Teaching Research On The Line Side Location Relationship Of Solid Geometry Based On APOS Theory

Solid geometry plays an important role in cultivating students' spatial imagination ability and logical reasoning ability.To analyze the relationship and properties of three-dimensional space graphics,it is necessary to start with elements.Therefore,the content of "line and plane position relationship" is particularly important.There are many concepts,theorems and properties in this part,which seem to be easy to understand and intuitive,but it is difficult for students to abstract the specific position relations of points,lines and planes from the three-dimensional graphics,combined with the abstract logic language in the proofs,often make students feel not to lead to learning difficulties.In traditional teaching,most teachers pay little attention to the concept understanding and formation process of students in the early stage,and focus on the training of students' skills and problem-solving skills,which leads to students' inability to flexibly apply concepts in the later stage of learning,and they are caught in the predicament of rote memorization and mechanical imitation training.This is in line with the emphasis on the process of the new curriculum and the teaching philosophy that motivates students to explore the process of knowledge formation as the subject of learning.This is quite different from the teaching idea advocated by the new curriculum,which emphasizes more on the results and more on the process and encourages students as the main body of learning to explore the formation of knowledge.This paper attempts to study the teaching of solid geometry concept with the guidance of APOS theory.This paper first studies relevant theories at home and abroad through literature analysis,introduces APOS theory and its four-stage model in detail,analyzes the feasibility of the application of this theory in the teaching of solid geometry,and deeply studies the different stages of APOS theory guiding the concept of solid geometry;Secondly,using the method of questionnaire survey and interviews to investigate the learning situation of "line-to-face position relationship" for high school students and the teaching methods used by the teachers in class,the purpose is to understand the current situation and reasons of teaching and learning of solid geometry concepts,and based on this,the stereo geometry teaching is incorporated into APOS theory,and the teaching of the concept of solid geometry is designed.Finally,two specific teaching cases are used to demonstrate the concrete implementation of the application of APOS theory to the teaching of solid geometry concepts.Through the teaching in four stages of "activity","process","object","illustration",the teacher guides the students to do hands-on operation,reflect on the activity process and form a stable object of the concept,so as to help the students to construct the knowledge structure of the position relationship of three-dimensional geometric lines and planes.Through the comparative experiment between the experimental class and the control class,SPSS software was used to analyze and compare the test scores of the two classes.The experimental results show that basing on the APOS theory,the conceptual teaching model has higher enthusiasm and initiative for students to participate in the class,which is conducive to the development of students' non-intellectual factors;the improvement of students' test results indicates that it is obviously beneficial for students to sort out the complex concepts of solid geometry.Meanwhile,the teaching process is conducive to enhancing students' awareness of inquiry and ability to solve problems.Based on the research,some Suggestions on applying APOS theory to guiding concept teaching are put forward:(1)the teaching content under the guidance of APOS theory should be exploratory;(2)The four stages of APOS theory are a progressive process.The teaching arrangement should ensure the integrity and internal connection of the process;(3)Situation creation is for better teaching and is not the ultimate goal.Therefore,the appropriateness of situation creation should be paid attention to in the "activity" stage;(4)The teaching emphasizes mathematical thinking and methods and helps students construct schemas;(5)The four stages of APOS theory are applied to analyze and diagnose the problems students encounter in the learning process and in turn to guide classroom teaching.