If we want to actually fix elementary math education, that would be simple. Singapore has developed a math curriculum that puts them top in the world in testing. Every research study that has used their system has found that it works far better than we do. But we have an entire educational establishment whose profits depend on our having periodic crises that let them rewrite all of the textbooks and charge top dollar retraining all of our teachers. Switching to something that works wouldn't make them money, so they will undermine the political process to guarantee that it doesn't happen.
As for homework, that's a giant can of worms. There is plenty of research on homework. It shows that homework is net neutral on actual learning, but a strong negative on creating stress. Digging in, it turns out that it can help or hurt, but whether it helps or hurts depends on whether there is someone at home who makes sure that the child does correct practice rather than incorrect practice. Therefore assigning homework's main impact (after home stress) is to widen the educational gap between children of different socioeconomic statuses.
The problem with common core homework is that the children don't know how to do it, the parents can't figure out what the teacher wants, and the end result is utter confusion. I've seen this first hand. I have a masters in math, but I'd look at my son's 4th grade homework and say, "I can think of several things that the teacher might want, but I have no idea which one she does." The end result was utter confusion in my son. Confusion that resulted in his lacking basic skills until we hired a tutor to fix that.
Anyways Common Core is a complete and utter disaster. We aren't too far from parents' resentment rising up and causing a new reform movement that will predictably get hijacked by the same interests who guaranteed that Common Core would fail. Which is nothing new. It has happened every 5-10 years for longer than I've been alive...