> Anything I try to hold in my head goes away as soon as I stop "looking" at it. I have a horrible time doing multiplication in my head when I have to carry numbers. Because that number that I'm carrying is floating there above the problem. But if I take my eyes off it to do the next multiplication bit, it flies away. Similarly, when I do the first multiplication and get the first digit, if I'm not continuously flitting my internal gaze back to that number while doing the rest of the problem, I'll lose it.
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> For example, the problem I gave earlier, 24x7. I do the 7x4 first, and get 28. Put down 8, carry the two. Now comes the insanely hard part. I have to flit my mental gaze back and forth between the 8 and the 2, or else I'll lose one or both of them.

This, and everything else Dave described in this thread about the way he does mental maths, is exactly the way I do it. Maths was the only subject I had trouble with at school, and I even know why -- I was out of school for four months at the age of about seven, and during that time I got far enough behind on the basics of arithmetic that I ended up with a "maths is scary and difficult" mental block after I got back to school. Then this just accumulated for the entire rest of my school life.

I can do basic maths only by writing out the sums. If I have no way to do this, I have to visualise writing it out, and remember where I put all the numbers on my imaginary visualised piece of paper. It's a horrible, difficult way to do it, and I hate having to do it that way, and yes it does make your mind hurt to do it that way. In many cases I also have to visualise the objects themselves, as Dave mentioned in his original post, and just count them up in my mental picture. Aaargh.

Some day when I have time, I would like to go back and take high school level maths again, to see if I can overcome this irrational terror of numbers. I just barely managed to pass maths in Form 5 (age 15), the last year in which it was a compulsory subject when I was at school. So I'd like to do Form 5 maths again, and then do the Form 6 & 7 levels as well, just so I'd know I can do it.