Research On Trigonometric Function Teaching Design Combining APOS Theory And Variant Teaching

Mathematical concepts are the foundation of mathematical learning.The Mathematics Curriculum Standard(2017 Edition,2020 Revision)of General High School points out that “functions are the most basic concepts in modern mathematics which are used to describe objectively existing relationships and laws in reality.”Function is the main line of mathematics teaching in high school and as a part of function,trigonometric function also has an important position.The teaching of trigonometric functions includes two aspects: theory and application.However,the premise of being able to apply the concept is to understand the concept itself.But in the current teaching environment,there are a few teachers who do not fully consider the students’ thinking habits and inadequate conceptual analysis,which causes students to be not good at applying concepts to solve problems.We summarized the composite theory which is suitable for the concept teaching of trigonometric function by integrating APOS theory and variant teaching.Firstly,we review the concepts,characteristics,and research status of APOS theory and variants theoretically by collating literature.Secondly,we learn about the current teaching situation of the trigonometric function part by conducting a questionnaire survey.Through teacher interviews,we learn about the problems existing in the actual teaching of the trigonometric function part from the teacher’s perspective and the key points which teaching design is needed.Thirdly,we summarize the necessity and feasibility of combining APOS theory with variant teaching through literature reading analysis.Finally,we integrate the two theories into a consistent theory,in which the four stages of APOS theory are taken as the main structure,and variant situations and variant topics are interspersed in the teaching links of the four stages.Then we propose a trigonometric function teaching design combining two theories.And through the teaching experiment,the effectiveness of the teaching design combining the two theories to the students’ grasp of the concept knowledge of trigonometric function is tested.In summary,we analyze and summarize the teaching model of concept combining APOS theory with variant teaching,provide a trigonometric function teaching design schema of combining the two theories,and conduct teaching experiments to verify the positive effect of combining the two theories on students’ learning of trigonometric functions.And we provide new ideas for front-line teachers to conduct trigonometric function concept teaching.