Here, research on teaching and on learning coincide most closely. The study of student misconcep tions and their influence on subsequent learning has been among the most fertile topics for cognitive research. We are gathering an ever growing body of knowledge about the misconceptions of students and about the instructional conditions necessary to overcome and transform those initial conceptions. Such research-based knowledge, an important component of the pedagogical understanding of subject matter, should be included at the heart of our definition of needed pedagogical knowledge.