I’m working on a paper that will be submitted for publication. It mostly records and expands on my NCTM presentation in Denver a while back.
Along the way, I decided to a bit of looking into the claims I have made about the standard view of what it means. I did it the lazy way. Google search on “Ready for Calculus”.
See for yourself. (Click on the images to be taken to original sources on the web.)
I did find one that had a different nature.
The most important precalculus concept is the notion of a functional relationship between two variable quantities. This relationship may take many forms: linear functions, power functions, exponential functions, logarithmic functions, trig functions, polynomial functions, rational functions… Functions from these basic families may be combined, transformed, and inverted to produce still more functional forms. Functions also appear in various representations: formulas, graphs, data sets… You will have to be familiar with the basic families of functions, and all of their representations, in order to succeed in your study of calculus. The concept of function underlies everything that calculus considers.
This was nice, and if you’re at all interested in this topic, you should go read the essay in its entirety. (Don’t worry, it’s short.)
And now let’s all imagine how a community college developmental math program that took Exhibit D more seriously than Exhibits A—C would be different from the present-day state of affairs.