The use of a graphing calculator is considered an integral part of the AP Calculus course, and is permissible on parts of the AP Calculus Exams. Students should use this technology on a regular basis so that they become adept at using their graphing calculators. Students should also have experience with the basic paper-and-pencil techniques of calculus and be able to apply them when technological tools are unavailable or inappropriate.

(From The College Board's AP Calculus calculator policy.)

Yesterday's post was about a sticky tech issue. This one's more about ideology.

Fierce debate raged in the 1990s over whether graphing calculators should be used in mathematics education at all. Proponents thought graphing calculators opened new vistas of understanding, as students could play and experiment, and see instantly how functions are affected by different tweaks. Detractors said graphing calculators killed the ability to work things out by hand; that they're a crux, and true understanding is only obtained by pencil-and-paper repetition of the proper methods.

Arguably, the issue ended (in the United States) with the AP test adoption of the graphing calculator. What resulted was a deeper and more difficult test; not only did students still need pencil and paper methods, but they had to apply the calculator to answer higher-level questions.

(No, not every student will make it to AP classes, but I believe curriculum should be written with the assumption that some will.)

However, the issue never truly died, because there was (and still is) a hidden ideological struggle going on:

Should our primary focus in algebra be on symbolic manipulation, or is visualization and synthesis an important aspect?

In other words, are graphical methods and applications just an afterthought?

While this doesn't seem to relate directly to social technology, the interesting enhancements computers can offer don't attract the interest of a symbolic-manipulation-only teacher. Alternately, graphing calculators can be thought of as the gateway application -- take a teacher comfortable with them, and it's easy to hook them on related Internet apps. For the Internet to be truly useful, teachers need to see there is a world beyond factoring binomials.

So, if you're a technology coordinator with a resistant math department, there's one question you might ask: are there teachers who haven't taken their class set of calculators out of their boxes? If so, there might be more going on than mere tech resistance.

Jason Dyer, Guest Blogger