that's why montessori math is so impressive. it starts with counting out beads one at a time by the hundreds until they have internalized that. then they get beads on a stiff wire 10 at a time, and repeat the process counting them out up to a 1000. and so forth until eventually they hold in their hands blocks of 1000 beads glued together in a cube, and only after they have internalized that the beads get replaced with more abstract woodblocks and sticks. and all that happens in the first year or so at the age of 3.