The Logo programming language was designed to support students' construction of knowledge about mathematics, problem-solving, and elementary computer science (Papert, 1980). A decade of Logo use in the classroom has led to a body of research that suggests that Logo-based instruction can support students' development of specific mathematical understandings (Lehrer, Sancilio, & Randle, 1989; Thompson & Wang, 1988), problem-solving strategies (Carver & Klahr, 1986; Swan, 1990), and computer science concepts (DeCorte, Verschaffel, & Schrooten, 1989), when those topics are explicitly taught. Nonetheless, many questions remain unanswered regarding the ways in which individual students construct knowledge within Logo environments and the ways such constructions can be supported, expanded, and developed. These questions deserve systematic exploration.

The study reported in this article grew out of several years of quantitative research concerned with the development of effective Logo-based interventions for the teaching and learning of problem solving (Swan, 1989, 1990; Swan & Black, 1989). Although that body of work successfully demonstrated that a particular kind of Logo-based problem solving intervention could support the development of specific problem-solving strategies, it revealed little of what individual students were doing that caused positive increases in their problem-solving abilities, and it did not address the problem-solving strategies those students brought to the intervention.

The investigation reported in this article represents a preliminary step in the latter direction. The investigation concerned itself with the problem-solving strategies individual students bring to and utilize within Logo programming contexts and with how such strategies are related to students' domain knowledge and cognitive styles. The belief that students bring unique, personal knowledge and practices to their school experiences guided this investigation, along with the belief that a systematic investigation of a small part of that experience within the constrained and reflective domain of Logo problemsolving might yield insights into the diversity of ways in which students approach and organize their problem-solving activities. In particular, this study explores two differing explanations for the diversity found in problem-solving behaviors: (a) the developmental explanation (Ginsburg & Opper, 1980; Piaget, 1971), which holds that such diversity represents evolutionary stages through which people naturally pass as they develop mature problem-solving behaviors, and (bJ the dispositional explanation (Turkle & Papert, 1990), which argues that such diversity represents mature "cognitive styles" that are equally valid on their own terms. In so doing, the study develops a methodology based on the traditional Piagetian clinical interview and proposes a third possible explanation, based on domain knowledge, for the diversity of observed problem-solving behaviors.