Basic Numeracy
How much mathematics do people really need? Obviously everyone needs to be able to count, add up, and subtract, or they can’t cope with the financial side of daily life. They might learn to do it with calculators, but they need to understand what their calculations mean, and they need to be able to tell when the results they get are obviously wrong. This is actually more than is currently universally achieved, and we shouldn’t be satisfied.
Beyond that, multiplication is obviously highly useful in all kinds of quite ordinary situations, and to a slightly lesser extent, so is division. Again, understanding what you’re doing with your calculator, and recognizing when the result is nonsense, is probably sufficient for most people most of the time.
Most of the rest of mathematics, I’d suggest, can be left to specialists. I’m not saying that it should be left to a tiny minority of specialists; I think we need quite a lot of people more numerate than that, but it doesn’t need to be universal. This is just as well, because it certainly isn’t universal – but perhaps we could be more accepting of that reality. There’s no reason to force everyone to try to go beyond the basics.
I said most of the rest of mathematics, not the whole of the rest of mathematics – because there are a couple of other areas that I think are so important that everyone (except those with a significant mental deficit) ought to understand them reasonably well. And this is where I think the powers that be have got it wrong: it’s not what they regard as the next step after basic arithmetic. The two areas are these: Orders of Magnitude, and Probability and Statistics. Without a basic understanding of these, people really aren’t equipped to make rational decisions about all kinds of issues. Much of politics and economics is irrational precisely because the overwhelming majority of the population simply don’t have a grasp of these two areas. Who cares whether most people can solve quadratic equations or not? I don’t*. But I care very much that most people lose track of the relative values of sums of money once they have more than five or six digits, and that they can’t compare the magnitude of risks in any sensible way. See Travel Safety Statistics for an example.
*even though my best degree is in mathematics, and I have been a maths teacher.