Mostly from lesser-known blogs —
Superplexa!: Why are square roots so hard to learn?
A third difference between forward and inverse functions is linguistic. We often speak of inverse functions as undoing forward functions, and this can create some really nasty linguistic contortions. I can explain the concept of a square root by drawing a square with, say, an area of four and asking how long each edge is, which isn’t so bad. But the only way to actually talk about the computational aspect (possibly because of the complexities pointed out above) is to ask “how long would each edge have to be to make a square of area four?” which I suspect is harder to process than “what’s the area of this square whose edges are each length 2?
Possibly Philosophy: Is ZFC Arithmetically Sound?
The question at stake: why should we believe that ZFC doesn’t prove any false statements about numbers? That is, while of course we should believe ZFC is consistent and ω-consistent, that is no reason to expect it not to prove false things: perhaps even false things about numbers that we could, in some sense, verify.
Sociological Images: The Truth About Gender and Math
Boys do better in only about ½ of the OECD nations. For nearly all the other countries, there were no significant sex differences. In Iceland, girls outshine boys significantly . . . Still, even in Iceland, girls overwhelmingly express more negative attitudes towards math.
Rip’s Applied Mathematics Blog: Calculus: Organizing techniques of integration
I constructed this algorithm when I was a first-year graduate student. I was TAing the sophomore math course, and I had to explain to my students what they needed to know from their freshman year in order to solve first-order differential equations. I started out, of course, with a list of techniques culled from their first-year calculus book, and then discovered that they needed a list of known integrals, because they simply didn’t recognize them . . . This organization (or algorithm or checklist) does assume that you have learned the specific integrals and the special and general techniques. If you’re struggling to get these details right, you’re not ready for the algorithm yet.