Last time we discussed the "distance effect," by which people can tell more easily which of two numbers is larger when those numbers are far apart.
The closer the numbers, the longer it takes us to compare them. This suggests to some psychologists that we solve such problems with a mental number line. That's the line grade school teachers drew on the blackboard with one, two, three marked off along it.
More evidence for the existence of a mental number line comes from cases of stroke victims who develop "acalculia," or the inability to handle numbers. Of particular interest is the 1980s case of a Frenchman called Monsieur N., who as a result of damage to his brain could no longer say what number comes between 7 and 9 or after 3 but before 5. Neurologists noticed that, while his answers to such questions were apparently guesses, he never guessed very far off the mark. That is, he wouldn't guess 42 as an answer to the question "What is three plus five?" but he might guess "six."
Monsieur N. seemed to have lost the ability to think of numbers as specific entities and handle mathematical procedures such as addition or subtraction, but he retained a rough sense of where numbers fell on a number line. For example, he knew that "9" was a lot of children for one woman, but not enough for a school. The case of Monsieur N. suggests that generating a mental number line may be a distinct ability, than the ability to do actual math.