Museum educators often think about what they want children to take away with them from museum visits. But at least as important is what children bring to these visits. Research in developmental psychology shows that children and adolescents progress through a sequence of ways of understanding knowledge and knowing--understanding that lies at the core of museum experiences. Museum educators should be aware of these different ways of understanding and how they may (or may not) support people's museum experiences. In this article we describe this sequence of understandings and consider ways in which educators can support progression to its most advanced level--one at which inquiry, analysis, evaluation, and debate are valued and regarded as worth the intellectual effort they require. (Contains 1 table and 14 notes.)