I'll take a stab at this... im assuming the days are written (ie. Monday, Tuesday, etc etc)
If your column goes A1:A15 then it would be as follows
=COUNTIF(A1:A15,"Monday")
I can't think of a way you can do with *without* adding additional columns.
I can only tell you how I would do it in Excel, but that should work for numbers.
The WEEKDAY formula will tell you which dates are a Monday. You can then simply use COUNTIF to count the number of Mondays. You can obviously do this for any weekday, or add them all together to get a total number of weekdays.