If teachers don't know at least ten methods of how to multiply, they shouldn't be teaching multiplication to more than nine students. It's easy and important to understand multiplication in depth if you are entrusted to teach it to young minds.
And that doesn't mean "tricks." Tricks trivialize anything they are attached to. How can I say this? Because I am a professional magician. We (at least the good ones) hate "tricks". One all thing magicians know, is that as soon as you teach the trick, the magic is gone. It takes all the appreciation out of the effect.
A thoughtful magician would never show anyone how to do anything until they are ready to appreciate the thought and effort behind it.
One of the dangers of teaching tricks is that you, as the teacher, might actually think that you are seeing a light bulb go off when the child says, "Oh, I get it!" But that is the same false light bulb that we magicians see every time a person says "Oh, I see how he did it now!" when someone tells him how a particular magic effect is done. They only know the most superficial part of the method. They can't actually do the effect to any worthwhile degree, they only "know how it's done!"
It's like the hip jazz musician who meets the suburban musicologist, and says about him, "Yeah man, that cat knows
where it's at, too bad he doesn't know
what it is."
The same goes for teaching multiplication. You must teach the reasons that the method works. If the child isn't ready to understand the reason, s/he is not ready to use the trick. In other words, it shouldn't be a trivial trick - it should be a meaningful method.
How do you do this?
You have to get to know the child, and where s/he is with math so far. What so many pedagogues forget, is that education is about the student, not about the material (or the damned curriculum). If the child struggles with addition, take a step back and cover that until the child understands it in his bones before you try to teach him multiplication.
It doesn't matter that you have to cover curriculum. It doesn't matter that you are "on the multiplication unit" in school at this point. Clearly the pupil is not. You are a teacher, you know this. The administrators don't, I know, know. This is a problem. You can please them, or you can teach math. You can't do both. If you can't fight a bad system that you're in, you are the system.
So you figure out if the child is ready to learn what you plan to teach them. If they struggle with "the tables," and you are about to teach them the standard algorithm, you must get them up to speed until the real light bulbs goes off in their heads - until they understand that "times" (with whole numbers) means "groups of". Have you explained that to them well enough? Do you understand it yourself?
It doesn't matter which of the typical methods are taught in schools if they are going to be taught as "tricks" or taught as "show-and-tell" of "how to do it." None of them will have any meaning.
And by meaning, I don't mean, "grades went up." You can get great grades with "tricks." It makes teachers’ work easier. But it doesn't teach anything valuable in the long run. If you teach for understanding, you get lasting value. If you teach with tricks and games, you are teaching that math is only good if it is not about the math. Great lesson, huh?
Education is not about inculcation of any algorithm. It is about students gaining insight, knowledge and lasting value. You can't do that with "just shut up and learn this method," just as you can't do it with, "I'll shut up and let you teach yourself." Those are the ultimate false dichotomy in education of our time.
If you're a teacher, you're probably fed up with the bad mojo from the policy-makers. You need to get your own mojo working.
