"a" + infinitive verb = confusion

[ElDanés]

This has been baffling me for a quite a while now. It's a frequent construction, so I find it annoying that I don't know how to use it. I'm only able to read it, and understand the meaning.

This is taken from a Spanish reader I found, third line:

"Aprendo la aritmética, a leer y a escribir."
I learn arithmetics, to read and to write.

Why is a used in this sentence together with both leer and escribir? I thought that leer and escribir in themselves meant to read and to write, so it seems for me like a doubling of the to. I know that it may "just be like that," but I'd wish to learn the usage of it, so that I would be able to write such sentences myself.

Personally, I would just do it like:

Aprendo la aritmética, leer y escribir.

Thanks!