TobyBartels comments on Learned Blankness - Less Wrong
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Comments (186)
Great article! I didn't realize how I blank on some of those.
I'd like to self-centeredly bring up a similar anecdote, which forms part of my frustration how people give unnecessarily-complex explanations, typically based on their own poor understanding.
In chemistry class, when we were learning about radioactive decay and how it's measured in half-lives, we were given a (relatively) opaque formula, "as if from the sky on stone tablets". I think it was
mass_final = mass_initial * exp(-0.693 * t / t_halflife)
And students worked hard to memorize it, not seeing where it came from. So I pointed out, "You know, that equation's just saying you multiply by one-half, raised to the number of half-lives that passed."
"Ohhhhhhhhhhhh! It's so much simpler that way!" And yet a test question was, "What is the constant in the exponent for the radioactive decay formula?" Who cares?
Wow, a footnote on this one and not even a link to the xkcd about it? ;-)
When I teach College Algebra at the community college where I work, one of the standard applications in the chapter on exponents and logarithms is half-life. The required text doesn't give the half-life formula above, but instead gives
mass_final = mass_initial * exp(k * t)
and shows how to calculate k by using t_halflife for t (and 1/2 mass_initial for mass_final).
This is a useful general method, but in the course of explaining why radioactive decay is exponential and what half-life means, I naturally derive
mass_final = mass_intial * (1/2) ^ (t / t_halflife),
so I just tell them to use that.
Maybe I'm cheating them because I'm making them do less work, but I like to think that some of them leave the class understanding what the heck a half-life is.