Senior Middle School Students' Understanding Of Trigonometric Functions

The trigonometric function is an important concept in high school mathematics. It is rather difficult for teacher's teaching and student's learning because it not only extends the study in functions but also expands the study in trigonometry. Great mportance should be attached to understanding of the essence of mathematics in mathematics teaching based on the Standard for High School Mathematics Curriculum. Therefore, mathematics teaching in high schools should try to reveal the developing process and essence of mathematics concepts, principles and conclusions. The concept of the trigonometric function differs in the descriptions and requirements in mathematics teaching material for high school and for secondary vocational school. This difference affects directly the teaching of trigonometric functions. The difference about this in teaching material is mainly embodied in defining the trigonometric function. Some definitions are based on the ending side of an angle; some definitions are based on the unit circle; some definitions give priority to the application of the unit circle and the trigonometric function lines. The difference has resulted in some arguments among teachers. The effects for student's learning, caused by these differences, need to be studied.Based on this, the following issues are mainly illustrated in this article:1. How do the students understand the trigonometric function? Can the students explain the properties of a trigonometric function using their understanding of it?2. Is it more helpful for students to understand the trigonometric function by defining it in terms of the unit circle?3. Does historical parallelism exist in students' understanding of the concept of the trigonometric function?4. Which types of errors occur when students solve trigonometric problems?The author samples 238 students of Grade one and Grade three from Taizhou Middle School and Qingpu High School and research by test and interview method. It is found that:1. Generally speaking, the students shows poor understanding of the concept of trigonometric function and they have no idea about the corresponding relations among it; but the students can solve some simple problems using the graphics of trigonometric function to get to know some qualities of it.2. The unit circle is more helpful for students to understand the trigonometric functions.3. No historical parallelism is found in student's understanding of trigonometric function.4. Students understand the concept of errors in the trigonometric functions grouped into eight types,the understanding of the nature of errors in the trigonometric functions grouped into eight types,there are four major types of errors in the understanding of the trigonometric lines.5. The students of different schools and grade understand the concept of trigonometric are significantly different.