I know some teachers and parents incorporate the terms "ten-one" or "ten-and-one", ten-two, and so on, as alternate terms for eleven, twelve thirteen etc. Has anyone ever taught the whole system, including multiplication tables etc. using those terms, and ignored, or side-lined the vernacular terms until later?
I'm asking because it's much easier for very young kids to learn that way. That's why (or mostly why, IMO) four year old Chinese children can count to 40, on average, while American children don't get that far till a year later. That's a huge gap, at that age. Asian kids are climbing all over the number line like they own it, while the kids in the rest of the world suck their thumbs and watch.
The reason is, the use of base-ten counting gives them a set of magic ladders, which join together perfectly, and are all exactly the same. Unfortunately, the rest of the world has a different approach, and base-ten counting isn't used.
Instead of a set of magic ladders, ten rungs long, the first two ladders are hacked up, with the 12 rungs on the first, and only 8 on the next. And they have funny backward names, which keep on changing. All very confusing. Even their trusty fingers become useless, because they have to go "off hands' to get to the top of the first ladder, and when they get there, they don't know where they are, or where they are going next.
Has anyone tried teaching the actual system, using base-ten counting, and delaying the use of vernacular terms like "eleven" until after basic calculation has been learned?
Would it be reasonable to suggest that doing that would in no way impair a child's language development, and that they would easily change over to saying "eleven" when appropriate, rather than "ten-one"?