The splits demonstrated by little school miss dancing (7)
I believe the answer is:
schisms
'the splits' is the definition.
('schism' can be a synonym of 'split')
'little school miss dancing' is the wordplay.
'little school' becomes 'sch' (abbreviation. I am not sure about the 'little' bit.).
'dancing' is an anagram indicator.
'miss' with letters rearranged gives 'isms'.
'sch'+'isms'='SCHISMS'
'demonstrated by' is the link.
Can you help me to learn more?
(Other definitions for schisms that I've seen before include "Breaches in the church" , "Breaches in churches" , "Religious disunities" .)