This study characterizes how learning and teaching differs as the responsibility for choosing curriculum goals and the strategies to reach those goals shifts between teacher and the students. Three different pedagogical approaches were used with 125 seventh-grade and eighth-grade students. All three curricula focus on electromagnetism, and were taught by two teachers in different schools over a two-week period. When students had control over the strategies employed to reach goals, their engagement stayed high. All three curricula advanced student understanding to some degree; however, large and significant gains were seen only for the pedagogy in which teachers set the specific learning goals and students had control over how to achieve them. Microdevelopment, a principle by which short-term learning recapitulates the stages seen in long-term developmental growth, is found to be a useful framework for curriculum development and for analyzing changes in student understanding. In general, initial "tinkering" activities are best followed by attempts at representing phenomena, only then to be followed by abstract conceptualization. On balance, we find that students benefit most from freedom to control the procedures that they generate in response to well-structured goals presented by the teacher. (Contains 6 figures, 5 tables and 5 notes.)