Why "common core" maths isn't as stupid as you think

Every so often, I see a post show up in my news feed about how "common core" maths is new, and thus, terrible. Well, not quite. It's mostly people who don't understand it because, for one thing, they've been shown an example that's deliberately cherry picked to show it looking dumb, but for another, they haven't had the method behind it explained.

And, well, if there's one thing I love doing, it's explaining maths things like a nerd!



Now, I want to ignore for a start, the fact that the new method of maths isn't "common core". I'm going to get this horribly wrong, because I'm not American and the name "common core" comes from the new American teaching standards. The fact that it includes this new style of doing maths is kinda just a coincidence. America isn't the only country teaching students this method, my younger sister was being taught it a year or so ago.
But to me, this is kinda pointless semantics. I want to explain the method behind this, so to do this, let's start with the example constantly being shown.

32 - 12

Now, hopefully anyone can look at this and figure the answer is 20. The problem comes from trying to actually properly figure it out by hand. The old method and the new method side-by-side look something like this:

You get the same answer either way, but the old way on the left looks much easier. There's only one step, and the way on the left just adds in more ways you can make errors. Why would anyone use it? Where do those numbers even come from?

I'll answer the second first. What you're never shown in this example is what's actually being done. You just get shown some weird numbers and, if you don't understand what the method is, of course they'll look strange.
The point behind the new method is that, well, the human brain is really awful at maths. Seriously. Our brains are simply not wired that way. Our brains evolved in an environment where the only useful numbers were "one enemy" and "lots and lots of enemies". That's why we invented the calculator.
So the new method is designed to get the numbers to something nice and friendly. Specifically, multiples of 5 and 10, because multiples of 5 and 10 are pretty much the easiest numbers to deal with. 12 + 3 = 15, 15 is a nicer number than 12, 15 + 5 = 20, and 20 is a much nicer number than 12.
The other thing it's designed to do is to skip subtraction entirely. Our brains are pretty awful at that too, and pretty much any time anyone subtracts anything in their head, they're actually just thinking "now what number adds to make it up to the full amount?" Subtraction is, at its core, reverse addition, and that's the way our brain subtracts too. By leaving out any actually subtraction, we make it easier for ourselves to actually subtract in our head. Keep in mind that, this also poorly represents how the second method actually works. You don't do all those additions, then do that last addition at the end. You keep a running total as you go. You go, "oh 12 + 3 = 15, 15 + 5 = 20, 5 + 3 = 8 and I'll keep that in the back of my head, 20 + 10 = 30, 8 + 10 = 18, good thing I didn't forget that 8 I said I'd remember, 30 + 2 = 32, 18 + 2 = 20".

Because that's the main point behind this new method of maths. To teach students how to subtract in their head in a way that is easy, actually works with out brains and not against and, most importantly, has a smaller chance of errors. Let's face it, pretty much any time you need to do some subtraction, or any other complicated maths problem, and you've got a pen and paper handy, you've almost certainly also got a calculator handy, either on your computer or on your cellphone. Nobody really needs to know how to do pen-and-paper maths except as an absolute last resort. Being able to do it in your head, however, is pretty handy.

Let's look at a different example.

31 - 12

Oh dear. That old method isn't looking quite so good any more. It still kinda looks better though, right? Also, note I skipped a step in the second one there. While the example shows adding to multiples of 5, I don't really see the point in that. To me, it's easier to go straight to multiples of 10. That way, until the final step, you're only ever adding a one multiple of ten to a different multiple of different.

But also remember what I said. Half the point is being able to do this in your head. How do you carry the 1 in your head? It's doable, but it's easy to slip up.

The difference becomes more obvious when you start having 4 or so digit numbers. Like, say... counting out change!

Let's say, you're buying something for $3.45 and you're paying with a $20 and you want to know how much change you get. Let's look at both methods again!

20 - 3.45

Look at the convoluted way the old method takes to figure out change, whereas the new method is much, much easier to do in your head. A lot of cashiers already know this method for counting out change, but suddenly, when it's labelled "common core", it's terrible? I know I'd used it a few times before I'd heard the phrase "common core", because it's easier to do in your head.

Lastly, though, I want to use a nicely cherry picked example to, well, demonstrate why cherry picking is stupid but also to illustrate my point again.

