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Hooray for New Math

First, watch the following video on Common core multiplication.

Pretty ridiculous right? What a crazily complicate way to do simple multiplication. The lady made coffee, and let her dog out to play after solving the problem in the same amount of time it took the teacher to solve it.

What a waste of time.

Except…

The video is a crock. Garbage. A distraction at best and a deliberate disruption at worst. Here’s why.

  1. The teacher is not solving the problem; she’s teaching her students how to solve the problem. That always takes way more time than actually solving the problem. This comparison is broken from the set up. It’s a crock.
  2. THE TWO METHODS ARE IDENTICAL! We should suspect that intuitively since they come up with the same answer, but this video, and much of the yelling and screaming about Common core (almost all of it politically motivated and not driven by education) completely miss this point.

Allow me to demonstrate.

common core

As you can see, all the steps are there, same on each side. One way is exactly equivalent to the other in complication, number of steps, and, most importantly, the end result. The only difference in the two algorithms is that Common Core starts with the tens place instead of the ones, and doesn’t bother adding the sum until the last step.

That’s it.

So why all the fussing and fighting?

Mainly, because most of us have forgotten how we learned to do math in the first place. We learned it, practiced it, and internalized it until we no longer noticed the steps we went through for each problem. We just did it. We might never have really understood what we were doing; we just followed the steps and got the answers our teachers wanted.

And that leads to why Common Core changed the approach to math. It’s about understanding. It’s about developing a feel for numbers. In the problem used as an example, by doing the high value numbers first, I have a rough approximation of the answer immediately; I already have a feel for where the answer is going to be. I can do the detail work to refine my answer later.

We do that all the time in the real world right? Think about ordering building supplies for a floor. I take the measurements, round to the nearest foot, throw in 10% for waste, and place my order. On a 10’5″ x 12′ 7″ floor, I’m gong to estimate 130 square feet of materials, plus 10% and order 143 square feet of flooring.

Why not teach math the way most of us actually use it?

Now for the science/engineering/technical folks, we need to get the right answer to a higher level of precision, but even for us, getting a feel for the numbers is important. We rely on calculators and computers in a major way. Unless we’ve developed a strong feel for numbers and magnitudes, we’ll never notice an egregious error and might accidentally plant a probe 30 feet into Mars instead of placing it into orbit around Mars.

So yes, there may be some value in the Common Core approach, even if it does cause parents some hair-pulling nightmares. (And teachers. The biggest problem with Common Core math is far too many teachers don’t understand math and do it by rote. It’s hard to teach what you don’t understand.)

There is a large part of the Common Core curricula that is questionable; there’s a bunch of ideology injected into all areas. But the new math algorithms aren’t part of that.

Here’s the fun part. None of this, not the changes, not the algorithms, not the protests are new in any way. We’ve been here before.

Exhibit A from 1965:

What’s really funny about this is that I grew up with New Math so I understand it fine, but he loses me in the first part, when he talks about how it used to be. Even better, the new math that drove parents bugnuts in 1965 is now the ‘only way math should be done, by golly!”

By the way, if you don’t know who Tom Lehrer is, look him up on YouTube. Absolutely brilliant satirist, and a very funny fellow.

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