TobyBartels comments on Learned Blankness - Less Wrong

130 Post author: AnnaSalamon 18 April 2011 06:55PM

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Comment author: SilasBarta 18 April 2011 07:29:38PM *  28 points [-]

Great article! I didn't realize how I blank on some of those.

When I tutored math, new students acted as though the laws of exponents (or whatever we were learning) had fallen from the sky on stone tablets. They clung rigidly to the handed-down procedures. It didn’t occur to them to try to understand, or to improvise.

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?

Sandra runs helpless to her roommate when her computer breaks -- she isn’t “good with computers”. Her roommate, by contrast, clicks on one thing and then another, doing Google searches and puzzling it out.[4]

Wow, a footnote on this one and not even a link to the xkcd about it? ;-)

Comment author: TobyBartels 21 April 2011 08:05:51AM *  5 points [-]

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.