Study On Learning Trajectory Of Radian

The study of angle carries out every stage of primary and secondary schools.Students learn how to measure the angle in primary school,In high school,they learn another measurement method,Radian.Because of the great difference between the Radian and the angle system,most students have encountered difficulties in the learning process of the radian system.In order to help students understand the Radian,we need to design a reasonable learning trajectory.The problem of this paper is: what is the pre-set learning trajectory for the Radian? What is the learning trajectory designed and implemented by teachers? How to form a perfect learning trajectory? How to verify whether the learning trajectory has been improved?We mainly adopt the method of action research.Two parallel classes are selected.First,L teacher designs learning trajectory A by himself and teaches in class A.after the teaching,L teacher and researcher analyze and discuss the classroom teaching;According to the test results and students' knowledge mastery.Then,L teacher designs a new learning trajectory B again,teaches in class B and tests again after class.We analyze and compare the students' performance in class with their test results,and finally get the optimized learning trajectory of Radian:First,recall the meaning of 1-degree angle,analogize the length of mass,get the angle and other representation methods.Through the clock of different sizes in life,we think that the angle may be related to the arc length and radius,and abstract the concentric circles of different sizes from them.With the intuitive data,we can get that the larger the angle is,the greater the ratio of the arc length to the radius is.Then the arc length formula under the angle system is used to test the conjecture,so as to define the angle of 1 radian: the center angle of the arc whose length is equal to the radius length.Then guide the students to transform the angle and radian,get the conversion formula from the center angle of the circle circumference,and let the students master the mutual transformation of radian and angle through simple exercises.The area algorithm under radian system is obtained by analogy with the algorithm of sector area,which guides students to summarize the function of Radian: to realize the function of simplifying formula.In addition,the latter learning trigonometric function usually takes the angle as the independent variable,but the independent variable in the periodic phenomenon is not necessarily the angle,which explains the rationality of selecting the Radian and embodies its advantages.Based on the above results,we propose the following suggestions:(1)in the compilation of teaching materials,it is necessary to avoid directly giving the definition of radian system,and to organize and design exploratory activities for students to explore by themselves.(2)Teachers should combine the history of Radian and make appropriate adjustment to explain the generation process of knowledge.(3)Teachers should adhere to the combination of intuition and abstraction.