A calculated field will always use the Sum of the selected fields, even
if you have used a different function in the pivot table, such as Count.

As a workaround, you could add a column to the source data table, with a
heading of SchoolsCount. Enter a 1 in each row for the SchoolsCount.
Then, refresh the pivot table, and add the SchoolsCount field to the
data area, as Sum.
Use the SchoolsCount field in the calculated field, instead of the
Schools field.