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 What is Line Land?

Line Land is the land in which numbers come to represent a sequence of steps along an ordered path, not just the names that are assigned to set sizes of different magnitude. Perhaps the most important transition that children must make, as they move from the world of small countable objects to the world of abstract numbers and numerical operations, is to treat the physical addition or subtraction of objects as equivalent to the movement forward or backward along a line. All children eventually make this correspondence; however, until they do, they are unable to move from physical operations to mental operations with any insight.