The cognitive processes that are activated in the course of problem solving are diverse and complex, and they are likely to be organized in a non-linear manner. Among these processes, the following components may be identified:

  1. Searching for information, and structuring and integrating it into a mental representation of the problem ("situational model").
  2. Reasoning, based on the situational model.
  3. Planning actions and other solution steps.
  4. Executing and evaluating solution steps.
  5. Continuous processing of external information and feedback.

Baxter and Glaser (1997) present a similar list of cognitive activities labeled "general components of competence in problem solving": problem representation, solution strategies, self-monitoring, and explanations.

Analytical problem solving in everyday contexts, as measured by the ALL problem-solving instrument, focuses on the components 1 to 3 (and to some extent 4).

2.1.2 Psychological models

Psychological models of these processes and the mental structures (representations) on which they operate have changed over the history of psychology, each tailored to the particular kinds of problems that were focused by the respective research paradigm. In the early years of cognitive psychology, for example, "insight" was seen as a major mechanism. This concept was appropriate in limited but ill-defined problem situations, where a sudden restructuring or reinterpretation of the problem yields the solution. Newell and Simon (1972), in their seminal book "Human problem solving", which served as a framework for numerous studies in cognitive information processing and artificial intelligence, described problem solving as a process of search in a "problem space" consisting of states (including given state and target state) and operators. This model was appropriate for the study of well-defined, "puzzle"-type problems. While Newell and Simon believed they had discovered rather universal mechanisms, research on scientific reasoning and expertise later proved that problem solving strongly depends on the use of domain-specific knowledge which was described in terms of rule systems, schemata, mental models or "mental tools" (see e.g. Chi, Glaser, and Farr, 1988; Weinert and Kluwe, 1987). At the same time, it became clear that meta-cognition plays a vital role for both problem-solving processes and the outcomes of problem-solving activities (Brown, 1987; Flavell, 1976). Meta-cognition is defined as the process of planning, monitoring, evaluating and regulating ongoing cognitions as well as the knowledge and beliefs about cognitive functioning.

In order to find out how well people can solve particular types of problems, it is not necessary to identify mental structures or process components in detail. Assessment frameworks need not meet the sophistication of cognitive-psychological models. However, even a purely functional approach to problem-solving assessment has to take into account some important results of psychological research, associated with the key terms "general intelligence", "complex problem solving", and "domain specificity". The following section provides a short overview of these findings and discusses the implications for the design of problem-solving assessments.