Mathematical Giftedness Plus Dyscalculia
The section about Dyscalculia caught my eye:
"There are two general areas of weakness that can contribute to problems with mathematics. One is a weakness in mathematical reasoning ability, which results in difficulty understanding math concepts. Children with problems in this area may have difficulty estimating amounts, understanding relative value (greater than, less than), or understanding abstract or symbolic concepts in math ("ten's place, hundred's place", money, fractions, etc.).
Another general area of weakness that can contribute to problems with mathematics is memory for arithmetic operations. Children with problems in this area have difficulty remembering number facts (e.g., multiplication tables), sequences/steps used in math problems, or computing easy calculations in their head. Some children may demonstrate problems in just one of these general areas, while others may have difficulty in both areas."
I've always had a hard time deciding if I'm good or bad at math. (Or whether I like or hate math.) Sometimes I struggle with mathematical things that others find easy, and other times I find mathematical things easy that others struggle with. And reading that passage, I finally realized that I'm actually both! I am gifted at one of those aspects, and disabled in the other!
I have always found mathematical concepts easy to grasp - especially visuospatial concepts. Geometry and Statistics are two of the easiest areas of math for me to understand, and with both of those I've found I have an intuitive idea of the 'ballpark' of the correct answer, even if I don't know the exact numbers. For this reason, multiple choice questions on math tests can sometimes be easy for me, when only one answer possibly could be correct. I can also readily spot when someone else's math reasoning is logically flawed. This aspect of math is not only easy for me, but can also be extremely fun, especially when the data I'm looking for matters to me and when I can avoid the mechanics of math as much as possible. (As regular readers of my blog will know from my SPSS posts, ever since I discovered SPSS, I've been doing statistical analyses for fun.)
Memory for arithmetic operations, or what I sometimes call 'recipe math', is very difficult for me. I still haven't completely memorized my times tables, though the ones I haven't memorized I've figured out shortcuts to solving (such as 5 * x = x / 2 * 10). I rarely memorize arithmetic operations either, instead I figure it out anew whenever I'm given a problem requiring that operation. (I really appreciate how university math exams provide you with the formulas instead of expecting you to memorize them, though I still have to work at figuring out which formula is which.) The most frustrating thing about math, for me, is that when I make mistakes, they're often very silly mistakes - I know how to do the problem, but I did an F-test instead of a T-test, or I thought 8 * 7 was 49, or something like that. I've been told over and over that this kind of thing is helped by practice, but if practice helps this for me, it takes far more practice than I can tolerate actually doing.
The good thing about this pattern of strengths and weaknesses is that it's the exact opposite of a computer's pattern of math skills. Computers are extremely good at basic operations, but it's a lot harder to program them to understand mathematical concepts. As a result, it's very easy to compensate for this type of dyscalculia - just give the person a computer program (like SPSS) that can do the basic operations for them.
The hard thing is that schools are really not designed for this kind of learning style. They're a better fit for the opposite pattern - a kid who struggles with math concepts but is really good at memorizing operations and performing them. (My father taught some kids who, if given a word problem with insufficient data to actually solve it, would input random numbers on the page - once even the date - and solve it based on those numbers. To me, this indicates someone who is doing math they really don't understand.) I really believe that, if I'd been taught math in a way suited to my learning style from the very start, I'd have excelled at it, and it could very well have been one of my favorite subjects.
Incidentally, this particular pattern seems to be a common pattern of math skills for both autistic and ADHD individuals, in my experience. This may partly explain why some autistic people are extremely good at math and others are dyscalculic (although there are some conceptual dyscalculic autistics too, most of whom seem to have NVLD).