Based on current models of problem solving within cognitive psychology, this study focused on the spontaneous problem solving strategies used by children as they first learned LOGO computer programming, and on strategy transformations that took place during the problem solving process. The research consisted of a six weeks programming training project using Turtle graphics on Texas Instrument Computers with 19 students in a combined second and third grade classroom. Data were collected from two math tests, teacher ratings of reading and spelling skills, a self concept inventory (the Student's Perception of Ability Scale), records of student time on the computer, and three pencil and paper programming tests. In addition, the programming strategies of eight students were studied closely on the Tower of Hanoi puzzle which has structural similarities to the LOGO language and facilitates similar forms of problem solving. Two main spontaneous problem solving strategies were identified: partitioning and encompassing. These strategies reflected the different ways in which the children represented the task problems (either as extended series or as subunits for unit building), thus managing their memory resources. While unanticipated sex differences in strategies were identified, they were not generalizable due to the research design. (BS)