[intellegacy]

>One recent example I saw (a colleague works on coaching teachers in common core) was a class of elementary students who could correctly multiply 4/7 * 5/9, but couldn't shade in 1/4 of a square. They memorized and rehearsed the procedure for multiplication, but never built understanding of what they were doing.

the author's argument is that you build understanding by doing. learning the forms and perfecting your "doing" of them is fundamental to developing insights into what is going on

some students make the leap themselves, some students need it explained to them, either way, the student needs to know the HOW before they can understand the WHY