1000 - 999

Wow! That old method is so slow and terrible! Why would anyone use it?

Answering Genesis: Interpreting the Evidence

One of the main position's held by Answers in Genesis is that they don't have different evidence, they just view the evidence through their own world view, while "evolutionists" view evidence through a different world view. As I've said before, this is really just so that, when evidence contradicting their position is given to them, especially transitional forms, they can claim to just be interpreting it differently.

That guy on the right looks like a porn star. Just sayin'.

And so, I wanna take a look at this view. See if it stands up to scrutiny. Because, of course, it doesn't.

Answering Genesis: "Hiding in the Light"

This is another very "observational science" based episode of Cosmos, so Answers in Genesis really didn't have a huge amount of material to whine about. So, instead they went for their usual fall-back strategy of whining about abiogenesis, whining about the big bang theory, playing the victim and, of course, "it's just historical science! That means I can reject it out of hand and ignore any evidence supporting it!"

I was honestly expecting to not have a lot of a fun with this, but hey, let's have some fun!

Answering Genesis: "A Sky Full of Ghosts"

Yay! Finally caught up with the Cosmos series! And the latest episode was great for a simple reason: It presented a pretty simple and obvious reason why the universe cannot be only 6000 years old, as predicted by biblical creationists, giving Cosmos its first direct attack on young earth Creationists. And boy, did it get Answers in Genesis mad.

The episode itself was pretty interesting, though I'd hoped it had talked more about relativity. Relativity is pretty awesome, but the stuff about black holes was also pretty interesting, though I'd hoped it would talk about Hawking radiation a bit too. But oh well. One of the slightly disappointing things about the new Cosmos series is that the episodes themselves are only 45 minutes long without ads, while the original series had hour long episodes. So there's a wee bit that needs to be trimmed and it does show sometimes.

But that's beside the point. Let's talk about creationists!

Answering Genesis: "When Knowledge Conquered Fear"

I have to admit, the first time I saw this episode, I really didn't see much in there that would object creationists. It pretty much just talks about how comets were originally seen as harbingers of destruction, then explains how Halley, Newton and a few others discovered what they are, how gravity works and some other really cool science. I forgot though, creationists are offended by pretty much any science that doesn't apparently confirm their interpretation of Genesis. So naturally, they got pretty annoyed at this one too.

Why?

Please note: there are several instances of objectionable language in this episode of Cosmos.

... Oh. Wait, what?

Answering Genesis: "Some of the Things That Molecules Do"

The second episode of Neil deGrasse Tyson's Cosmos was considered almost entirely with the subject of biological evolution; naturally, this is not a subject that creationists are happy with, and Answers in Genesis's review of the episode shows that. But, despite everything, Darwin's theory is one of the most well understood and well tested theory in all of science. The only reason people don't accept it, as far as I'm aware, is because they either don't actually understand what the theory is (hence my earlier blog post on it), or they simply refuse to, usually for religious reasons, and can only do this by "interpreting" evidence differently.

I want to make a short disclaimer here first though. I'm not a biologist. My majors were physics and maths, and I did my utmost best to avoid biology at university. I'm not entirely sure why, but hey, what can you do. So my understanding of some of the principles of biology are flawed and I might well make mistakes. Please, please, don't take those as mistakes in the theory of evolution. It's almost certainly a mistake in my own understanding.

But enough of that. Let's get into the review!

Answering Genesis: "Standing Up in the Milky Way"

As most people are probably decently aware, astrophysicist Neil deGrasse Tyson is currently airing a rebooting of Carl Sagan's famous Cosmos series. As someone who's very interested in science, loves learning about where we came from and how the universe works, I was very pleased to hear this and have been watching it and, for the most part, thoroughly enjoying it. If you haven't seen it yet, or Carl Sagan's original series, I highly recommend it. It's very educational, brings up a lot of very interesting science, and has a lot of interesting and deep thoughts on where we came from and our place in the cosmos.

Naturally though, seeing as a lot of the topic is the scientific understanding of our past, this made a lot of creationists, well, not very happy. Answers in Genesis has been posting a series with their reviews of the Cosmos series, so I want to take this time to look at their arguments, analyse them and, well, defend the Cosmos against them.

So! Let's begin!