Research And Analysis On The Implementation Of Trigonometric Function Teaching Design Based On APOS Theory

Trigonometric function is a kind of basic and important function in senior high school.It has a full and wide application in various fields,including production practice,other disciplines and mathematics.At the same time,trigonometric function learning is a further understanding of the concept of function.Compared with exponential function,logarithmic function,power function and other basic elementary functions,trigonometric function is a special function that can depict periodic changes in the real world,such as the vibration and propagation of waves,electrocardiogram,the fluctuation of tides and the problem of spheres,which are closely related to trigonometric function.According to historical records,the early development of trigonometric function is closely related to astronomy.In the high school mathematics course,trigonometric function is a knowledge point which must be mastered and required to be skillfully applied.Therefore,the research on trigonometric function has its profound historical value and practical application value.With the deepening of the new curriculum reform,"what kind of people to educate,how to teach" is an urgent problem for educators.From the perspective of mathematics,the requirements of mathematics core literacy are put forward in the "mathematics curriculum standards for ordinary senior high schools".More importantly,As practical teachers,we should think about how to design teaching reasonably in order to achieve the improvement of students' mathematical ability and accomplishment,and how to implement teaching in order to achieve such educational purposes.It is in line with the students' psychological process of learning mathematical knowledge,and closely in line with the way learners construct knowledge structure.Therefore,the author studies the teaching content of trigonometric function based on APOS theory.In this paper,the methods of literature research,questionnaire survey,individual interview and comparative study are used to design and implement the teaching content of trigonometric function based on the theoretical basis of APOS.The experimental group and the control group are set up to carry out the teaching design under the guidance of APOS theory,and the experimental results are compared and analyzed.The author has distributed 110 questionnaires,and effectively recovered 104 and based on the APOS theory,this paper analyzes the students' understanding level of trigonometric function,and evaluates the implementation effect of instructional design effectively.The conclusions are as follows:(1)the APOS theory has a positive guiding value for the instructional design of trigonometric function;(2)The teaching based on APOS theory can promote students to understand the generation of any angle,the arc system and the application of trigonometric function of any angle and its properties;(3)The learning process is divided into four stages:activity stage,procedure stage,object stage and schema stage for teaching design and explanation,which effectively promotes students'understanding of the four cognitive states of mathematical knowledge:perception,formation,understanding and improvement of mathematical knowledge.