A Study On The Teaching Of Acute Angle Trigonometric Function Concept In Junior Middle School Based On APOS Theory

Function is an important theoretical tool for describing changes in quantitative relationships,and an important foundation for further learning of mathematics.Among them,the level of understanding of function concepts has become an important factor in determining the effect of function learning.APOS theory is a constructivist theory,which focuses on the concept generation process,the learner's constructive thinking and the learner's mental construction state,which is in line with the mathematics teaching at the junior high school stage.APOS theory can provide theoretical guidance for function concept teaching,which can greatly reduce the difficulty of function teaching.At the junior high school stage,students are just exposed to the concept of acute Angle trigonometry.It is difficult for students to grasp the essence of the concept and it is more difficult to understand.Teaching needs to help students carry out perceptual knowledge,abstract reflection,grasp the essence,form mathematical objects in their minds,and construct a complete knowledge structure diagram based on operational activities.This is very consistent with the four stages of APOS theory,so it is very necessary to integrate the APOS theory into the teaching design of the acute-angle trigonometric function concept.The knowledge structure diagram of APOS is very consistent with the four stages of the APOS theory,so it is very necessary to integrate the APOS theory into the function concept teaching design.The first part of this article explains the importance of function concept teaching and APOS theory,and the necessity of integrating APOS theory into function concept teaching,and then puts forward the research questions of this article.The second part combs and introduces the related work of APOS theory and the concept teaching of acute trigonometric functions at home and abroad,which provides a theoretical basis for the research of this article.In the third part,through questionnaire surveys with students and interviews teachers,according to the four stages of APOS theory,the problems that arise when students learn acute trigonometric functions are analyzed:(1)The problem in the operation stage is that students cannot accurately memorize related concepts;(2)The problem in the process stage is that the dependent variable and the independent variable of the acute-angled trigonometric function cannot be distinguished;(3)The problem in the object stage is the inability to understand the meaning of the trigonometric function symbol and the calculation problem;(4)The problem in the schema stage is that it is easy to confuse the value of the trigonometric function,and it is impossible to accurately find the appropriate trigonometric function to solve the problem.In response to the problems found above,the author puts forward corresponding teaching strategies in the fourth part according to the four stages of the APOS theory:(1)The operation stage should use the intuition of life to introduce concepts;(2)The process stage should undergo a conceptual understanding process,pay attention to the internalization of knowledge;(3)The object stage should increase the knowledge of mathematical objects and understand the essence of trigonometric functions;(4)In the schema stage,we must strengthen the connection between knowledge,clarify the connotation and extension of the concept of acute-angle trigonometric functions,and establish an appropriate mental schema.In the fifth part of this article,based on the APOS theory,the author made a teaching design for the concepts of tangent,sine and cosine of acute-angled trigonometric functions,and further compared and analyzed the observed traditional classroom teaching about acute-angled trigonometric functions.And put forward research and reflection in the sixth part of the article.