An examination of the major concerns, a public view of, practical applications, examples, probability theory and number theory.

Clearly, then, helping high school and early college students achieve mastery of complex subject matter such as calculus frequently requires more than a cursory understanding of how young learners acquire and retain knowledge and what processes serve to facilitate this acquisition and retention. For instance, in their study, Conceptual knowledge of introductory calculus, White and Mitchelmore (1996) point out that, Research into the understanding of calculus has shown a whole spectrum of concepts that cause problems for students. In particular, student difficulties with the abstract concepts of rate of change and function are well documented. These concepts involve mathematical objects or processes specific to calculus. Another aspect that needs to be considered is the question of what other concepts are involved in applying calculus knowledge (p. 79).