Faculty backs learner doing badly in mathematical process (4,8)
I believe the answer is:
long division
'mathematical process' is the definition.
(long division is a kind of mathematical process)
'faculty backs learner doing badly' is the wordplay.
'faculty' becomes 'vision' (vision is a kind of faculty).
'backs' is a charade indicator (letters next to each other).
'learner' becomes 'l'.
'badly' indicates anagramming the letters.
'doing' is an anagram of 'ongdi'.
'l'+'ongdi'='longdi'
'vision' after 'longdi' is 'LONG DIVISION'.
'in' acts as a link.
(Other definitions for long division that I've seen before include "Mathematical operation" , "Mathematical calculation" , "(Pre-calculator) arithmetical process" , "Dealing with large numbers" , "tedious disagreement" .)