Dyscalculia?

That's really impressive that you can do mental math so quickly. 

I still do a lot of arithmetic mentally, without calculators or pen or paper, using mental algebra.

To test myself, just now I calculated

19 X 19 = 361 in under 5 seconds, without formal multiplication.

19 X 19 = 400 - 2 X 19 - 1

I was terrible at basic math, except I loved doing long division with pen and paper. So I was a strange one. 

People used to say things like "you won't have a calculator with you all the time when you're older" or things like "You'll look dumb if you pull out a calculator to count money" when I was young, but now people have phones, and they use the calculator all the time. I guess it's not weird to use a calculator in public anymore. 

I have a confession, although I have a Maths degree, I never learnt to do long division with pen and paper.  I just use a calculator.

Thank you.  That's interesting.  This is in relation to someone very close to me.  A person who is excellent at explaining concepts and understanding more abstract, higher level maths and science, but who struggles with basic weights and measures - i.e. the practical knowledge of space you describe.  

It feels to me as though it could be linked with being autistic, but I'd not thought of linking it with learning styles.    

Plus it fits in with many in my family who are great with theoretical concepts but fall down on everyday practical tasks that seem to come more naturally to many.  Part of a spikey profile, I think, but one which can lead to a lot of frustration.  

I think that there are different areas of math that you are explaining. Like there is the geometry, ratios, proportions, weights of measurements, that requires the practical knowledge of space, the 3D environment that you're reciding in, that is visually conceptualized. 

And then there is the more abstract part of math, that is more like a language, that is made from logic and patterns, that is like formulas, that can be so infinite that it can only be easily written as numbers and symbols, but cannot be easily drawn out in a visual way (unless you're using some kind of advanced computer system). 

I mean, a person can do better on one, and worse on the other, and vice versa, or they can do well on both, because it's just different areas of math and the way you learn.

It reminds me of the Common Core math that was implimented in the usa. Traditional math required memorization, one right method, one right answer, and it was rigid. You are just given formulas, you just plug in numbers, and you get the right answer, without really understanding what the formulas are for. 

But Common Core math had more visuals, had many alternative methods to get the right answer, and it was great for people who needed more visual diagrams to solve math problems, but worse for people who don't do well on learning visually.

But there was a shift in student marks. The one's who were doing well on traditional math failed on Common Core math, and those who were failing on traditional math were succeeding on Common Core math. (Basically the kids that had good marks started failing, and the kids who were failing got good marks).

I believe that people are good at different areas of math, and if they are taught the method that works best for them, everyone can excel.  

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I forgot to mention, I have dyscalculia and I can mix up numbers when I read them (I didn't even know I was doing this, but my answers always came out wrong to my frustration), and I had problems with math throughout school, and math anxiety. But I retaught myself math when I was older, and after trying out and learning many different methods, I can now do mental math, something I never do before and believed I could never achieve. I think everyone learns differently, and no one method fits all. And if you are not good at something, just try to approach it from another angle.