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Default COUNTIF with Dates

I have two spreadsheets set up. One will be filled individually by employees
and the other will be used by management to track progress.
In the employees spreadsheet I have the following dates:
10/23/2008
10/27/2008
10/29/2008
10/28/2008
11/3/2008

In the management spreadsheet there will be two cells that they will modify
based on the reporting period desired
Start Date: 10/27/08 (this data is in A2)
End Date: 10/31/08 (this data is in B2)
I've been attempting to use COUNTIF to count the instances in which the
date is start date but <end date. I have tried several combinations to no
avail.
first: =COUNTIF(range,"A2<B2")
I am hoping for a result of 3, but always get back 0.
I also tried: =countif(range,"A2")-countif(range,"B2")
Result is also 0.

Any ideas?
 
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