A dialogue between two secondary school students engaged in solving a problem is the basis for the assertion that the students differ in their problem solving capabilities; that is, they reduce the complexity of the situation in different ways. The discussion also suggests that students do not use the same form of competence. They make sense of the complex situation in different ways. It is also maintained that existing theories are able to explain different aspects of the problem solving process and competence. However, because no single theory encompasses all the aspects, a more comprehensive theory is proposed. This theory encompasses the notion that the person, through ideas, is able to consider and anticipate problem solving operations, thus displaying competence. More precisely, the person is in control through four processes: (1) efficacy, the degree to which the person experiences the feeling of control of the problem solving process itself; (2) achievement, the degree to which the person experiences that he or she is approaching the goal; (3) ruggedness, the degree of difficulty the person feels he or she has to overcome to solve the problem; and (4) availability, the degree to which the person feels that he or she has access to vital resources. With this frame of reference, an interpretation of the two students' problem solving processes is carried out using Perspective Text Analysis (B. Bierschenk and I. Bierschenk, 1993), a technique for making visible the structural relations of texts. It is also suggested that it is possible to apply catastrophe theory to make a model of problem-solving behavior. (Contains 8 figures and 29 references.) (Author/SLD)