Idiot Dan failed maths (8)
I believe the answer is:
addition
'maths' is the definition.
Although both the answer and definition are singular nouns, I cannot understand how they can define each other.
'idiot dan failed' is the wordplay.
'failed' indicates anagramming the letters.
'idiot'+'dan'='idiotdan'
'idiotdan' is an anagram of 'ADDITION'.
Can you help me to learn more?
(Other definitions for addition that I've seen before include "I don't aid (anag.)" , "Process of summation" , "Combination of numbers to find the sum" , "'Increase, augmentation (8)'" , "Mathematical procedure" .)