From what I've seen around here and read, "rigorous" means "lots of homework."
This is for sure what our school district means! Homework starts in K and takes roughly 45mins. By 2nd grade, DS is doing around 1.5hrs worth of homework a night. And this is doing work that isn't even difficult. It just takes that long to read each problem, and write down the answers! I shudder to think how long the other students who don't understand the concepts are taking.
I'm getting to the point of going on a homework strike. The math homework is completely silly for my DS. A full page of math problems (in which he has to show 4 different ways to get the answer for each problem) that are simply addition and subtraction! For a child who can multiply, divide and do fractions! The only worthwhile part of the homework appears to be the writing work, but sadly it doesn't appear she's taught the children HOW to do it, just simply sent home the worksheets and left it up to the parents to teach the concepts of reading analysis, summarizing, event identification and cause/effect.