Human-Like Mathematical Reasoning

Humans often solve arithmetic problems the "long way". The optimal bit-based methods of the computer are not natural and, as such, not employed by humans. Several psychological experiments have been performed showing that, not only are the arithmetic operations used by humans not optimal, but the long-hand algorithms can be suboptimal and sometimes inconsistent. Some humans classify problems before approaching them (even the classifications can be inconsistent) and use a personal method that varies consistently with the class of problem.

VanLehn argues that a non-LIFO goal reconstruction technique can reproduce this behavior. An essential component to the reproduction of this behavior is that goals cannot be managed by a LIFO stack. Teton has more discussion.