Count IF Between Dates in Excel based on a name


I want to count the cells that contain a certain name in the assigned to column on one sheet only if the task start date is within a certain date range i.e the current week. 

For example, count how many times the "Assigned To" column on Project Plan sheet contains the name John Smith

The two sheets are Project Plan & Resources. 

The COUNTIF formula on the Resources sheet to count all tasks assigned to an individual based off their name in the Assigned to Column in the Project Plan sheet is: 


=COUNTIF({Project Plan Range 3}, =[Team Member]2) 

From here I've been trying to add the function to also check for the within the last 7 days criteria.

=COUNTIF({Project Plan Range 3}, =[Team Member]2) AND ({Project Plan Range 4} ????

Project Plan Range 4 in this case being the Task Start Date Column


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