Formula for average with column heading and column subheading

Hopefully this will make sense and be easy enough for someone more learned (and less hungover) than I.

I have a table which has test scores. At the top of each column in row 1 is the name of the subject, and in row 2 the test title, for example

I want to calculate the average of the values for a matching value in row 1 and row 2. 

I thought the correct formula might be something like

=AVERAGEIFS(A3:F6, A1:F1,"BI", K2:F2, "3rd")

but this keeps giving me a value error, so I guess I am doing something wrong. 

Can any kind soul help me out here?