Responsibilist approaches to virtue epistemology examine the epistemic significance of intellectual virtues like curiosity, attentiveness, intellectual humility, open-mindedness, intellectual courage, and intellectual tenacity. On one way of thinking about these traits, they are the deep personal qualities or character traits of a good thinker or learner. Given the intimate connection between intellectual virtues and good thinking and learning, responsibilist virtue epistemology appears ripe for application to educational theory and practice. At a minimum, growth in intellectual virtues seems like a worthy educational aim. But is such an aim realistic? There are at least three objections to thinking that it is. In this paper, I defend the enterprise of educating for growth in intellectual virtues against each of these objections. I conclude that if pursued in the right way, intellectual character growth is a worthy and realistic educational aim--one that justifies rethinking some fundamental educational priorities and practices.