I learned the poem but a bit differently. My version has actual rhyme & meter…
Thirty days hath September
April, June, and November.
When short February’s done
All the rest have thirty-one.
You have to remember that “Short February” is 28 (or 29) days but you have to remember that for the awful version you were taught, too. 
This is just about as I remember it. Never heard of the knuckle method.
I was taught both the knuckle method and the rhyme at some point before jr high.
It was mentioned in our 6th-grade Social Sciences book; we found it quaint, having grown on the poem (Spanish version of course):
30 días tiene Noviembre,
con Abril, Junio y Septiembre,
28 sólo uno
y los demás 31.
30 days hath November,
with April, June and September,
28 there’s only one
and the rest have 31.
I mentioned it at home: Dad knew the knuckles version, Mom didn’t. It took several repeats to get her to accept that yes, it worked.