A couple related thoughts: I'm coming to this largely because of how many of my students in any class (even sophomore statistics) get helplessly tangled up over something as simple as an if/then statement. Or a subset relationship (e.g., normal curves are bell-shaped, but bell-shaped is not the same thing as normal). Or an "and" statement (the z-interval procedure requires a simple random sample, known population standard deviation, and a normal sampling distribution of the mean... the last of which can be established by either a normal population or a large sample size).
I'm reminded of my first programming book in the 6th grade which introduced "and" and "or" operators and just said, "the meaning of these should be obvious", with an example of each. It may not be a priori obvious to everyone, but it really shouldn't take very long, and could pay off enormous benefits later.
Coincidentally, I just came across a delightful blog post by John Barnes on the same subject titled, "The Hobo Queen of the Sciences". Here are a few terrific highlight quotes:
And then I got Ms. Pounding Shouter... She thumped the podium, she pointed at people and accused them of not understanding her, she ordered them to believe what she told them to... "I was totally logical. I pointed things out real loud and told people they were dumb if they didn't believe it, and I yelled so they'd get the point."And also:
Last and far from least, in a related course where I used to teach listening for logic as a way of improving listening comprehension and retention, one student asked me at the end of the class, "Why wasn't I taught this in fourth grade?"
Of course, to his credit John goes on to explain the vested interests that don't want fourth-graders -- or jury members -- knowing the basics of logic and reasoning.
Read it here.