Programming in Logo is uniquely suited to students' reflections on their own thinking and problem-solving because the programming process involves both the symbolic representation of step-by-step solutions and the dynamic testing and refinement of those solutions. As Turkle and Papert (1990) note, the computational object is "on the border between an abstract idea and a concrete physical object." This article takes the similar position that because a correspondence can be drawn between the thought processes of student programmers and the programming commands they use to solve particular problems, Logo programming might be an ideal environment for the investigation of children's problem-solving strategies. The methodology used here, then, is a variation on the traditional Piagetian clinical interview (Ginsburg & Opper, 1980). The participating students were asked to solve Logo programming problems, and their problem-solving behaviors were videotaped. During that process, the researcher asked questions about why the students were doing certain things and offered help intended to cue particular cognitive behaviors. The researcher also kept a record of the commands students used to solve the problems, believing these represented their manipulation of the materials, the "concrete ideas/ abstract objects" of Logo programming.

The study was conducted with 11 fourth- and fifth-grade students at a private elementary school in Brattleboro, Vermont. Participating students included 1 fourth grade and 4 fifth-grade girls, and 4 fourth-grade and 2 fifth-grade boys. All students came from rural, middle-classfamilies. They rangedin age from 8.75 to 11.5 years, andin ability from learning-disabled to academically gifted. All were beginning Logo programmers. They had been meeting once a week with the author for approximately 10 weeks at the time the study was conducted, and used the LCSI Logo Writer version of the language on Apple IIe computers.

Each student was given three graphic designs drawn on cardboard and asked to reproduce them on the computer (Figure 1). The first was a square with a triangle on its right edge, the second was a square in the upper right corner of the computer screen, and the third was a border drawn around the screen. The three designs were chosen because they were relatively simple but could be broken into two or more distinct parts in terms of their solutions and because those solutions could be related one to another.

The students were simply asked to reproduce the designs. They were given no constraints concerning how they should draw them, other than that they should use Logo and that the result should appear on the computer screen. Interestingly, although all the students had experience writing Logo procedures, all but one used Logo's immediate mode to solve the problems, and that student merely used procedures he had already created. As the students solved each of the problems, they were asked to tell what they were thinking. They were also asked for explanations of certain behaviors, and they were provided with support when they needed it. Each student's work on all three problems was videotaped, and their conversations with the researcher were transcribed. In addition, all the programming commands used in each solution were recorded. The transcriptions and the command records were then integrated to produce the problem-solving protocols used as data in the study.