Research On The Teaching Of Inversetrigonometric Functions Based On Thinking Visualization

In recent years,with the deepening of teaching reform,the teaching methods and ideas of mathematics classroom are also constantly improved.Mathematics classroom should take students as the main body.Teaching ideas should cultivate students' mathematics core literacy and cultivate students' ability to use mathematics,analyze practical problems and solve practical problems,not just problem-solving ability.At the same time,as a high school content with certain difficulties in teaching and learning,inverse trigonometric function is also worthy of in-depth study by front-line teachers on how to better enable students to understand and use the content of inverse trigonometric function.In order to cultivate students' core mathematical literacy,guide students' learning methods and better teach the chapter of inverse trigonometric function,the author decided to carry out the teaching research of inverse trigonometric function with thinking visualization as the teaching idea.In order to design the teaching course of thinking visual inverse trigonometric function with specific practical value,this paper studies the following three problems,including(1)what is the situation of senior three students in concept understanding,problem solving and learning emotion before completing the first round of inverse trigonometric function review(2)After completing the teaching of inverse trigonometric function developed with the concept of thinking visualization,what changes do students have in the above three aspects(3)What are the opinions and suggestions of senior high school front-line teachers on the anti trigonometric function course developed with the concept of thinking visualization?Firstly,35 questionnaires were distributed to a demonstration experimental high school in Shanghai,and 35 valid questionnaires were recovered.Through the analysis of the data collected in the questionnaire,the following conclusions about students' concept understanding,problem solving and learning emotion were obtained:(1)In terms of concept understanding,after completing the course of inverse trigonometric function in senior high school,senior high school students do not have systematic review and training before the first round of review in senior three.When students are required to describe the geometric meaning of specific arcsine,it is very easy to omit restrictions such as "range in" and "sine value is",This shows that senior three students do not fully grasp the definition of inverse trigonometric function,and students also encounter obstacles when making the image of inverse trigonometric function.The reasons for this are unclear,do not know which definition domain to construct the inverse trigonometric function,and do not know the relationship between the original function and the image of inverse function,which belongs to the learning situation of the chapter of inverse function.(2)In terms of problem solving,it can be found from the correct rate of problem solving of senior three students that the insufficient mastery of the definition has a great impact on students' problem solving,because most of the inverse trigonometric function problems need to take into account the definition domain and other constraints,and one third of the students complete the trigonometric ratio and range of the known angle and calculate the angle,It does not consider the limitation of the inverse trigonometric function on the range of angles,but directly applies the inverse trigonometric symbol,and a few do not know how to solve the problem directly.(3)In the aspect of learning emotion,nearly one third of the students expressed their incomprehension and learning difficulties for the inverse trigonometric function.Then,this paper involves four courses with the teaching objectives of improving students' learning emotion,concept understanding and problem solving,and the themes of what is mind mapping and how to use it,the application of mind mapping in function review,the application of mind mapping in inverse function review and the application of mind mapping in inverse trigonometric function review,Classroom practice was carried out,35 students participated in the course practice,and one teacher attended each class.In order to understand the course effect,five students participated in the course practice were interviewed after class.It was found that the students had improved in learning emotion,concept understanding and problem solving,and achieved the expected effect of the course.Finally,this paper interviewed the teachers who participated in the research.All three teachers expressed their support for the thinking visualization course.At the same time,they evaluated the course designed by this research as "if students can better master the thinking and learning methods of thinking visualization",and said that it is worth looking forward to the development of basic courses.This study also gets some educational enlightenment.The four thinking visualization courses designed are included in the appendix for readers' reference.