Not just “Multiplication Facts”
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I recently read a post on another blog concerning the two most important elements that children should master in math in order to succeed. The author suggests that basic skill with multiplication and basic mastery of fractions are the two essentials.
I am of the same opinion. The author also thinks that memorization and drills are the best way. On that, I’m not so sure. Yes and no.
Here’s my take:
Although mastery of multiplication is essential, “memorization” is not the only (nor is it usually the best) way.
We like to lull ourselves into a false sense of righteouness (which seems to be turning into the new national pass-time) by talking about “multiplication facts,” or “getting back to basics.” “Just give me the facts…”
Well, “just the facts” is worthless unless you have a way to process and understand those facts. The “tables” and “charts” don’t teach anything about understanding. Some people learn with them. Fine. But not everyone does, and that is fine, too. The people who seem to learn best don’t rely on them, though.
In countries where the children demolish American kids at math (Like Russia, China, India and many others) children were never shown any “tables.” They learned either by repeated addition, or with one of the best manipulatives of all - an abacus.
In recent decades, even those countries have stopped using abacii (mostly because of trendy calculators) and the average student’s skill with basic math there has decreased.
Just because the term “manipulatives” has become a trendy catch-phrase for companies that want to squeeze as much money out of school districts as possible doesn’t mean that all manipulatives are silly.
Furthermore, it is true that we must remember basic math facts, but it is not true that the best or most efficient way is to drill tables. Rote memory is counter-productive for a lot of students. If it weren’t, we’d have had at least one generation of students who’d have 100% mastery of the tables. But that never happened.
As for “memorization,” as a teacher of memory-techniques, it never ceases to amaze me that we require kids to memorize this or that, but we seldom teach them how. Makes you think, doesn’t it? We should require that children remember things, and then teach them ways to do that. Rote memory and drills is usually not the best way.
Are you afraid of snakes? You never forget to be afraid of them, do you, yet you didn’t have to spend much time drilling to remember that you don’t like snakes. This is not the time for me to go into how to remember things (that is a huge, but fun, topic) but it needs to be at least mentioned that there are lots of techniques that you might look into.
Teachers must realize that although child-based learning (a kind of “constructivism”) is not a very good solution, there are still other ways of attacking problems. One-size-fits-all is never true (ever buy anything that was one-size-fits-all that actually fit well?)
Not all alternative solutions are “child-based,” either (as witnessed by the abacus).
To wrap up - Skill with multiplication is not just a matter of drilling “the multiplication facts.” As you must know by now, my favorite method for teaching basic multiplication (and one that is almost universally enjoyed and easily learned by children and adults) is taught in my booklet. “Numbers Juggling - Times Without the Tables.” This booklet teaches without tables (hence the name) and you can learn, or learn how to teach the multiplications from one to ten in a day.
It’s not “child-based,” it’s not “information based,” or “fact-based.” Yes, it takes all of those things into account, but it is a total system for learning and understanding basic multiplication. I guess that makes it “multiplication based.” Imagine that! Learning multiplication by learning multiplication. No trendy theories, just the goods.
Tags: learning multiplication facts
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Comment by Khaled
I’ve never been a mathematics teacher, but I always enjoyed the subject in grade school and enjoy “juggling numbers,” just for the fun of it, even now while I’m in grad school.
In my own experience, memorizing tables as a child worked quite well for me. I can see that it doesn’t have to be one-approach-fits-all, though.
Comment by MommaKnows
I agree wholeheartedly! There is a place for drill. Drill does help with automatic recall of the facts. But all kids learn differently, and drill isn’t always the best way to learn it in the first place. I have homeschooled for ten years, and am a firm believer in teaching to learning styles. One of my daughters learned her multiplication facts through stories. Ex: “I ate (8) and (x) I ate (8) and I got sick for (64) a week!” She learned ALL of her math facts in three short sittings, this way. Another child learned them using manipulatives (Math U See curriculum is wonderful!) and another, just the facts, ma’am. We use short timed drills from time to time for all, but each learns their own way. I am interested in checking out your book. :)
Comment by Nick
I’m sorry to contradict you, but as learned in USSR (now Russia) - we do learned there by the multiplication table!
It was called “Pythagoras table”.
And if you buy in Russia the student notebook for doing math you always have the mult. table on its back cover.
Comment by Brian
Nick,
I love to be contradicted if I can learn something from it! Thanks for setting me straight.
I had a friend from Russia who was a math professor, and she said that when she was a kid they had other methods for learning the tables, and multiplication in general. There was a special Russian abacus (I’ve seen it elsewhere, too) and sometimes used what I’ve heard called, “the Russian peasant method,” and they didn’t obsess on the tables, as schools tend to do here.
I wonder what the factors are that make Russian students generally so much better than Americans at basic math. Got any Ideas? I’d love the input.
There have been reports that Chinese, Japanese, and Indian students are not as good with basic math as past generations were, since the use of abacii has declined and the use of calculators has gone up.
On the other hand, the somewhat-recent Japanese craze of the ancient art of Anzan (mental math using an imaginary soroban) has produced loads of kids who are amazing calculators.
Comment by Tom Biesanz
There are fun ways to learn chunks of the multiplication table (The Threes, The Sevens, The Eights, etc.) from patterns that give a bigger picture. Check out MisterNumbers on Youtube. It is amazing. The overview and patterns in Right Brain Math help lock in learning and understanding. There is also the EZ Times Table that allows kids to create the whole times tables from patterns.
Professor Homunculus sez:
I’m not exactly sure what to do with this kind of comment. Technically it is “spam.” A blatant unsolicited advertisement. Although I sell products as well, I know it is really bad form to just go to other people’s websites and drop my advertisement on it without even so much as commenting on the post.
But I’ll let this one go because of a few factors.
One, the product is a bit interesting. I can’t say I’d ever endorse something like it, but the method is a least a bit of a mild diversion.
Another factor is this - since the commenter has opened himself up for it, here’s my take on it:
This is exactly the kind of pap method of talking down to children without actually teaching them anything that I eschew. I’m sure “Mister Numbers” is a nice guy, but the old “See-kiddies-math-can-be-fun” bit only works for kids who would accept any old method anyway.
Although the actual method is interesting, I think the only actually interesting thing about it would be the explanation of why it works. That would only work for people who are way past the stage of learning simple multiplication, though. The method itself is just as complicated as memorizing tables.
There’s no serious streamlining, and the methods are not extensible. You need a different method for each of the digits. Cute, but not really effective.
The specious claim of “right brain” math appears pretty flimsy, as well.
So, Tom, I’d be happy to have some readers check out your site and decide for themselves, but next time, I wish you’d show a little more “netiquette” before you spam me. Had you asked first, I would have mentioned that I didn’t think you’d want my critique.