It's clearly useful and appropriate to show fractions as a relation of a part to a whole, as a portion of something, but it's almost always depicted in 2 dimens

It's clearly useful and appropriate to show fractions as a relation of a part to a whole, as a portion of something, but it's almost always depicted in 2 dimensions (typically a circle) and therefore restricted to comparing to just one whole (i.e. the denominator of the fraction in reduced form). Using 1 dimension allows us to compare the portion to not just one whole but many familiar wholes, the natural numbers. I think it would also be useful to co-develop intuition of space and portions in 3 dimensions. Maybe not everyone can get to it, I don't know, but the paper: http://www.psy.cmu.edu/~siegler/121-siegler-etal-tics.pdf http://www.psy.cmu.edu/~siegler/121-siegler-etal-tics.pdf