS theory to guide teaching.The research shows that compared with traditional concept teaching,concept teaching from the perspective of APOS theory is more conducive to improving students’ classroom participation,reflecting students’ subjectivity,improving students’ understanding of concepts,and developing students’ mathematical ability and literacy.