Arthur has failed to understand the Conservation concept. In general, children learn the seven Piagetian tasks in this order: number (typically mastered by age 6), length, liquid, mass, area, weight, and volume (usually acquired by age 10).
The Swiss psychologist Jean Piaget was the first to examine conservation as a young child's ability for logical reasoning. To put it simply, being able to maintain means knowing that a quantity stays the same when modified by being stretched, cut, elongated, spread out, shrunk, poured, etc.
The amount of liquid hasn't changed, thus a young child who has grasped the idea of liquid conservation can understand this. If the child points to the taller glass, inquire as to why they think it holds more water. You can pour the water back into the first cup as part of this task to show that the quantity hasn't changed, even if the child isn't cognitively ready to understand why.
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