Once again, folks on the MTBoS (Math Twitter Blog-O-Sphere) are railing against the evil and horrible TRICKS.
When I”m working with adults, and they’ve got a “trick,” and I give them a complex abstract explanation, what will they remember?
I was asked about using tricks as bridges adn this one came to mind: Dividing fractions.
“Copy, Change, Flip.” If it’s in utter isolation, yes, it’s pretty darned meaning less. *However,* so are the other things the students memorize to get through.
However, in our pre-algebra curriculum they’ve already learned that 7 – (-3) is 10 … and while we do spent a *lot* of time working with number lines and the “opposite” concept, they don’t necessarily remember that as well as they remember “Keep CHange Change.”
Starting from a position of confidence means they can look at the problem and figure out *why* the answer is right instead wondering if the answer is right.
Now, how abstract I get with explaining that division by fractions is similar to adding negatives depends on the student, but that idea that “hey, remember 7 – -3 being the same as 7 + 3? [golden review opportunity!] This works like that. Subtraction is the opposite of adding, negative is the opposite of positive… welp, division is the opposite of multiplying and the reciprocal is the opposite of a fraction — they’re the things that undo each other.”
When I rule the world, we’ll spend a lot more time figuring out what ‘half of” things are and why that’s the same as dividing by two — and then that dividing by a half is the same as multiplying by two – than ridiculous things like figuring out how many 3/4 yards can be cut from 27 4/7 feet, just sayin’… again, providing lots of examples that actually make sense so that students can figure out why an answer is right instead of trying some strategy they just wish for being right..