This study developed representations of the LOGO programming process which provide the basis for strategy analyses and a new perspective on problem solving in complex, semantically rich task environments such as LOGO. Nine students, ages 10 to 14, who had been identified as gifted and had previous programming experience, were trained in the rudiments of LOGO. The focus of the analysis was the performance of the students on three tasks which involved graphics, word-and-list, and interactive game programming. Software tools were developed to collect and analyze the subjects' interactions with the computer while programming. The product of the analysis was a problem behavior graph which plots the programmer's path through the two problem spaces involved in LOGO programming. These graphs are the basis for identification of the programmers' strategies. Three different layers of strategies were exhibited: top-down design strategies, depth-first component base strategies, and subsidiary search and debugging strategies. The model elaborated through the strategy analysis highlights the role of the task environment in supporting the students' problem solving, and it calls into question views concerning the relationship between strategies and knowledge and the way in which goals direct the problem solving process. An illustration of an analysis of the stages in collecting and analyzing the programming process is appended. (Contains 25 references.) (Author/KRN)