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As an important public basic course in higher vocational colleges, higher mathematics is not only the foundation of learning other specialized course, but also it is an important carrier of the training of students' comprehensive quality. However, about the teaching of higher mathematics in higher vocational colleges in our country, the teaching arrangement and teaching methods can't pay attention to the cultivation of students' ability to solve practical problems. The majority of students believe that mathematics is useless so that they are not interested in the studying of higher mathematics. Combined with the teaching book Calculus: Early Transcendental (5thed) of foreign high-quality vocational education resources,About the concept of derivative, for example, we carry on comparative analysis to higher mathematics teaching of Chinese and foreign higher vocational colleges, then put forward an important enlightenments on the higher mathematics teaching in higher vocational colleges in our country. Higher mathematics as a basic public required course in higher vocational colleges, on the one hand, it is the important foundation of students' learning related professional knowledge; on the other hand it plays an important role in improving students' comprehensive quality and cultivating students' learning ability. Higher vocational education in China started relatively late, higher mathematics teaching in higher vocational education mainly follows the teaching methods of ordinary colleges and universities. Textbooks generally are concise editions of Higher Mathematics teaching materials of ordinary colleges and universities. The arrangement of teaching material and teacher's teaching reflects the characteristics of heavy theory, light practice. At the same time, not pay attention to train the students’ ability of applying mathematical knowledge to solve practical problems, thus easy for students to produce the concept of "mathematics is useless", and can't arouse the students' interest in learning higher mathematics. A survey found that the majority of our students do not know how to make full use of the knowledge of mathematical to solve practical problems after school, even if it is a very simple math problem, they would ask for the help of professionals. The reason is mainly because of lack of some good training during the school, along with lack of the awareness of the applying their own learning mathematical knowledge at the university to the practical problems life. Abroad Higher Mathematics Teaching in terms of the arrangement of the materials or the method of teaching is more attentive to mathematics awareness of students, and relations between mathematics and everyday life. In the teaching and practice, for example, choose some things students are familiar with. Focus on the cultivation of the students' ability to use the knowledge of advanced mathematics to solve practical problems. Combined with the teaching book for foreign high-quality vocational education resources ,Calculus: Early Transcendental(5thed),which is written by James Stewart ,Bai Fengshan mainly translated. Teaching of the concept of the derivative as an example, higher mathematics teaching methods of Chinese and foreign vocational colleges were analyzed and propose a significant enlightenment to Higher Vocational Mathematics Teaching in China. Derivative is the foundation of calculus, and an important tool of study the function to solve practical problems. The definition of the concept of the derivative in textbooks of higher vocational college in China is similar. First is the case, slope of the tangent and speed of non-uniform motion International Conference on Education Technology and Information System (ICETIS 2013) © 2013. The authors Published by Atlantis Press 874 are usually used, and then directly cut into the theme of explaining the concept of the derivative. Emergence of the cases is very stiff, and fewer teachers explain the relationship of the cited cases with derivative, even a beginner often does not understand cited cases appear here. After the introduction of the concept of derivative is the derivative calculation method, the whole process is boring, does not reflect the value of the application of mathematics. This way of teaching is not conducive to the cultivation of students' consciousness about the application of math, and students cannot establish a contact between math with the issues in real life .What is worse, in the future work and life it is very difficult for them to be able to think of the derivative as a good method to solve some practical problems. For that, on Calculus: Early Transcendental (5thed) written by James Stewart, the definition of the derivative has a good reference. James Stewart first lists lots of examples, which were involved in various fields, to fully reveal the nature of derivatives, so that readers can fully grasp the essence of derivative and its application value. On the basis of the above, draws the concept of derivative, then go back and then further exploit the meaning of derivative to solve practical problems in all areas of life. The process of James Stewart arranging the concept of derivative is introduced is as follows: firstly, the introduction of instances: (1)Tangent: Suppose the equation of the curve C is ) (x f y = , find the tangent of C at the point )) ( , ( a f a P , first find a point a x x f x Q ≠ )), ( , ( in the vicinity of the point P, calculate the slope a x a f x f mPQ − − = ) ( ) ( of the secant PQ , When x approaches a, namely the point Q approaches the point P, If PQ m approaches a constant m, then the straight line m passing through the point P is a tangent. (2)Speed: Suppose equation of motion of the object along the linear motion is ) (t f s = , the average speed from 1 t to 2 t is 1 2 1 2 ) ( ) ( t t t f t f − − , when 1 t Approaching 2 t , average speed is the instantaneous speed of the object in time 1 t .That is ( ) 1 2 1 2 1 ) ( ) ( lim 1 2 t t t f t f t v t t − − = → . Cited cases for the concept of the derivative in our country's teaching material will stop here, then the concept of the derivative should be the introduced, generally later the relationship between the derivative and other practical problems will not be mentioned, and instead of putting forward the concept of the derivative, James Stewart continues to introduce instances so as to further guide the students to fully reveal the nature of the derivative. At the same time, continue to introduce examples from physics, chemistry, biology and psychology. (1)Application in the field of physics: The instantaneous change rate of mass (linear density of the non-uniform rod ρ ), the instantaneous change rate of the power through the wire (instantaneous current intensity I ), the instantaneous rate of change of the temperature of the object (instantaneous cooling rateT ), and the like. Linear density of the non-uniform rod:Has a non-uniform thin rods, take the end of bar as the origin, the distribution for the coordinates of any point on the rod is in the interval [0, x], the mass m of stick is a function ) (x f m = of x, The mass of the rod lies between 0 x x = and x x = is ) ( ) ( 0 x f x f = , average density of this part of rod is 0 0 ) ( ) ( x x x f x f − − whose limit is rate of change of the mass of the rod under 0 x with respect to the length, when 0 x x → , that is the linear density of the rod at the point 0 x namely ( )

Based on the comparison of Chinese and foreign teaching methods of Higher Mathematics in Higher Vocational Colleges ----- The concept of the derivative as an example