The example of having two equal lines of checkers and then increasing the spacing of checkers in one line and asking which live has more checkers is meant to test for

This example is meant to test for what is called the conservation of numbers. This concept was first discovered by Piaget, and it means that there is a moment when an individual (in this case, a child) realizes that space or mass does not equal the amount of something. In this situation, a child would realize that there are the same amount of checkers in each line regardless of how long one line is compared to the other.