Trigonometric Functions Based On Apos Theory Teaching Design Research

Trigonometric function is the last basic elementary function in thehigh school stage, it is not only a further understanding of the functiondefinition, but also a further deepening of the periodic function andfunction thought. In actual teaching, the trigonometric function is oneof the difficult mathematical contents for students to understand. Soteachers are highly required in teaching.This paper tries to analyze andresearch trigonometric function teaching based on the mathematicslearning theory---APOS idea which was put forward by themathematics educator Dubiuskey. Therefore, this paper focuses on howto optimize the teaching process of trigonometric function by using theAPOS theory. Meanwhile it proposes some related teaching mode,teaching design, etc.The content of the paper is mainly divided into six aspects: First, itaims at the comprehensive analysis and research of the relatedliterature of APOS theory, finding that APOS theory, which is a learningtheory with mathematical subject characteristics, provides a model formathematics teaching. Second, it aims at the analysis and research ofthe status quo of teaching and learning of trigonometric function,expounding the feasibility of application and necessity of the APOStheory in the teaching of trigonometric function. Third, combining APOStheory with trigonometric functions teaching, it aims at the constructionof the teaching mode of trigonometric function structure diagram andimplementation process, providing theoretical guidance for thespecific teaching design. Fourth, in the direction of the APOS theory, itaims at the six typical case teaching design in the teaching of trianglefunction, reflecting in the practice and making it a paradigm ofteaching. Fifth, it aims at the analysis of students’ common barriers instudy in the practice of teaching, putting forward the strategy to solve so that teachers can make the teaching design more close to the levelof students cognition. Sixth, it aims at the experience of the differencebetween theory and practice in the process of teaching of theapplication of the APOS theory, pointing out such problems as thelimitations of the application of the theory.This paper focuses on the teaching mode of the trigonometricfunction, teaching design, students learning disabilities andcorresponding solutions under the guidance of the APOS theory so thatwe can find the linking spot between teaching and learning which ismore adaptable to the development of the students when exploringthe new teaching theory and teaching mode, and can provideteaching reference for the high school trigonometric function teaching.