When I was very little, my mom used to make me sit on the square table in our living room and taught me Italian verbs. Today she tells me that, faced with the verb andare (to go), I came up with my pure and simple io ando, tu andi, egli anda, noi andiamo, voi andate, essi andano.
I was wrong, of course, but in my defense I can say that I was a kid, not yet corrupted by the vagaries of adulthood 
The fact is that andare, as well as dare (to give) and stare (to stay), is an irregular verb of the 1st conjugation (-are). Its etymology is quite uncertain, but it certainly borrows from the Latin verb vadĕre.
The correct conjugation of the Italian verb andare is:
io vado (I go)
tu vai (you go)
egli va (he goes)
noi andiamo (we go)
voi andate (you go)
essi vanno (they go)
The presence, in this verb, of two etymological roots, and- and vad-, constitutes a suppletivismo primario — just a high-flown definition used by grammarians.
It’s interesting to note that, in the Tuscan regional language, as well as in old novels of the nineteenth century, you can find vo as the first person singular: Io vo al mare as to mean Io vado al mare. Perpetua, a character described by Alessandro Manzoni in his novel I promessi sposi, says: Aspettate, aspettate, vo e torno. That is: vado e torno.
Please be careful what kind of resources you refer to, in order to learn the Italian language. I just came across a website (http://www.byki.com/lists/Italian/Present-verb-tense.html) that offers some wrong examples of the Italian present verb tense, and just…guess what? io ando, lui anda, loro andano.
Arrggh!
Your mom and I would get along very well! I conjugate an Italian verb aloud, usually an irregular one, every day while I’m making the bed. Weird but true. I love to see how kids internalize grammar rules and apply them, even in error. When my son was very little (he’s now 28), he used to say, “I amn’t going to do that!” This is incorrect but logical since it’s okay to say “you’re not” or “you aren’t,” “he’s not” or “he isn’t,” we’re not” or “we aren’t,” and “they’re not” or “they aren’t.” On the other hand, while you can say “I’m not,” “I amn’t” is not acceptable.
Yes, yours is a weird passion!
Well, at least it makes you an excellent Italian speaker! 
Your written Italian is at the same level of a native speaker, I’m impressed. I think that the flow of thoughts of the children sticks to a regular, direct and logical path. It is not very different from the method adopted by those who try to “compensate” their lack of knowledge of the grammar, and end up making blunders. Indeed, coming up with Io ando is not very different from writing coscenza (without a i). It is just an attempt to compensate, bringing the words back into a logical context. By the way, I love I amn’t.