They have another New Math, only this one makes a lot more sense than the 1970s version. In his parody of the new math, Tom Lehrer mentioned that many parents were embarrassed at being unable to do their child's arithmetic homework. As a public service, let me link you to an article and video to help parents understand the new teaching terms of "gridding" and "chunking."
I was surprised to discover that when I'm doing long multiplication or division in my head, most of the time that's exactly what I'm doing: gridding and chunking. My dad didn't call it that, but those are (some of) the tricks.
A lot of commenters are worried the "new" methods prevent kids from learning why they are doing it. I think that's way off base. Multiplication (gridding) is just a faster way of doing addition and division (chunking) is a faster way of subtracting something ... a lot of times. By teaching kids to solve easier problems and add the answers up by gridding and chunking they are learning how multiplication and division are just addition and subtraction sped up.