Sophian, C. (1999). Children's ways of knowing: Lessons from cognitive development research. In J. Copley (Ed.), Mathematics in the early years, pp. 11-20. Reston, VA: National Council of Teachers of Mathematics.

Among the most basic goals of cognitive development research is to specify what children know at different ages. What makes this seemingly straightforward question challenging is that it is necessary to consider not just how much children know but how well, or in what manner, they know it. Children may look like they lack knowledge on one version of a cognitive-developmental task, and yet succeed when a small procedural change is made. Equally, they may respond correctly to one problem and then revert to a prior, incorrect, strategy on the next . Three bodies of cognitive-development research to illustrate and illuminate these complexities: (a) age comparisons of children's knowledge-based reasoning across different tasks or conditions; (b) contextualist research on the ways in which children's knowledge is linked to familiar activities; and (c) microgenetic research on the evolution of children's knowledge with practice. The chapter concludes with a discussion of the implications of this research for early mathematics education.

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