Understanding Of High School Students In Shanghai About Radian

"Angle" is a complicated concept in school mathematics. Learning how to measure an angle is vital to the cognition of angle. Students have been taught to use degree to measure angles since they were at elementary schools. However, when students are in their high schools, they will come into contact with a completely new measurement of angle—radian. Since "radian" means using the length of an arc to measure an angle, it absolutely differs from degree measure, which causes some troubles for students during their relevant learning process. Thus, some students and even some teachers think it unnecessary to learn radian measure.This paper focus on the practical situation of radian learning of students, and raises the following questions—How well do students cognize the concept of radian and what are the main problems affecting their learning? How well can students convert between the two measurements, use them or link them to their concepts? Whether do students have deep thinking about the two measurements or compare them carefully? Whether do students bridge a link between the use of right triangle or unit circle and the concept of radian? The paper has recorded two researches aiming at students of grade two of high school according to the four questions, in order to help readers to know the students'learning practice about radian concept and raise some valuable suggestions for practical radian teaching.The paper draws the following conclusions according to the two research results:1. Students have concept confusion about radian measure, limited concept image of radian,and rarely associate radian with other mathematics concepts.2. Although students have a good command of converting one measure to the other, but they fail to realize the meaning of the convert formula. What is more, students hardly do well when the variable of a trigonometric function is expressed in radian which is actually a real number.3. When asked whether it is convenient to use radian measure, students saying "no" are almost equal to students who say "yes" in amount. However, because of their habit and the thought that degree measure is "direct", they still tend strongly to use "degree" measure. As a result, most students don't see the necessity of learning radian measure and never conduct deep compare between the two measures. Meanwhile, students' understanding of radian concept is greatly affected by their understanding of degree concept.4. When dealing with trigonometric problems, students show good familiarity with the use of right triangle, but little familiarity with unit circle. Moreover, students who master radian measure usually are able to connect unit circle with other trigonometric knowledge, and apply them to settling practical problems.Last but not least, the paper also offers some advice on advancing the text arrangement and teaching methods about radian according to the two research findings.