Research On Teaching Design Of High School Mathematics Concept Deep Learning Based On APOS Theory

Since the implementation of the new college entrance examination,as of the end of June 2022,29 provinces,including Henan Province,have launched the new college entrance examination.The proposition concept of the new college entrance examination has shifted from knowledge proposition to ability proposition and literacy proposition,aiming to test students’ ability to analyze and solve problems,guiding them to achieve a transformation from "problem solving" to "problem solving".The mathematical proposition of the college entrance examination also pays more and more attention to the examination of mathematical concepts,mathematical thinking methods and innovative thinking.The "General High School Mathematics Curriculum Standards(2017 Edition,2020 Revision)" points out that efforts should be made to develop students’ core competences,and the core concept and value pursuit of deep learning should be deeply aligned with the curriculum concept aimed at core competences.Deep learning is the learning of developing competences and an important path to implementing core competences.In this context,promoting deep learning of high school mathematical concepts is of great significance.The teaching effect guided by APOS theory is directed towards the performance of deep learning.In order to better promote students’ deep learning of high school mathematical concepts,this study uses APOS theory as the guidance,mathematical concept teaching as the carrier,and deep learning as the purpose to carry out teaching design research.By using literature analysis method,sort out the current research status,clarify core concepts,and determine the theoretical basis.Through investigation and research methods,analyze the basic situation of deep learning of mathematical concepts for first year high school students under the new college entrance examination.Construct a teaching design route for deep learning of high school mathematical concepts based on APOS theory,and write teaching design cases.Through experimental research methods,conduct experimental tests on the effectiveness and feasibility of the constructed teaching design route.Using survey research methods,questionnaire and interview surveys are conducted on some senior high school students and mathematics teachers at the school where the internship is conducted to understand the basic situation of implementing deep learning of mathematical concepts for senior high school students under the new college entrance examination.Through analysis and integration of the survey results,it is found that the overall average score of the students participating in the survey is at a moderate level,but some students still have the following problems:(1)the consciousness of cooperative inquiry and communication expression is not strong;(2)lack of critical awareness;(3)lack of awareness of conceptual integration and construction;(4)lack of transfer creativity.Based on the interview results with teachers,targeted optimization strategies are proposed to address the existing problems,providing factual basis for the construction of subsequent teaching design routes.A teaching design route for deep learning of high school mathematics concepts based on APOS theory is constructed.Combining the problems and optimization suggestions in deep learning of high school mathematics concepts,based on the cognitive characteristics of high school students,teaching design principles is formulated,and the teaching design route is constructed.It is divided into five stages:(1)preparation stage: referring to the curriculum standards,analyzing and estimating,and setting goals;(2)operation stage: creating scenarios,perceiving activities,and introducing concepts;(3)process stage:problem driven,abstract essence,and form concepts;(4)object stage: critical understanding,practical application,deepening concepts;(5)schema stage: transfer creation,integration construction,system concept.Based on the constructed teaching design route,specific teaching design cases are written with the content of "radian system" and "concept of trigonometric function".Using experimental research methods,two parallel classes in the first grade of the internship school are used as the experimental class and the control class,respectively,to test the effectiveness and feasibility of the constructed teaching design route.After the teaching experiment,it is found that the post test scores of the experimental class are significantly better than the control class as a whole.Through the post test questionnaire,it is found that there are significant differences in the dimensions of integrated construction,transfer application,and evaluation reflection between the experimental class and the control class,and the experimental class is superior to the control class.This verifies the effectiveness and feasibility of the constructed teaching design route for deep learning of high school mathematical concepts based on APOS theory,which can provide certain reference significance for practical teaching.