A friend of mine just finished her college courses to become a high school science teacher. While she's waiting for a job in the public school system, she's making ends meet by teaching elementary students in a private Catholic school. I'm always interested in new curriculum (still trying to find a good fit for us*).
I eagerly asked her what curriculum the private school was using. She couldn't remember the actual name, so I just asked her what the kids were learning for 3rd graders. She emphasized math facts and rudimentary multiplication. She pointed out that it really didn't make any sense to teach them anything else because they weren't ready for it. I listened carefully, but in a kind of daze.
See, I had just taught my daughter long division with multiple digits (like 2508 divided by 43). I am not writing this to brag (but lets face it, I am quite proud of her and her willingness and desire to learn more than what she knows even when she knows it's going to be a struggle)**. I am writing this to point out that in public school, this kid, who is perfectly capable of doing much, much more than is even conceived of by the public education teaching paradigms, would be sitting bored to tears in a 3rd grade classroom with no hope of being really challenged. I have her at home and I can introduce her to a new concept when she's ready--not on some arbitrary calendar date (even some homeschool curriculums would easily fall into this trap).
*I have had Saxon for 2nd and 3rd grade, but I do not like how they deal with addition facts, the sheer repitition (yes--I skip it, but I paid for all of those pages I'm not using), and the place-value system. I do like how they introduce word problems quite concretely and I generally like the material that is covered, as long as we ignore how long it takes to introduce it.
**And she asked to do it. Her other 8 and 9 year old friends in Montessori are also working on long division (maybe not with multiple digits in the divisor). Other people who learn that I just taught a 3rd grader long division get an incredulous expression on their face. Yes, my daughter is smart--I can't take that away from her. After I explain fundamentals, she even sees the correlation to other parts of math, like how division and fractions are essentially the same. I really only ever need to show something to her once or twice and she learns "how to do it". A lot of it has to do with her wonderful understanding of math from Montessori, though we haven't used Montessori for any advanced multiplication or division--we've done that totally abstractly. I haven't yet taught her how to divide fractions to get the decimal representation, I want to introduce some goemetry first and reintroduce the tenths, hundredths, etc.