First Aid for Multiplication

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A few years ago, a student wrote me the following question, which I think is very relevant for most children in the US, and that means for their parents and their teachers, too. Math inefficiency is a national epidemic, and it is a crying shame. Here’s what she wrote, and what I answered:

muliplycation

how can i rember my multiplycation? i don not know my multiplycation that well i need an answer. i am going to the sixth grade now i need to know my multiplycation. please answer my question.

I gave this response:

There are a lot of answers to your question. The problem is, schools only test you on stuff, and they obviously didn’t teach you that stuff well enough.

School policy-makers tend to think that there is only one way to do something. That keeps them from finding out things that apply to specific students. They sacrifice the minority for the majority. Unfortunately, that minority is close to 50% of the student population of the U.S. So they are sacrificing way too many pupils. Let me explain:

Have your teachers ever explained why you may not have “gotten” multiplication, while some other students have? Have they helped you figure out the things you are doing differently from the kids who “get” it, and how to change those things so that you do get it? I’ll bet they haven’t. So, let’s explore some things.

How is your spelling? I’m sure you think it’s fine, (because almost all kids think their spelling is fine).
Here’s a hint - Your spelling is not as good as you think. How can I say this? Because you misspelled “multiplication” four times, two different ways. Also, you misspelled the word “remember.” You also mis-typed some other words, and didn’t pay attention to your grammar (capital letters for example.)

Don’t worry - that is not “bad.” I won’t punish you for it. No one is grading you here. Unfortunately, you punish yourself with it. Consistently not paying attention to details has its costs. One is that you cannot appreciate math if you don’t pay attention to some details.

Unfortunately, most teachers don’t teach you to “care” about how math works, so there is no reason to care about the details. Math just seems like one boring memorization lesson about things that don’t matter.

That is not the case, though. Math is soooo cool. It’s just that some math teachers tend to be boring. You should go to the library and check out some books on math puzzles, recreational math, and other stuff like that. That will give you some motivation to learn. Ask the librarian for help. Don’t take out any books that seem boring to you. If none are interesting, go to another library, then another, then another. You’ll find some books in the 798.3 section, or thereabouts.

It is important that you realize that even if this stuff does not make sense to you now, you know that details are going to affect your life eventually. So, instead of worrying about “how am I going to understand math?” think about “how can I make friends with the 3 times table?” (I assume you are ok with the 2 times table). That is the secret. Make friends with each “table” first. Write down (preferably on an index card that you can carry around with you):

0*3=
1*3=
2*3=
3*3=
4*3=
5*3=
6*3=
7*3=
8*3=
9*3=
10*3=

and do them. If you can’t do them, just add 3 as many times as you need to and write the answer.

Do that a bunch of times. Carry the list around for a day. Repeat it aloud. Don’t repeat “3,6,9,12,15,18,21…” etc. That will only give you the answers. Instead, repeat: “Zero times three is zero, one times three is three, two times three is six…” Do it till you have it “in your bones.” Don’t stop just because you are bored. If you are bored with it, you didn’t get it “in your bones” yet.

Nothing that you really get can bore you. It is just when you don’t understand it and don’t want to practice that you get bored. Practice beyond the boredom-point.

Then do it with the 4-times table. But don’t do it on the same day. More than one number a day is rushing it. You have learned multiplication for years, and still don’t get it. One of the reasons for that is that your teachers and the school system rush you. You are expected to get it at their speed, and it doesn’t always work that way. That doesn’t mean you are dumb, it just means you had your mind on other things. Now put your mind on this.

Once you are confident with each digit, go to the next. But let me warn you of something - Most kids like to say they get something way before they really do. Don’t fake yourself out. Don’t say, “This is boring, ’cause I know it already,” before you really do. If you are from the US (and by your spelling, I’d say you probably are) you may have that tendency to want to say you can do something, rather than be able to really do it. It is a cultural disease we have here. Saying you can do something seems to be more important that actually being able to do it. That is because people are afraid that they are not living up to someone else’s expectations.

Don’t worry about anyone else They don’t have to know what you are doing, or how well you are doing it, until you are satisfied with yourself. So don’t fake yourself out. If you do that, the evil school administrators have won. Trust your own brain, and don’t short-change yourself, OK?

If you really follow this method, in two weeks, you will be better than most college students at the multiplication tables up to ten. You will have taken a few minutes out of each day, for only two weeks, and changed the way you feel about yourself and your ability to learn for the rest of your life. There may be nothing you ever do that will be this good for your future. Try it and let me know if I was wrong.

This method is not the only answer. There are others. But this one will definitely work if you do it, without rushing, and with lots of concentration.

If you are serious about learning basic multiplication, I can recommend my booklet, “Numbers Juggling - Times Without the Tables.” The booklet is made exactly for kids like you, (and their parents and teachers) who want to learn, but don’t always know where to turn.

By the time you get to the four times table, you will see (as you probably already know) that 3*4 is the same as 4*3. But this time, when you get to 4*3.instead of thinking, “Yeah, I already know that - how boring!” you will feel like it is seeing and old friend again. You will think, “Cool, I recognize that one.” Math can make you feel good about numbers instead of bad. You just need the right teacher.

Develop your skill at concentrating by the above method. Learning to concentrate will help a smart kid like you get better at spelling, too.

I wish you a lot of luck and fun.

Hi-Ho!

Professor Homunculus


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