When students bring a different approach to doing math
Simple question: Does the different approach produce the correct answer? Does it WORK? Why does it work?
If a kid 'works out' that 6 x 6 = 36 by simply memorizing the multiplication table, it works. It's useful.
If a kid works out that 6 x 6 = 36 by by remembering 6 x 2 = 12 and that 12 x 3 = 36, that also works and is also useful.
If a kid does 6 + 6 + 6 + 6 + 6 + 6 on their fingers, well, that's not great, but it DOES work, and if they can do it fast enough, they can probably struggle their way to a grade C. Still useful.
If a kid thinks 6+6 is slightly more than 10, and if I do it two more times it's gonna be more-than-slightly-more than 30, so I'm gonna guess a number in the mid 30's, well, congrats on the successful ballpark figure, and if the kid actually explained how they came to that number they're, uh... pretty lazy, but their brain is actually working. Enjoy your grade F, but take solace in the fact that you are smart enough to do better if you try.
If a kid just writes 66, and when asked what the fuck they're smoking says 'SIX TIME SIX A' SIXTY SIX! IT JUS' SOUNDS RIGHT TO ME!' it doesn't work, it's not useful, and the kid is a fucking dunce.
I think the worst are the galaxy-brained mid-wits on twitter that might make some dumb argument like: but in programming, if you concatenate strings i.e. "6" + "6", then you'd get "66", so he's not wrong. I hate the 2+2=5 arguments with a passion because they are so willfully disingenuous and generally boils down to a mistranslation or redefining of terms mid-equation. 10 + 10 doesn't equal 100 just because you calculated the result in binary and then read it in decimal again.
Simple question: Does the different approach produce the correct answer? Does it WORK? Why does it work?
If a kid 'works out' that 6 x 6 = 36 by simply memorizing the multiplication table, it works. It's useful.
If a kid works out that 6 x 6 = 36 by by remembering 6 x 2 = 12 and that 12 x 3 = 36, that also works and is also useful.
If a kid does 6 + 6 + 6 + 6 + 6 + 6 on their fingers, well, that's not great, but it DOES work, and if they can do it fast enough, they can probably struggle their way to a grade C. Still useful.
If a kid thinks 6+6 is slightly more than 10, and if I do it two more times it's gonna be more-than-slightly-more than 30, so I'm gonna guess a number in the mid 30's, well, congrats on the successful ballpark figure, and if the kid actually explained how they came to that number they're, uh... pretty lazy, but their brain is actually working. Enjoy your grade F, but take solace in the fact that you are smart enough to do better if you try.
If a kid just writes 66, and when asked what the fuck they're smoking says 'SIX TIME SIX A' SIXTY SIX! IT JUS' SOUNDS RIGHT TO ME!' it doesn't work, it's not useful, and the kid is a fucking dunce.
I think the worst are the galaxy-brained mid-wits on twitter that might make some dumb argument like: but in programming, if you concatenate strings i.e. "6" + "6", then you'd get "66", so he's not wrong. I hate the 2+2=5 arguments with a passion because they are so willfully disingenuous and generally boils down to a mistranslation or redefining of terms mid-equation. 10 + 10 doesn't equal 100 just because you calculated the result in binary and then read it in decimal again.