## How Maths Helps a Democracy

As another election passes, we have been subjected to a lot of arguments about money. One party will promise to spend £800 million on something, another party will respond saying their figures don't add up and it will actually cost £2.5 billion, and the arguments go on and on. It seems like everyday there is a new spending promise followed by a row over it.

But do voters actually grasp all the figures correctly? One thing we also hear about is employers moaning about a lack of numeracy skills among employees, so I would expect many voters aren't able to properly compare figures. And if you can't understand the costs of the promises, then you are left to trust the newspapers to accurately report on them, and given the British media's lack of impartiality, I don't think that is a good idea. So can voters be properly taking part in a democracy if they don't have the numeracy skills to evaluate a party's promises?

I've been talking to students this week about the costs and many have no idea at all of what a million, billion, or trillion really is, other than they are "big numbers". I asked some average year 9 students and some lower ability year 11s (grade E/D) to write in figures 1 million, 1 billion, and 1 trillion. About a third got 1 million correct, and only about 10% got 1 billion and 1 trillion right.

Many students who got 1 million wrong wrote it as 10000. When I put a comma in it for them, they were able to see that 10,000 was ten thousand and realised they had made a mistake. Unfortunately the same wasn't true when we moved on to billions and trillions.

The incorrect answers often had 1 million as 10000, and they then added an extra 0 for 1 billion, and another 0 for 1 trillion. If you think about it, this makes perfect sense to them. The "names" for numbers they learn start with tens, then hundreds, then thousands. And each time we add an extra 0. So the next "name" is million, so why not just add an extra 0 for that? They don't seem to think of say "10s of millions" as another column name in the place value chart. They view them as a quantity of millions, and their place value understanding doesn't extend to numbers above a certain size.

Place value problems seemed to be behind much of the msitakes. For the students who could write 1 million out, I asked what 20 million looked like. The answer was correct: 20,000,000. But then when asked what 2 billion looked like they followed through their incorrect answer for 1 billion, and wrote 20000000 (20,000,000 but they weren't putting commas or gaps in). They then decided that 2 billion was the same as 20 million. Looking at what they thought 1 billion was and what 10 million was (the same thing for them), they decided that that meant that a billion was ten times more than a million.

So when the government says that they will cut £9 billion from the welfare bill, and then there is also talk of CEOs earning over £10 million, that cut to the welfare budget might not seem like such a big deal. Voters can't make informed choices of who to vote for if they can't understand the maths involved. Maybe by the time people are adults everyone is better at understanding these figures, but that's certainly not what is implied by the reams of stats put out by bodies like National Numeracy.

What can be done about this? Well for a start, when students enter secondary school, and we maths teachers look into their place value understanding, we should also try to extend it. Help them develop fluency with millions, billions, and trillions. We could also regularly look at newspaper headlines about the nation's finances (there are plenty these days) and discuss them, work out what the numbers mean and how much they are worth. This would all help to develop student's number sense which is a huge issue with many low achieving students. We can also have a good answer the the question "when will I need maths?" - "Everyday if you're to participate in our democracy."

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