Well how do you think the rest of us memorized them?
The problem with tricks is that it takes a while to locate the right one to use. Since we’re in a base-10 system, I find it much easier to not only know your 10-families (8&2, 5&5, etc.) but to know your 5 families (4+1, 2+3). When I see those “bastards” like 8+5, I see the 8 as 5+3 and simultaneously as 10-2. So I can see that there’s a 3 that shouldn’t disappear from my answer. The problem I find with tricks like the doubles is that 14 is a useless number. It’s not round at all. So when you get something like 234, can you easily see that it’s 220+14? Not really. But a number will always be in base-10 so the tricks will never change.
All I’m really saying is to train not only on 10s but on 5s too, so that 8+5 or 3+6 isn’t a bastard at all.
I don’t know; the implication perhaps is that they were memorised by rote.
…and I’m not actually saying that’s a bad thing. I just joined the debate to make two points:
Not memorising the times table is not necessarily crippling. I never made an effort to memorise the times table and yet I’ve always been very fast at completing maths tasks/exams and have done very well academically in that area. (I don’t mean to be big-headed but it’s necessary in the current debate).
If memorising maths “facts” pushes out teaching aimed at manipulating numbers comfortably, then I think the priorities are wrong. Children should be aware that maths is logical and that you can often find a solution multiple ways just by reasoning out a problem.
My husband and I were just discussing this a little while ago, so here’s my thought. Of course kids need to know that math is logical and that you can take the numbers apart and play with them a lot of different ways. We always teach the logic of the math facts when we do each batch, and I presume everyone else does too. What you do is grab your manipulatives, play around with them and have the kid work out each set, then do a lot of repetition for memorization.
But what I’ve noticed with my kid is that once she has material learned well–say the addition facts (since we’re still working on quick retrieval of times tables)–she starts being able to play with the numbers on her own, in her head. She starts telling me ways she’s found to do that. Real understanding and mastery seem to come after repetition and memorization and long use. My husband, a math and physics whiz, commented that you have to know the scales before you can jam. If you have the basics down bone-deep, you can play freely.
FWIW, last night while going over multiplication tables with my 8 year old, I pointed out to her that n[sup]2[/sup] - 1 = (n+1) * (n-1). She was enthralled. I tried to prove it to her algebraically, but that was a little beyond her. But you definitely can find neat mathematical principles like that just from the times tables.