Critical Thinking, an oxymoron

"Facts are quick to teach: The capital of New York state is Albany. Critical thinking is time-consuming to teach and involves provoking students to wonder why, for example, the capital of New York state is Albany" is quoted from a blog in the New York Times, after a "Dead Prez’s tirade" anonymously.

It is curious that asking why(?) Albany is New York's capital is regarded as critical thinking. What's so critical about it? Without knowing how to look up some history, without knowing how to spell, without knowing how to use the internet and library, why would someone think that the problem can be "solved" using thinking? Critical thinking in mathematics makes sense in the solitude of one's brain, but "critical thinking" about an historical oddity doesn't make sense.

Sometimes "critical thinking" in a social context is thought to be somehow thinking outside the box about social problems to suggest solutions which are "off the wall" different. In some sense or other, this is truly thinking, although falling in love with one's own suggestions implies that it is difficult to consider more than one option for a solution model.

But thinking remains the hardest thing we do. It takes focus to keep ourselves involved in thinking, critical or not. It takes discipline. It's wearying, and distractions abound to seduce one into day dreaming or some other mental activity other than real thinking.

We teachers are faulted for "teaching to the test", but, the tools of thinking are necessary but not sufficient for "critical thinking". Thus mathematics, physics, and chemistry thinking requires that one not think about arithmetic! Thus the tool of arithmetic is a necessary but not sufficient precursor of thinking about engineering or biology or any other quantitative subject.

Now when one thinks about truly elementary arithmetic, one easily concludes that either one learns it through practice, practice, practice, or, one never gets to Carnegie Hall (arithmetically speaking). Today, I had a student divide 10^{10} by 10^{16} and decide that the answer was negative. That's serious; this is a student who was maleducated in grade school and/or high school, who is now floundering in a course which assumes that this kind of arithmetic is beyond elementary. It's trivial and shouldn't cause a college student any trouble what-so-ever. Worse, the damage that's been done to her is irreversible. It can't be undone. She may be happy with herself, but I'm not happy with her. And I'm sure when she's a mother, her children will end up maleducated also.