High School Seniors Calculus Cognitive Level Of Thinking On Research

Calculus is the foundation of high mathematics. Derivative and integral calculus are the fundamental concepts of calculus. Some contents related to derivative have become the key elements of math teaching in senior school. From the past practical teaching experience, this part is also difficult in teaching. The research of the cognitive process of high school students in learning calculus is worthy of attention in math education. This paper will view derivative as a carrier and test four ordinary classes in two high schools in Beijing. The author finds that:(1)Obvious gender differences exist in grasp of some contents of derivative: boys show more initiative than girls;(2)For students ,the grasp of the low-level thinking (operation) in derivative is good. The girls seem slightly better than boys;(3)The grasp of the high-level thinking of some contents of derivative rely much more on the low-level thinking (to get the conclusion from past experience ,few people can give proof from the concept directly).(4)Reinforcement learning(review)shows obvious effect of improvement in students'grasp of low-level thinking ,but ineffective when it comes to the high-level thinking.