The solution was to use =ARRAYFORMULA. Here are my working examples:
=ArrayFormula('Student Submissions'!A:C)
for basic copying of columns
=ARRAYFORMULA(If('Student Submissions'!D3:D='Student Submissions'!D3,1,0))
for IF statements
=ArrayFormula(mmult(D3:I;TRANSPOSE(sign(column(D3:I)))))
for SUM
=ARRAYFORMULA(J3:J/6*100)
for AVERAGE and percent
Note: I found these answers in the Google Product forums but cannot find the link again.