I find that most of my students aren't terribly concerned with why things are the way they are in mathematics. I am of the opinion that this is because when students ask why questions when they are young, they don't get answers. If they ask "why is a negative times a negative a positive" they get an answer like "just because," or, if they are home-schooled, "because I said so." I'd like to discuss some of those why topics in math, most of which I don't think are asked that often.
Little known math fact: When you divide by a fraction, you multiply by its reciprocal. I say "little known" because every student ever forgets this fact from one day to the next. Maybe, just maybe, if they understood why you multiply by the reciprocal they'd remember. Putting equations in a blog is pretty hard, so I am going to get a bit tricky:
Little known math fact: When you divide by a fraction, you multiply by its reciprocal. I say "little known" because every student ever forgets this fact from one day to the next. Maybe, just maybe, if they understood why you multiply by the reciprocal they'd remember. Putting equations in a blog is pretty hard, so I am going to get a bit tricky:
If
I show this to my students, I let them know before and after showing it that
they don’t need to “get it,” but it’s worth seeing. For a couple students it
makes sense (and they seem to find it clever, and hopefully deepen their
appreciation of the subject). I was never taught this, I was nerdy enough to
look it up. Now I know why.
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