ABSTRACT
This chapter elaborates on a simple example of how people construct mathematical objects, namely numbers. Research on how children construct numbers directly challenges the Platonist position that numbers and other mathematical objects exist in the world, independent of human thought. Numbers, like 7, are not out there to simply see; people make 7 and use it to organize what they perceive as, say, seven yellow bricks. Like all other mathematical objects, constructing numbers involves coordinating actions: first sensorimotor actions, such as pointing and reciting number words, and then mental actions that people can perform in imagination. Numbers, in particular, require actions that produce and transform units, including composite units. This chapter also explains subitizing as an innate tendency humans have, from birth, that supports the construction of numbers.
