The Value of Quick Addition Skills

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“In mathematics the art of proposing a question must be held of higher value than solving it.”

Georg Cantor

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About a month ago, Penny commented on this post.

Here is an except from that comment:

“Frankly, I don’t care if an elementary school child can add long columns of numbers in their head - it is an almost worthless skill. I do care if they can think about mathematical concepts.

Better to teach them to come up with simple proofs (not memorized proofs) of basic facts in math.

Better that they should understand what a prime number is, and why we care about prime numbers.

Better that they should learn to enjoy slow, deep thought about puzzles and concepts.

That is where the gold standard in math education is.”

I wanted to revisit this thought, because Penny brought up some great points. I don’t disagree with any of them. But I must say that I, as well as a lot of the readers are coming from a different place. Penny is a brilliant research mathematician. A lot of us, on the other hand, basically have a history of thinking that we sucked at math (at least until we came upon Math Mojo, and learned that almost no one sucks at math, but some sometimes the way math is taught sucks.)

I wanted to address some of the points Penny made, because those points made me think a lot this month. Here’s

Added Value

Penny, I agree that the points you brought up are better than simply being able to add long columns of numbers in your head, but I wouldn’t dismiss learning quick addition.

One reason is the practical value. I catch plenty of mistakes at the checkout counter.

But the real reason is that it is one of the first real mental-math skills that gives you the feeling of what I call “numbers juggling.” This isn’t a trivial thing, either. I’ll go into depth about it in a future post, but I’ll touch on it here, because it’s important.

All you need is balls…

I don’t know if you are aware, but I used to be a busker (street-performer) in Europe. I mostly did magic, but I also juggled in my act. I’m not exactly a brilliant juggler, but I’ve gotten to the point where juggling is practically meditation. There is an amazing circular “feeling” you can get while juggling. It is not just from the patterns that the balls make in the air, but also from how your eyes follow the arcs, and other feelings in your body.

When I practice speed-math I get a similar “rush.” Other people have reported the same thing. I imagine that it’s caused by (among other things) the patterns my eyes make while manipulating imaginary numbers in the air.

This feeling makes the whole phenomenon of reckoning with numbers more “plastic.” (People who like to talk about “modalities” and only have a superficial understanding of what “kinesthetic” means might call it “kinesthetic.”)

This perceived plasticity makes math, and many other abstract concepts more understandable to me than they otherwise would be.

I imagine that many people could use this to their benefit, and that’s one of the reasons I started Math Mojo.

I’m no Einstein, but…

Penny went on to mention this about her daughter:

“She is now a molecular biologist. She is still no whiz at adding numbers in her head!”

Of course, not everybody has to learn every math skill, but I don’t think there’s a reason not to learn something. Einstein had a great memory and orientation for concepts, but he still occasionally had to phone his wife to find his way home. Is that good?

Some lightning calculators were idiot-savants, it is true. But that does not mean that lightning-calculating is useless (it’s the skill that gave them the “savant” part of that label, after all).

Other lightning calculators include the astronomer Trueman Henry Stafford, the physicist André Marie Ampère, the mathematicians Srinivasa Ramanujan, Wim Klein, John Wallis, Sir William Rowan Hamilton, Norbert Wiener, A.C. Aitken, and no less than Johann Friedrich Gauss. And of course let us not forget that Brittney Spears is noted as an accomplished calculating prodigy. (Ok, I only threw that in there to see if you were paying attention.)

These people generally exhibited their prodigious calculating abilities when they were young, and their skills waned as they got older.

They’re only going through a phase…

It’s interesting to consider if it could be that as they matured mathematically, their fascination with pure calculations wore off as they investigated more fascinatingly complicated things. And could it be that they would never have developed that maturity if they had not gone through the lightning-calculating stage of their development?

Could it be that their fascination with math was developed so intensely by that phase, where it might not have been otherwise? Maybe some types of personalities are a perfect match for ready-reckoning, and we’d do them a disservice by dismissing it as trivial.

All I know is that we are letting a lot of children through the cracks, and it would be a shame not to give them the opportunity to grab on to something that might turn them onto a path that might lead them to higher knowledge on their own terms, not just what we think should be valuable.

When they have to re-write simple arithmetic, we are teaching them that using a crutch is good. It’s the right way, it’s the only way. That sucks!

Understanding and practicing mental math is good for visualization, mental flexibility, understanding that new pathways can be better.

For most people, not doing arithmetic mentally is like not learning to run. “I can walk already. I’ll just learn how to build wheelchairs and cars. That’s progress.” And never learn to run? But what “value” does running have? Oh, come on, that would be just a ridiculous question.

I’d like to thank all the readers who know a lot more about math than I do, and come and comment on this site. It gives me so much opportunity to think and communicate. I hope it does the same for Math Mojo readers.

Mission Position

Part of the mission of Math Mojo is to be a liason between the people struggling with math, and the people who love, enjoy and understand math. Normally they never meet.

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