Depending on your intended meaning. "Downward spiral" and "vicious cycle" are both used to described degeneration of some sort, but there is a slight difference in meaning.
A "vicious cycle" is defined as
"one trouble leads to another that aggravates the first"
Which is applicable in your case, as his bad learning creates problems that prevent him learning properly in future, etc.
However, a "downward spiral", as defined by Wiktionary, is
"1.A series of thoughts or actions which feeds back into itself, causing a situation to become progressively worse. It is worse than a vicious circle, which is self-sustaining in its current state.
That is, a "vicious cycle" doesn't seem to get anyworse, it just goes around and around in a repetition. But a downward spiral is a progressive degeneration phenomenon.
Depending on the context of your situation, you would use one or the other. For me, just from looking at the example you have given, I would use "vicious cycle", as he doesn't seem to be descending into a worse state other than not learning properly.