"Fill in the box" is not referring to sums. It's referring to extremely rigid homework where you fill out each step in a process to finding out a result very precisely. It coincides with the horrific bubble tests where you select 1 of 5 answers and there is no partial credit.
This style of learning is what dominates US schools now from basic arithmetic all of the way up through advanced calculus.
The filling in of the boxes is most fairly compared to finding the typo in the complicated regex, or the file with incorrect permissions on the web server