ABSTRACT
I begin this chapter with an apparent contradiction: School mathematics— especially beyond the primary grades—seems difficult and inaccessible to many people. Yet most young children entering school have a great deal of knowledge about quantities and their relations. What is more, children’s knowledge of quantity relations seems to be organized in ways that are coherent with the formal structures of mathematics, including some fundamental laws of algebra. How can it be that children know so much about mathematics and yet have such a hard time learning it in school? My efforts to answer this question raise a series of fundamental questions about the nature of knowledge and cognitive competence, the relations between cognition and social processes, and the role of schooling in adaptive sociocognitive development.
