What is the most important math to teach?

This morning's Register-Guard contained a letter to the editor about the cost of the war in Iraq. In the final paragraph, it computed as follows. The American population of 298 million spends $69.6 billion on the war annually. That's $2335 per person.

By coincidence, on Sunday I was in a discussion with some friends, including a former high school math teacher, about the relative importance of different aspects of mathematics. I deprecated algebra, they defended it, but in the end we agreed that statistics and probability were given short shrift in public schools.

If I'd seen this letter at the time, I would have moved another subject to top of the "most neglected" heap, namely mental order-of-magnitude calculations. In these days of ubiquitous calculators, getting the mantissa to a dozen decimal places is easy. The big mistakes tend to be orders of magnitude. You can usually catch them by some simple reality checks.

If 298 million people spend 298 million dollars, that's a dollar each. If they spend 298 billion, it's going to be a thousand bucks each. Anything less than that means less than $1000, so the Iraq War can't cost $2335 per person. In fact, it's $234 to the closest dollar. A substantial amount but, nevertheless, a tenth.

There are lots of complicated math problems presented to Oregon high school students during the CIM exams. None that I've seen are of the form, "Without using a calculator, which of the following answers makes sense?" There should be some.