middle school vs schooling

middle school

noun
  • An educational level or stage between primary school and secondary school. 

  • A school which crosses the traditional divide between primary school and secondary school. 

schooling

noun
  • Institutional education; attendance of school. 

  • Training or instruction. 

  • The training of a horse at dressage. 

How often have the words middle school and schooling occurred in a corpus of books? (source: Google Ngram Viewer )