Originally written 30 years ago, this paper is an analysis of the central challenge of schooling--that of engaging fully the powers of students' minds in classroom learning. This challenge maintains its relevance today. The work of engaging what John Dewey referred to as students' "inner attention" becomes the focus of an investigation of students' current ideas in a variety of subject matters. This investigation reveals areas in which their ideas diverge from the established curriculum. It uses the methodology of Critical Exploration, which was developed by Eleanor Duckworth as a teaching and research methodology that both reveals learners' ideas and encourages their active creation of meaning. This methodology provides students with rich and complex curriculum materials for their own manipulation; it also provides them the freedom to express, however tentatively, their ideas, to take them seriously, and to follow them through. As a result of these studies of learning, I put forward the view that a significant part of the responsibility for students' alienation from classroom learning lies with a conception of knowledge, often reflected in curriculum, that is too rigid to take their ideas into account. I elaborate this view in an analysis of the aspects of particular subject matters that alienate students if the students are not given adequate ways of entering them. I make the case that these same complexities can be used as compelling invitations into deeper knowledge.