Example: The concept of velocity
* D. E. Trowbridge and L. C. McDermott, Am. J. Phys. 48, 1020-1028 (1980)
Distinguishing a quantity and its rate of change is difficult, even for students who have successfully completed calculus.
Careful studies* (including detailed interviews) show that students have trouble figuring out what the graph of a motion’s velocity will look like.