There’s an argument in favor of teaching basic computational skills that starts something line this: The reason you need to be able to do arithmetic hand is that if your calculator ever breaks down…
If you ever hear a math teacher try to defend basic arithmetic facility on this basis, stop them right there and ask them if they know how to process coffee beans, dress a rabbit, smelt iron, and weave cloth.
Because that’s what the “if your calculator breaks down” argument comes down to. If civilization ever collapses, it’s important to know how to do arithmetic by hand. No question about that…but if we base our educational system on what we’d need if civilization collapses, perhaps we’d be better off teaching how to make a fire, grow wheat, or forge metal.
So why do we need to teach arithmetic? There are two reasons. The commonly given reason is that it prepares students for algebra. This is only partially true: done properly, learning arithmetic does prepare students for algebra. Unfortunately, what gets taught as arithmetic generally doesn’t do that. (Here’s the test: if you see no fundamental difference between and minus , you were probably taught arithmetic correctly. If you see the two problems as different, you weren’t)
I’ve advanced this reason in my own classes, so you can take it as given that I believe it’s essentially valid.
But…it begs the question. Why should students learn algebra? The answer is that it’s a stepping stone to calculus, and that’s a requirement if you’re going into a STEM career.
This leads to an ongoing argument about this, based around the incontrovertible fact that most people don’t use algebra.
My response, rendered as a repostable meme:
And that’s the problem. As I see it, the fact that most people don’t use algebra doesn’t mean that algebra isn’t important. It means that we need to encourage its use among those in nonSTEM fields.
But why? Let’s go back to arithmetic. Anyone can calculate with technology. But it takes initiative to break out the piece of technology, so most people don’t bother. This means they take numbers and accept or reject them on the basis of what they believe is true about the world: whether it’s that millions of illegal immigrants vote in elections, or that a Wakandan prince wants to get 25 million in gold out of his country.
What we need, as a society, are citizens who calculate as readily and naturally as they breathe. What that doesn’t require is the ability to do arithmetic by hand.
What it does require is the ability to do arithmetic mentally. The reason is this: if you need a device to perform arithmetic, be it a calculator or pencil and paper, computing requires an extra step beyond the computation: it requires taking out the device and setting it up. As a result, 9 times out of 10, you won’t do it.
On the other hand, if you see and think to yourself, “Self, I I could do that in my head…”, then you’re much more likely to hear “Millions of illegal votes” and think “That means that a bunch of the people in the polling line with me weren’t legally registered…”
(Oh, and if you want to do in your head, here’s how: is two cents less than eight bucks, so figure: , minus two cents is . I’ll do more about common core arithmetic later)