Research On The Instructional Design Of Trigonometric Function Concept From The Perspective Of Structure

The study of structure view in mathematics was first put forward by The Bourbaki school.After that,through the development of Piaget and Bruner,structure view had a great influence on the reform of mathematics education in the United States.With the failure of reform,however,the structural view has not been forgotten.This is due to the positive impact of the structural view on mathematics education,combined with the concept of the new curriculum standard and the structural characteristics of trigonometric function itself,so this paper explores the teaching of trigonometric function concept based on the structural view.Based on the above research background,the following research questions are proposed :(1)based on the structural viewpoint,what is the structure of the concept of trigonometry in high school textbooks?(2)How do students understand the structure of trigonometric functions?(3)How do teachers promote students' understanding of the structure o f t r i g o n o m e t r i c f u n c t i o n s ?(4)H o w t o d e s i g n t h e t e a c h i n g o f trigonometric functions based on the structural view?In view of the above research problems,firstly,the core concepts of structure view are summarized by literature analysis method,and it is found that structure view is of great help to promote students' mathematics learning.It is mainly reflected in the following aspects: on the one hand,the structural view emphasizes the analysis of mathematical knowledge from the perspective of the whole and connection,and holds that the whole is not the sum of the parts,and it is beneficial to deepen the understanding of mathematics to understand the parts from the whole;On the other hand,mathematical content itself has certain structural characteristics,according to the different structural characteristics of different mathematical content to analyze the problem,is conducive to students to master the essential characteristics of mathematics.Before the teaching design,the structure of trigonometric function concept in A high school mathematics textbook is analyzed,and it is found that trigonometric function is the content under the theme of function.Therefore,under the function theme,the concept structure of trigonometric function has obvious function structure symbol characteristics and function structure method characteristics.In addition,according to the theory of structural teaching design,the power function,exponential function and logarithm function are the stages of teaching structure,while trigonometric function is the stage of using structure.Secondly,through interviews with students in a middle school in Chengdu,the students' awareness of trigonometric function concept structure,the practice of structure,the learning results of structure and how they hope teachers to help them learn the concept of trigonometric function are mainly interviewed.It is found that the students generally have a certain structural awareness of the concept of trigonometry,the ability to do the structure is not good,the effect of structure learning is not good,and they hope that teachers can explain trigonometry by analogy function.And respectively in chengdu and its surrounding eight teachers to interview,interview content around teachers of trigonometric function concept in this class before class,class,after class,find the class teachers generally use structure point of view to analyze the concept of trigonometric functions,but less in the class using the structure view,also widely used structure point of view to reflect on the teaching after class.Through the above analysis,based on the structural view and structural design theory,the concept of trigonometric function is designed from the four perspectives of teaching objectives,teaching content,teaching process and teaching evaluation,and the effect is implemented and tested at the same time.The classroom observation method was adopted to observe the performance of teachers and students in class,which improved students' participation in class,created a good atmosphere,and improved students' understanding of the concept of trigonometry.Some suggestions for teaching design are given as follows: first,teachers should dig out the structural features of teaching materials;Second,the structure view should be carried through the whole teaching from beginning to end,so that it is more conducive to the cultivation of students' structural consciousness and facilitate students to master mathematical knowledge systematically.