Investigation Of The Concept Of Derivative And Related Content Learning

Calculus is the basis of higher mathematics and the beginning of modern mathematics, it’s also a powerful tool in studying function. Furthermore, calculus is widely used in other fields except mathematics, and itself contains abundant thoughts and methods.So derivative’s importance is self-evident as it’s a nuclear concept of calculus.Since the reform and open up of China,calculus has entered and come in the teaching material of senior high school. In nearest curriculum reform of senior high school, the concept of derivative established in plenty of examples is used instead of quondam formalized concept.By means of analyzing literature and the survey of questionnaire, which is designed in the basis of APOS theory and mathematical concept’s learning theory, this text studies the following three problems:(1) What’s the current situation of senior high school students in studying the concept of derivative?(2) Which problems do they have?(3)Which revelations can these problems give us.Through the analysis of data, the author finds that students have the following problems in studying the concept of derivative:(1) they can’t thoroughly understand the concept of rate of change;(2) they have difficulties in learning the formalized concept of derivative;(3) they are easily influenced by actual situations when solving problems.The revelations are:(1) teachers need to strengthen the analysis of examples about rate of change;(2) teachers can rich the actual life backgrounds of concept of derivative;(3) teachers should properly introduce the phylogeny of derivative so that students can get how knowledge produces and develops.