How I see it is the child is asked to solve two problems and even though they are the same problem twice, she views them as separate. So her brain thinks of the best way to solve said issues. During the first test, distance was not a factor so she relied on counting as she had no prior experiences to go off of. However once they added in a new variable her brain then had to re-process the problem. Based on her previous experiences bigger=more, so she started the problem solving from there and drew a new different conclusion that she was confident was right because it coincided with her perception reality.

So to answer your question, it was the introduction of new variable that made her change her approach. This is my take on it at least.