Over the past decade, most American museum educators have adopted as their objective helping museum visitors "learn how to look." They have embraced various kinds of participatory and interactive learning programs, encouraging engagement with works of art in the museum gallery through a process of inquiry shared by visitors and their guides. The coauthors of this essay propose that the real ultimate objective of museum teaching should be conceived as offering the visitor a certain kind of experience. Citing John Dewey's key concept of "an experience," they describe how the experience of viewing a work of art unfolds slowly in time, through observation, conversation, and the proposal of possible meanings, to arrive at synthesis and a sense of understanding. The authors, who have taught for over fifteen years in their respective institutions, advocate for the centrality of gallery teaching to the mission of the museum, and posit an ideal pedagogy for museum education practice in the twenty-first century.