Why does the typed 'a' have a different prototype than the written 'a'?

Nope, never got into that. My daughter does, though.

Colophon may not have, but I certainly did - and slashed my 7s, and used the fancy “a”. Is this a phase Dopers go through in middle school?

I learned the simple way but started doing the “fancy” way in college as a bit of a conceit (also I think it looks better). It stuck. I still write the fancy way. This is how most of my co-workers can tell if I wrote something (“Oh, that’s GameHat’s crazy ‘a’. He wrote this note.”)

My lower case ‘t’ as used as a mathematical variable always gets a tail heading right like you see in many fonts, but most versions I write will not. The reason there is that you don’t want them to look like plus signs. Similarly, ‘z’ needs a bar to differentiate it from ‘2’. I still don’t have a good way of differentiating my sloppy ‘5’ from ‘s’ in my writing though. I also fail to remember to make my lower case ‘y’ curly and sometimes get it confused with ‘x’. And differentiating between ‘x’ and ‘X’? Just make one REALLY big.

Some foreign grad students I knew wrote 9 with an extremely hooked tail, far more than you you see in most fonts, looking like a lowercase g fully above the line.

You’ll see ‘7’ crossed by many whose ‘1’ it would otherwise greatly resemble, but that depends a lot on the person. My ‘1’ looks like a lower case ‘L’ and only gets serifs for emphasis. A lower case ‘L’ used as a variable is of course written as a cursive-style loop.

When I went to renew my passport, the clerk asked me if I was foreign born. That’s kind of an alarming question when one is trying to renew a US passport. It turns out that she thought my writing was very European. I guess it has some European roots, but to me it’s just practical.

My digits “one” are written very much in the German manner (to distinguish them from lower-case L, for example).
My “sevens” and Z’s and zeros have a slash through them to distinguish them from other characters.
My lower-case A’s have always been written with the flourish on top, since first grade, when I realized that it looks better in the books I was learning to read than it looked on the banner over the blackboard. (I still wasn’t able to draw a straight chimney on a rooftop, though.)
My lower-case X’s look kind of like the infinity symbol, but with the left side opened.

I slash my (number) 0’s which I think is European, possibly German, style.

It help’s distinguish them from the letter O. I’m in Engineering and believe me it can make a difference.

Fran Lebowitz has a quiz in one of her books that’s something like how to determine if you’re an heiress, and one of the questions goes something like:

Oh, yeah. Picked that up in college math.

[Re: slashed Z’s] Me too: complex analysis. So many z’s start to look like 2’s after a while without the slashes.

I’ve most recently gotten in the habit of replacing my printed l’s (els) with cursive, looped l’s. That’s for e-mail addresses, where the context may not help you distinguish between an ‘l’ from a ‘1’.