When my son was in high school he used to participate in math competitions. Also at his school was an otherwise so-so student who could do calulations in his head very quickly. Kids called him, "the human calculator." It was really quite impressive! However, he did not clean up at every competition because, quick as he was at the calculations, he was not always so quick at the concept. It sometimes took him a bit of extra time to figure out just what calculation he needed to do in order to solve a problem. My kid is also a math-in-his-head person, just not to the extent that "the human calcualtor was." But my kid is very good with the concepts, too. So sometimes he managed to bring home the top ribbon. Mine clobbered the other in the math SAT, too.
