Methodological issues in the use of protocol analysis for research into human problem solving processes are examined through a case study in which two students were videotaped as they worked together to solve mathematical problems "out loud." The students' chosen strategic or executive behavior in examining and solving a problem was studied, focusing on heuristic strategies. A macroscopic framework capturing the essential problem solving elements is described. Protocol episodes include reading, analysis, exploration, planning/implementation, verification and transitions between episodes where executive decisions can take place. The range and interrelationship of variables are discussed which affect the kinds of information emerging from verbal methodologies including the number of persons being taped, the degree of experimenter intervention, the nature and degree of freedom within instructions and intervention, the nature and comfort of the subjects' environment, and task variables. The uses and dangers of protocol analyses in research are discussed. (CM)