Research On The Characteristics Of High-quality Junior High School Mathematics Concept Teaching Courses Based On APOS Theor

Mathematical concepts are the “cells” of the mathematical knowledge system and the foundation of the mathematical building.However,there are some problems in the concept teaching in the classroom,such as emphasizing the conclusion,but not the process;only emphasizing the connotation of mathematical concepts,but ignoring the rich extension of the concept;teachers do not “objectify” the concept in teaching,and lack the grasp of the essence and meaning of mathematical concepts.This leads to students’ “false understanding” of concepts and their inability to grasp the essential properties of concepts.Therefore,this study integrates APOS theory into the research of teaching middle school mathematics concepts and provides new ideas for teachers’ teaching work by studying the characteristics of teaching behaviors in quality lessons of middle school mathematics concepts,as well as some pedagogical suggestions for novice teachers who are about to engage in front-line teaching.In this study,eight high-quality lessons of mathematical concepts were selected as the object of study in the “12th Junior High School Young Mathematics Teachers’ Lesson Demonstration Activity”,and regarding the coding table of teachers’ behaviors mentioned by Professor Ye Lijun in his paper,three teachers’ teaching behaviors of questioning,teaching speech,and teaching feedback were taken as the vertical dimension of the coding system,and the four stages of APOS theory were taken as the horizontal dimension of the coding system.As the horizontal dimension of the coding system,the three video analysis coding tables were constructed with these two dimensions.Immediately after,the author used the coding tables to code the transcript of the quality lesson video transcription sentence by sentence in NVivo11 Plus qualitative analysis software.Combined with the coding data,statistical charts,and lesson clips,the author analyzed the characteristics of the quality lesson of mathematics concept teaching in junior middle school as follows:(1)In the activity stage,problem situations are created,and prompted questions are used to require students to judge and think concerning what they have learned,and teachers adopt a combination of comprehension,evaluation,and literacy questioning;classroom interactions are mostly in questioning language,and in the perceptual cognitive stage,teachers supplement with declarative and enlightening language to guide students to explore the relationship between real situations and concepts;at the same time,teachers respond,the teacher interacts with students’ responses with a variety of classroom feedback behaviors,such as implicit feedback,written feedback,and repetition of students’ answers,to improve students’ classroom participation.(2)process stage,design questions,still mostly prompting questions,the number of evaluative questions significantly increased;the highest percentage of questioning language,in the process of guiding students to actively construct,teachers accept and agree with students’ ideas based on the problem,appropriate to put forward their interpretation,more use of language such as inspiration gradually develop students’ abstract generalization ability;enhance teacher-student emotional interaction,repeat the highest number of feedback methods for students’ answers,in the process of abstract generalization teachers supplemented with explanatory feedback,turn question feedback and other behaviors to inspire students to generalize and integrate.(3)In the object stage,in the process of constructing a concept into a concrete object,teachers’ prompting questions accounted for the highest proportion,and the number of memorization questions increased significantly,supplemented by comprehension and evaluation questions to guide students to build intuitive structures;in the process of refining symbolic representations and concise textual representations,teachers still focused more on questioning language,and the number of inspiring and motivating language increased significantly,and the number of individual explanations for students was higher than that of other stages;in the gradual and repeated operation from "process" to "object",teachers’ feedback methods are diversified,they mainly focus on repeating students’ answers,attach importance to written feedback and strong oral feedback,and other feedback types are similar.(4)In the schema stage,form a knowledge framework,the teacher uses prompting and comprehension questions to guide students to summarize and reflect;to review and summarize and construct new “schemas”,the teacher uses declarative language and questioning language,supplemented by feedback and inspirational language to help students improve their understanding of concepts;to create a positive and open classroom atmosphere,using various forms of feedback such as repeating students’ answers,explanatory feedback,and strong verbal feedback to affirm and praise students,and to guide students to self-reflect and strengthen their understanding of the schema of a concept.