This is a bit of a twist on the motorcycle and bike threads. There’s a lot of fascinating things about math. A trick I like that’s easy to explain to just about anyone is to find a cup or glass (occasionally a squat beer bottle) and to bet someone that it’s bigger around than it is tall. This is usually true for all but the tallest skinniest glasses and it hold for some beer bottles. It’s based on an old grade school buddy: C=pi*D
Multiply the diameter of a glass little over 3 and it quickly grows to be a larger length than the height of the glass. You can convince yourself of this with a piece of string or your hands.
But despite the mastery of time and space granted by mathematics (at least the most commonly studied kind) we are plagued by innumeracy and a fear of algebra. I feel we are too often forced to contend with two different options: Either math is intrinsically difficult, or math is universally poorly taught.
Neither or these explanations satisfies. If math were intrinsically difficult, then why does fear of math start with arithmetic or the barest basics of algebra? No mathematician considers these operations difficult (though plenty consider arithmetic tedious- because it is.) And can it really be true that most math instructors are terrible? This just strikes me as incredibly unlikely.
So what are the other options? I’m really asking here. My current personal hypothesis is that the symbolic language of math is a language you need to learn to read fluently, but learning to read it is not emphasized the way that learning to read English or French is. Oftentimes people need to sit down and “sound out” what’s happening on a page. This tends to snowball with the ordinary difficulty of acquiring any new skill and students end up behind, stressed out, and demotivated. By contrast, students are quite familiar with English before they’re assigned reading for history or science. Throw on some cultural baggage about how “math is hard” and you’ve built yourself a nice little layer cake. Whether my hypothesis is any correct or not, I suspect the real answer is also a layer cake.