aera-l | "Although about 70% of students entering the non-calculus-based Indiana University (IU) courses . . . . have completed a university calculus course, almost NONE SEEMS TO HAVE THE FOGGIEST NOTION OF THE GRAPHICAL MEANING OF A DERIVATIVE OR INTEGRAL. Similar calculus illiteracy is commonly found among students in calculus-based introductory physics courses at IU. In my judgment, these calculus interpretations are essential to the crucial OPERATIONAL DEFINITIONS of instantaneous position, velocity, and acceleration: the term 'substantive non-calculus-based mechanics course' is an oxymoron."
Regarding Guy Brandenberg's recommendation of Berlinski's (1997) "Tour of the Calculus," The publisher of that book states: "Were it not for the calculus, mathematicians would have no way to describe the acceleration of a motorcycle or the effect of gravity on thrown balls and distant planets, or to prove that a man could cross a room and eventually touch the opposite wall. Just how calculus makes these things possible and in doing so finds a correspondence between real numbers and the real world is the subject of this dazzling book by a writer of extraordinary clarity and stylistic brio. Even as he initiates us into the mysteries of real numbers, functions, and limits, Berlinski explores the furthest implications of his subject, revealing how the calculus reconciles the precision of numbers with the fluidity of the changing universe."
Compare the above with to Susan Ohanian's "I never seemed to gain any insight from this exercise. . . . [[of solving calculus problems in Courant's text]]. . . , which struck me then as plodding and now I don't have any idea what any of it means."
