Research On The Application Of Combination Of Number And Shape In Trigonometric Function Teaching

The combination of number and shape is an important mathematical idea in senior high school mathematics teaching,which can combine figures with algebra and broaden the idea of studying mathematics.trigonometric functions are used to portray the function model of periodic phenomena,which can fully reflect the idea of the combination of number and shape.However,it is difficult for students to combine knowledge with the thought of combining number and shape to solve problems in learning.therefore,further study on the application of the idea of the combination of number and shape in trigonometric functions teaching can help students understand trigonometric functions deeply through the penetration of the idea of the combination of number and shape in teaching,moreover,students can form an ideological method of using the conversion of numbers and shapes to solve problems.Firstly,the questionnaire and interview methods were used.On the basis of the theories related to the combination of number and shape,in accordance with the SOLO classification theory and the curriculum standards,a student questionnaire,a test paper and a teacher interview outline were designed,from which the level of students’ application of the combination of number and shape in trigonometric functions and the teacher’s penetration of the idea of the combination of number and shape were understood.Through the collation and analysis of the survey results,it was found that students lacked the habit of summarising and reflecting in the habit of doing problems.In terms of application,students were not very aware of the application of the idea of combination of number and shape,and were better at "solving shapes with numbers" than "helping numbers with shapes".The main problems students encountered when using the idea of combination of number and shape to solve problems were:inability to transform the number-shape representation and inaccurate diagramming.The teachers’ understanding of the idea of combination of number and shape was not thorough enough and they tended to mention the idea of combination number and shape in problem solving lessons.The first point is that teachers should update their teaching philosophy and enhance their awareness of the idea of combination of number and shape;the second point is that teachers should pay attention to the teaching materials in the trigonometric function chapters that contain the idea of combining numbers and shapes;the third point is that they should pay attention to the three languages of mathematics,pay attention to correspondence and transformation in teaching,and develop students’ awareness of transformation.The fourth point is that teachers should make good use of information technology and use drawing software to develop students’ graphing and diagramming skills on the basis of revealing the essence of knowledge.In addition,students should pay attention to developing the habit of summarising and reflecting,and consolidating the idea of combining numbers and shapes in practice.Finally,according to the classification of the level of application of number-shape combination and the high school mathematics textbook,the teaching design about trigonometric functions were written,and the stages of development of number-shape combination are reflected in the teaching design.