I have a hard time accepting this. My daughter is in 3rd grade and seems to have a reasonable grasp of fractions. They teach her about them at (public) school and we've discussed them at home. Sure, "1/3 + 2/7" is outside her reach, but simpler stuff, things she can visualize, are well within her grasp.
> why is 2/3 different from 2/6 anyway
Because 2 pieces of a pie that you cut into 3 pieces is more than 2 pieces of a pie that you cut into 6 pieces. She understands that 4/8 == 2/4 == 1/2. Sometimes she needs to think about it a bit, but she does "get it".
No disrespect, but you read HN and think that your daughter's take on math and the home context you provide for it is a sensibly representative starting point?
My daughter's now 25 and has been quite the nerd herself through the years (eventually landing in linguistics and speech pathology), but I'd never assume that the fascinations she had instrinsically and that I helped foster as a parent were really typical. I wish they were - and hey, here I am reading HN too :)
I think the homework her school gives out is a sensibly representative starting point. Why wouldn't it be?
That homework expects a reasonable understanding of fractions. Enough that the child doing them can understand the difference between the number of slices in a pie being representative of the bottom number of a fraction.
Sure, I do math exercises with my daughter that aren't representative of what they teach in school (square roots, the fact that parallel lines _do_ meet at the vanishing point in the real world, etc). But those things aren't what I'm basing my assumptions are; the expectations the school has of her are.
> why is 2/3 different from 2/6 anyway
Because 2 pieces of a pie that you cut into 3 pieces is more than 2 pieces of a pie that you cut into 6 pieces. She understands that 4/8 == 2/4 == 1/2. Sometimes she needs to think about it a bit, but she does "get it".