Reasoning out the answers is something I think my verbally gifted son is good at and why he is able to come up with his own way of figuring out answers to math problems faster than I could do it the way I was taught. When he explains to me how he gets the answers it often doesn't make sense to me. At 10 he still isn't that interested in math but he likes it more now that he doesn't have to do long division or multi-digit multiplication without a calculator and I let him work on what he wants to work on.
My son was homeschooled for first grade and we didn't spend much time on math. We sometimes used Singapore math workbooks but I had to be his scribe because of his handwriting issues and he often just played free online math games and we counted that as math for the day. The math games let him choose the level of difficulty and I know he liked to challenge himself and his handwriting issues didn't hold him back. By seven he had most of his multiplication facts memorized but there were five multiplication facts that he would sometimes get wrong if he had to answer them quickly. It was like he had some kind of mental block on just those five and if he went too long without doing multiplication he would have to relearn those five multiplication facts. I remember wondering why the school couldn't figure out how to make accommodations for my twice exceptional kid when all I had to do was let him play free online math games and I think I even said something about this to the special ed director when we showed him my son's WIAT scores. If my son had been forced to work on simple addition and subtraction at that age and had to do all the writing himself I don't think he would have seemed gifted in math at all. He would have hated math just as much as the coloring in the lines they wanted him to do at the "rudimentary elementary" as my son called it because all they wanted him to know was rudimentary skills and no more.
