Sloppiness in school unknown, introduction of mentoring key (8)
I believe the answer is:
schmaltz
'sloppiness' is the definition.
'in school unknown introduction of mentoring key' is the wordplay.
'in' indicates putting letters inside.
'school' becomes 'sch'.
'unknown' becomes 'z' (algebra).
'introduction of' indicates taking the first letters.
'key' becomes 'alt' (I've seen this in other clues**).
The initial letter of 'mentoring' is 'm'.
'sch'+'z'='schz'
'm'+'alt'='malt'
'schz' enclosing 'malt' is 'SCHMALTZ'.
(Other definitions for schmaltz that I've seen before include "Mushiness" , "mush" , "Extreme or excessive sentimentality" , "Jewish word meaning sugary sentimentality - has just one vowel" , "mawkishness" .)