Why are there 2 ways of writing the small letter “a”? i.e. one with the ‘roof’ and the other simply a circle with a verticle stroke to its right
All letters have multiple ways of writing them (especially if you include cursive). Take a look at “g” for example.
The different ways in type are due to type designers coming up with different ways to do it.
The two ways of writing an ‘a’ are exactly the same, except one has an extra frilly bit over the top of the loop.
What I want to know is why some capital letters differ so dramatically to the lowercase versions.
FWIW, I write “a” exactly as it appears in this post; which, I’ve noticed, seems to be far less popular than the circle-tail version.
I started writing ‘t’ with the tail at the bottom way back when because otherwise they looked too much like + in my math & physics notes.
I occasionally use the a-with-toupee just for the hell of it.
Go read Metamagical Themas by Douglas Hofsteder (sp?), in which he takes this question and goes nuts with it. He ends up discussing the nature of thought and perception and pattern recognition and all kind of deep, thought-provoking stuff, all starting with the ability to recognize multiple versions of the same letter.
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There are many different ways to write any letter, but most lower case letters have two basic forms–the cursive and manuscript forms. The letters a and g have three common forms, two handwriting (cursive and manuscript) and typeset. For all letters except a and g, the manual and typeset manuscript forms are the same.
For this, we can lay most of the blame (or give most of the credit) to Charles Zaner. Prior to the late 1800’s, most formal handwriting instruction was for cursive only and was seen as being as much an art form as a practical method of communication. Children often had great difficulty mastering the cursive forms, which required complex movements and good fine motor control. Zaner decided to develop a system better suited to young children’s larger movements. At the same time, he thought that it would aid children in learning to read if the letters they were being taught to write were similar to those in the books they were being taught to read.
To be sure, children were being taught to form letters that looked like those in books before Zaner; it wasn’t a brand new concept by any means. But Zaner’s method was the first widespread formalized method of manuscript handwriting instruction that focused on clarity and practicality over atractiveness.
In Zaner’s method, every letter of the alphabet except s could made by combining only five strokes (or six if you consider a half circle as a separate formation from a full circle): vertical line, horizontal line, slant left, slant right, and circle. Zaner designed his alphabet to closely resemble the common typeset alphabet, but found that the a and g (the kind with a circle on top and a squiggly line connected to another circle below) couldn’t easily be made using these formations, so he adopted alternative formations that better fit his system.
Others have since developed hybrid systems developed with the goal of making the transition to cursive easier and preventing common handwriting errors, the most popular being D’Nelian, which looks a lot like cursive with the connectors removed. Whether this is better is a major bone of contention between the two companies involved and in education circles.
OK, another one of my hokey folklore posts, please bear with me 
I remember hearing somewhere …
When the first printing presses were being used to mass produce copies of the written language, because of the quality of the ink and the coarseness of the type settings, the letters “o” and “a” could not be distinguished from each other on the page. And of course, that would cause great confusion and misinterpretation. Back then the “a” had its little tail, so they invented an “a” with a roof over its head.
To expand on Smeghead’s comment : i]Metamagical Themas* (the book) is a collection of the columns of the same name that Hofstadter wrote for Scientific American, with a few additions here and there. So you don’t have to read the whole thing to get to the ideas about written letters (but you might like it anyway).
Specific chapters to read would be 12 (“Variations on a Theme as the Crux of Creativity”) in which he shows 56 different styles of capital A and 23 "hei"s (Chinese character) , 13 (“Metafont, Metamathematics …”) in which he compares the same letter in different fonts and the same font in different alphabets, and especially 24 (“Analogies and Roles in Human and Machine Thinking”), which has 87 different lowercase "a"s all composed from segments of a simple pattern, like a segment number display on a calculator (the base pattern is a square divided into four smaller squares, with each square having an X in it).
I’m a kindergarten teacher. I was going to chime in about Zaner-Bloser but Number Six beat me to it.
Readers tend to encounter the print ‘a’ far more than the circle-with-a-tail version. Typically, you’re taught the ‘a’ with a cap first, and tend to bastardize your print writing with a cursive loop lowercase ‘a’ as you get more experienced writing. Check your own kindergarten papers, then compare them to later school writings and see.
Thanks 
I haven’t read it since high school, so I’m fuzzy on the details.