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.