I've used the term innumeracy fairly often on this blog, and I've had a few people write to ask me what it means. It's also, I think, a very important idea.
Innumeracy is math what illiteracy is to reading. It's the fundamental lack of ability to understand or use numbers or math. And like illiteracy, true innumeracy is relatively rare, but there are huge numbers of people who, while having some minimal understanding of number and arithmetic, are functionally innumerate: they are not capable of anything but the most trivial arithmetic; and how anything more complicated than simple basic arithmetic actually works is a total mystery to them.
It's frightening to realize just how widespread functional innumeracy is. The first time that it really struck me was during high school. I went to school in what was supposedly a very good school district in New Jersey. My older brother was planning to be a musician at the time. He hated math, but got adequate grades in it. My guess would be that on a percentile basis, he was probably better at math than something around 70% of the students in his graduating class. We were out shopping, and there was something he wanted to buy that was on sale for 20% off. My dad asked him how much it cost. The only way he knew how to figure out what 20% off meant was to sit down with a piece of paper and do cross-multiplication: (20/100)=(x/price), therefore 20×price=100×x, therefore x=20×price/100, and sale price = price-x.
My dad totally freaked out at this, and asked: "What does percent mean?" My brother could not answer. He really couldn't. He had no idea - he'd just been taught to mechanically do that cross-multiplication, but he had no idea what it meant. He couldn't even say what 20% of $100 was without writing it out as the cross-multiplication.
I don't mean this post as an insult to my brother - but rather as an example of how poorly our schools teach people to actually understand math. He's a bright guy, and he's capable of doing amazingly complex stuff. When he was in college, I went to visit him, and watched him doing music theory homework - and was amazed, because there were some very strong parallels between one kind of analysis he was doing on 12-tone serialist music and the kind of matrix algebra that I was learning at the time. So we're talking about a guy who, in the right setting, was entirely capable of learning matrix algebra. He - and the vast majority of people here in America - are perfectly capable of understanding basic math. But our school systems - except for the classes aimed at those of us who make our careers in mathematical fields - are either incapable of teaching math, or simply do not care that they do not teach most of their students the most basic mathematical literacy.
Innumeracy comes at a high price to our society. When people can't understand math,
that means that they're going to be making all sorts of important decisions based on
something even worse than ignorance. They don't just lack knowledge of the relevant facts that affect their decision - they lack the ability to even acquire the knowledge that they need to be able to make the decision.
If you can't understand basic math, how will you decide between different kinds of mortgages? How many people in America today have "interest-only" mortgages? How many of those people actually understand what an interest-only mortgage is, and what kind of risk they're taking with it?
If you can't understand basic math, how can you even do a household budget? How can you keep your spending within the bounds of your income, if you can't understand the meanings of price variations, if you can't understand the interest that you earn in a bank account and the interest that you pay to a credit card?
If you can't understand basic math, how are you going to evaluate the different tax and spending plans being proposed by politicians? How are you going to figure out when they're lying to you? (Well, okay, that one's easy: if their lips are moving, then they're lying. But still, how can you figure out what they're lying about?)
When some creationist liar comes along and quotes a bunch of math at you as a "proof" that science is all wrong about evolution, how can you recognize their lies? How can you distinguish between the people who say global warming is real, and the ones who say it's a lie? How can you evaluate their arguments, when they're based on math, if you have no real grasp of how math works?
The answer is: you can't.