They don't fall apart. So, you ask a child to count the pens here on my desk, and he does so and tells you there are nine. Such flexibility apparently comes straight out of the direct, inflexible connection between the principle and the skill of counting. In fact, the idea virtually is the behavior. To learn counting, then, is to learn the principle, even though a child enumerating the pens on Ohlsson's desk might not be able to say why he does it the way he does.
Subtraction is a different story.
In order to investigate the connection between the principles and the procedures in one topic of subtraction, Ohlsson taught HS how to subtract using two different procedures, or algorithms, and he taught each algorithm both conceptually and mechanically. The algorithms taught to HS were regrouping and augmenting . The 9 in 19 could then be subtracted from 12 instead of from 2. Augmenting, taught in Europe, simply adds equally to the minuend and the subtrahend. A comparison of the effectiveness of the four lessons not only moved toward settling an old dispute in early math education but also suggested a hypothesis for why arithmetic is so difficult for children to learn.