Research On Congruent Triangle Teaching Based On APOS Theory And Variable Teaching Integration

In the area of shapes and geometry,the learning of congruent triangles is a very crucial step.APOS theory can help teachers and students to better understand and construct concepts,thus providing a strong theoretical support for classroom teaching.Variational teaching is a common teaching method used by Chinese teachers.It refers to changing the conditions or conclusions of a problem so that students can understand the essential features of things by changing their non-essential features.This paper integrates APOS theory and variable teaching together,using congruent triangles as support,to investigate whether the integrated teaching model of the two theories is effective in improving practical teaching.The research methods in this article are literature research method,case study method,experimental research method,questionnaire survey method and interview method.On this basis,the article is divided into three stages: firstly,it compares the concepts of APOS theory and variable teaching,relevant research at home and abroad,and summarises the research results on concept teaching at home and abroad.Secondly,from the duality of mathematical concepts,the necessity and feasibility of integrating APOS theory and variation teaching are elaborated.Meanwhile,before the experiment,the current learning status of graphs and geometry is understood through questionnaires,and the teaching status is understood through teachers’ interviews,and then a variation teaching strategy based on APOS theory is proposed,and how to integrate variation teaching in the four stages of APOS is analysed in the light of the current teaching situation.The teaching design is also carried out using congruent triangles as a vehicle.Finally,two classes were selected,one as a control class and the other as an experimental class,with the control class following the traditional teaching model and the experimental class adopting the teaching model based on APOS theory and variable teaching.The results of the pre-test and post-test showed that the use of APOS theory and variant teaching improved students’ performance,increased their interest in learning,and deepened their understanding and mastery of congruent triangles,thus forming a more complete knowledge system in their minds.The results of the study show that the teaching model based on the integration of APOS theory and variation teaching is feasible and necessary to promote students’ mathematical achievement and stimulate their interest in mathematics,and is expected to provide concrete practical experience for teaching mathematical concepts in junior secondary schools.However,the teaching model constructed in this paper is still at a preliminary stage,with certain limitations in terms of experimental subjects and time,and the teaching process is still in the process of preliminary exploration and improvement regarding the setting of variation.