2. Problem solving from a scientific point of view

2.1 The concept of problem solving

2.1.1 Definition

For the purposes of the ALL study, we begin with a very general definition of problem solving as it is generally understood in psychological research (Hunt, 1994; Mayer, 1992; Mayer and Wittrock, 1996; Smith, 1991).

Problem solving is goal-directed thinking and action in situations for which no routine solution procedure is available. The problem solver has a more or less welldefined goal, but does not immediately know how to reach it. The incongruence of goals and admissible operators constitutes a problem. The understanding of the problem situation and its step-by-step transformation, based on planning and reasoning, constitute the process of problem solving.

This relatively broad definition makes it clear that problem solving is to be understood as a cognitive process. More specifically, we are exclusively concerned with cognitive-analytical problem solving. It is not to be confused with the intuitive everyday use of the term or with the clinical-psychological concept in which problem solving is associated with the resolution of social and emotional conflicts. Nevertheless, social context is also relevant for our definition of analytical problem solving, for example when problems have to be approached interactively and resolved through co-operation. Of course motivational factors such as interest in the topic and task-orientation also influence the problem-solving process. However, the quality of problem solving is primarily determined by the comprehension of the problem situation, the thinking processes used to approach the problem, and the appropriateness of the solution.

The problem itself can be characterized by different aspects:

  • The context can reflect different domains, which may be of a theoretical or a practical nature, related to academic situations or to the real world. Within these domains, problems can be more or less authentic.
  • The scope of a problem can range from working on limited, concrete parts of a task to planning and executing complex actions or evaluating multiple sequences of actions.
  • The problem can have a well-defined or an ill-defined goal, it can have transparent (explicitly named) or intransparent constraints, and involve few independent elements or numerous interconnected ones. These features determine the complexity of the problem.

How familiar the context is to the target population, whether the problem involves concrete tasks or complex actions, how well the goal is defined, how transparent the constraints are, how many elements the problem solver has to take into account and how strongly they are interconnected — all these features will determine the level of problem-solving competency that is required to solve a certain problem. The empirical difficulty, i.e. the probability of giving a correct solution, will depend on the relation between these problem features on the one hand, and the subjects' competency level on the other hand.