3 ms·

What's the formula to calculate the volume of a conical pyramid, off the top of your head? I learned that in grade 5, was drilled on it, haven't had to know sin

by flukus 7y ago

What's the formula to calculate the volume of a conical pyramid, off the top of your head? I learned that in grade 5, was drilled on it, haven't had to know since and no longer remember. A small example but one I think is fairly representative of at least 50% of what I learned in school. We waste a tonne of time teaching very specific things of limited use, formulas, dates of historic events and busy work like plotting exponentials on graph paper and long division, there's a lot of room to be teaching higher level concepts instead.

saagarjha 7y ago
The volume of any pointy thing is the area of the base times the height divided by three. It’s not necessarily the most useful thing I know, but I do use it from time to time. (Disclaimer: I did math competitively in grade school, so I have a lot more formulas burned into my head than I’d expect most other people to know. That doesn’t mean I don’t think people should forget how to do simple math like solve a linear equation in one variable, calculate interest, etc.)
gwd 7y ago
> What's the formula to calculate the volume of a conical pyramid, off the top of your head? I don't need to know the formula off the top of my head; I need to know what a conical pyramid is, what volume is, what a formula is, and how to use it. I guarantee that between me and someone who's never done geometry at all, I can find the volume of a conical pyramid faster and more reliably. You're right that memorizing specific formulas isn't useful; but using a large number of formulas over and over to gain mastery over the general idea certainly is.
- saagarjha 7y ago
  Deriving the formula for the volume of a pyramid manually is nontrivial, usually requiring either calculus or careful application of Cavalieri's principle. I know how to get it but it's not practical to do on the spot, so I treat it as an idiom.

by flukus 7y ago

saagarjha 7y ago

The volume of any pointy thing is the area of the base times the height divided by three. It’s not necessarily the most useful thing I know, but I do use it from time to time. (Disclaimer: I did math competitively in grade school, so I have a lot more formulas burned into my head than I’d expect most other people to know. That doesn’t mean I don’t think people should forget how to do simple math like solve a linear equation in one variable, calculate interest, etc.)

gwd 7y ago

> What's the formula to calculate the volume of a conical pyramid, off the top of your head? I don't need to know the formula off the top of my head; I need to know what a conical pyramid is, what volume is, what a formula is, and how to use it. I guarantee that between me and someone who's never done geometry at all, I can find the volume of a conical pyramid faster and more reliably. You're right that memorizing specific formulas isn't useful; but using a large number of formulas over and over to gain mastery over the general idea certainly is.

saagarjha 7y ago
Deriving the formula for the volume of a pyramid manually is nontrivial, usually requiring either calculus or careful application of Cavalieri's principle. I know how to get it but it's not practical to do on the spot, so I treat it as an idiom.