This chapter describes the Discovery and Reflection Notation (DARN), a graphical trace notation to support students’ reflection about, evaluation of, and appropriate debugging of their search processes and strategies in the context of selfdirected experimentation. Design of the notation was motivated by our studies of undergraduates’ scientific reasoning with computer-based laboratories (Glaser, Schauble, Raghavan, & Zeitz, in press; Schauble, Glaser, Raghavan, & Zeitz, 1991; Shute, Glaser, & Raghavan, 1989). In these studies, students worked with one or more computer-based laboratories that simulate phenomena in various subject-matter domains (microeconomics, d.c. circuits, and geometrical optics). In each of the studies, students were set the task of trying to rediscover the laws or principles that apply within the laboratory content domains, an objective typically pursued across several sessions and over a period of weeks. Because the computer labs simultaneously serve as stimuli and recording devices (they automatically store records of all student activity), it is possible with them to study learning and complex reasoning across an extended time and also across a significant range of subject matter.