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Really *WEIRD* thinking is important for doing math

Don’t Worry If You Didn’t Solve Any of the Math Problems that Went Viral
[Via Big Think]

Mathematicians believe Americans are letting their anxieties over math get the better of them.

[More]

Think Math is Hard? It’s WEIRD

Quick, what is the sum of all the numbers from 1-100?

Only the weirdest of the WEIRD like doing hard, analytical math problems.

WEIRD – Western, Educated, Industrialized, Rich, and Democratic – was coined to describe the culture that has come to dominate the planet in terms of culture.

And one of the unusual aspects of WEIRD culture, as I quoted elsewhere, is that it is more analytical than other cultures. It more easily breaks complex things down into simpler parts to examine than other cultures.

But even though WEIRD culture does analysis better than others, not everyone drops easily drops into analytical, System 2 thinking. By some measures, perhaps 15% of the global population does this.

Math Without Thinking

One of the reasons that math works is it is logical and analytical – it is based on a series of premises that lead inexorably to the answer.

Now some math is based on such simple premises that it requires little analysis. It relies on rapid, System 1 thinking It is why memorization works. We quickly know how to add or subtract. 

We do no analysis. This is probably why so many parents are worried about the analytical aspects of New Math. Math to them requires no analysis. If it does, they claim it is too hard.

So when people say “I’m lousy at math” it is usually in response to math problems that require analytical processes that few people wish to do.

Math is Weird

But many math problems are usually designed not to be easily solved by System 1 approaches. People have to use logical  analytical, System 2 thinking.

So, take the problems listed here. They are couched in ways that preclude rapid solutions. They force people to use analysis. But since most people do not do analysis well. they just throw their hands up.

The math is hard because analysis is hard. Our brains use up a lot of metabolic energy when using System 2. And this is imply not natural for most people.

Math is mostly tricks

The math here is actually quite easy. But it is not easy to do in one’s head.

Unless one knows the tricks. Tricks that analysis opens up.

For example, the question I posed up above? It is actually trivial to do it in one’s head but it requires a little bit of analysis to see the easy trick.

There are 50 pairs of numbers chosen from the ends of the series that can be added up (1+100, 2+99. etc.). Each of the sums adds up to 101. So 50 times 101 is 5050. 

I can do the same thing for adding up the numbers from 1 to 1000, or 1 to 1,000,000. Once analysis reveals the underlying simple premise, the math becomes easy.

But you have to do the analysis first. And the more you do it, the easier it becomes. So it becomes trivial to find the square of three digit numbers without using paper.

Math problems are fun but tricky

Each of the ‘hard’ problems in the article are actually pretty easy, once you find the analytical trick. Do not look at them as hard. Understand that there is usually some simplifying trick.

So the first one about Cheryl’s Birthday. It is not so much a math problem as it is an analytical, logical one. Thus it still requires a thinking process difficult for many. But there is a trick that makes it much simpler.

“Instead of looking for the right date, are there any dates I can find that cannot be the right date?” The trick is removing all the wrong dates until all that is left is he right one.

Once you see the trick, it becomes much easier.

Math is not hard. Analytical thinking is.