It's overblown hype. Kids should understand multiple algorithms for addition/subtraction/multiplication/division for the same reason that we teach CS undergrads multiple sorting algorithms.

The point isn't to be able to pound out a sorting algorithm on the spot, but that learning about sorting algorithms provides a good "prototype" of thinking about algorithms more generally. Ditto for mathematical operators.

The problem is that parents never really had a deep understanding of even basic arithmetic. It's a self-reproducing cycle, and the USA will continue to lag behind the rest of the developed world in mathematics if our primary standard is "how the past generation did things".

>What age groups are affected by Common Core?

K-12

> I wonder if this helps or hurts the homeschooling crowd.

Ostensibly helps, because more teaching aids/material will be available, and knowing several algorithms to achieve the same thing helps you understand the concept in a much deeper way.

Actually it doesn't matter, because home schoolers aren't obligated to follow CC standards, and are likely to treat anything CC-related as pure unadulterated evil without actually evaluating pedagogical evidence.