I will begin by revisiting a fascinating debate between Karl Popper and Thomas Kuhn, on whether scientists should be dogmatic or critical. I will also discuss how these thinkers disagreed about how scientists should be educated. I will then argue that both Popper and Kuhn were mistaken about scientific method, and present my alternative view, which involves thinking in terms of functions performed within (and by) a community. On this view, which also happens to reflect more accurately the way science is actually done, good science may involve highly dogmatic and highly critical scientists. I will close by examining some of the potential educational consequences.