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Complex problem solving research in North America and Europe: An integrative review

Joachim Funke

Department of Psychology, University of Heidelberg, Germany

Peter Frensch

Department of Psychology,

Humboldt University, Berlin, Germany

© 1995 by Joachim Funke & Peter Frensch


Complex problem solving is a relatively new research domain that is based on the assumption that complex, real-life problem solving has been largely ignored by traditional problem solving research. In this article, we contrast the two dominant approaches to studying complex problem solving, the North American and the European approaches. We present a definition of complex problem solving and describe a theoretical framework that accommodates the theoretical and empirical strides that have been made in understanding complex problem solving thus far, and may serve as a guide for future research. We discuss the dominant methodological approaches that have been employed to study complex problem solving, and offer our own recommendations on which of the various approaches might be the most promising one.


Many of our daily activities involve complex problem solving (henceforth CPS) of some sort. For example, we decide how to structure a theoretical paper on an academic topic, how to fix a car that has broken down, make plans for an extended vacation, and so on. Of course, not all problem solving is alike. There are problems that can be solved with relatively few mental steps, and there are problems that require extensive "thinking.” There are problems that we have never encountered before, and there are problems we are familiar with. There are problems that have very clear goals, and there are problems where the goals are far from clear. Complex problems, then, can be distinguished on any number of meaningful dimensions, and the solution processes, the mental steps we engage in when solving a problem, may differ widely for different types of problems.

In this article, we summarize the present dominant empirical approaches to studying complex problem solving, after providing a brief historical background within which the development of the dominant approaches in North America and Europe can be understood. In addition, we present a definition of complex problem solving, and describe a theoretical framework that accommodates the theoretical and empirical strides that have been made in understanding complex problem solving thus far, and serves as a guide for future research. Last but not least, we discuss the dominant methodological approaches that have been employed to study CPS, and offer our own recommendations on which approach might be the most promising.

Historical Roots and Current Situation

Beginning with the early experimental work of the Gestaltists in Germany (e.g., Duncker, 1935), and continuing through the sixties and early seventies, research on problem solving was typically conducted with relatively simple, laboratory tasks (e.g., Duncker's "X-ray” problem; Ewert & Lambert's, 1932, "disk” problem, later known as "Tower of Hanoi”) that were novel to subjects (e.g., Mayer, 1992). Simple novel tasks were used for various reasons: they had clearly defined optimal solutions, they were solvable within a relatively short time frame, subjects' problem solving steps could be traced, and so on. The underlying assumption was, of course, that simple tasks, such as the "Tower of Hanoi,” captured the main properties of "real” problems, and that the cognitive processes underlying subjects' solution attempts on simple problems were representative of the processes engaged in when solving "real” problems. Thus, simple problems were used for reasons of convenience, and generalizations to more complex problems were thought possible. Perhaps the best known and most impressive example of this line of research is the work by Newell and Simon (1972).

However, beginning in the seventies, researchers became increasingly convinced that empirical findings and theoretical concepts derived from simple laboratory tasks were not generalizable to more complex, real-life problems. Even worse, it appeared that the processes underlying CPS in different domains were different from each other (Sternberg, 1995). These realizations have led to rather different responses in North America and Europe.

In North America, initiated by the work of Herbert Simon on learning by doing in semantically rich domains (e.g., Anzai & Simon, 1979; Bhaskar & Simon, 1977), researchers began to investigate problem solving separately in different natural knowledge domains (e.g., physics, writing, chess playing) thus relinquishing on their attempts to extract a global theory of problem solving (e.g., Sternberg & Frensch, 1991). Instead, these researchers have frequently focused on the development of problem solving within a certain domain, that is on the development of expertise (e.g., Anderson, Boyle, & Reiser, 1985; Chase & Simon, 1973; Chi, Feltovich, & Glaser, 1981). Areas that have attracted rather intensive attention in North America include such diverse fields as reading (Stanovich & Cunningham, 1991), writing (Bryson, Bereiter, Scardamalia, & Joram, 1991), calculation (Sokol & McCloskey, 1991), political decision making (Voss, Wolfe, Lawrence, & Engle, 1991), managerial problem solving (Wagner, 1991), lawyers' reasoning (Amsel, Langer, & Loutzenhiser, 1991), mechanical problem solving (Hegarty, 1991), problem solving in electronics (Lesgold & Lajoie, 1991), computer skills (Kay, 1991), game playing (Frensch & Sternberg, 1991), and personal problem solving (Heppner & Krauskopf, 1987).

In Europe, two main approaches have surfaced, one initiated by Donald Broadbent (1977; see Berry & Broadbent, 1995) in Great Britain and the other one by Dietrich Dörner (1975, 1985; see Dörner & Wearing, 1995) in Germany. The two approaches have in common an emphasis on relatively complex, semantically rich, computerized laboratory tasks that are constructed to be similar to real-life problems. The approaches differ somewhat in their theoretical goals and methodology, however. The tradition initiated by Broadbent emphasizes the distinction between cognitive problem solving processes that operate under awareness versus outside of awareness, and typically employs mathematically well-defined computerized systems. The tradition initiated by Dörner, on the other hand, is interested in the interplay of the cognitive, motivational, and social components of problem solving, and utilizes very complex computerized scenarios that contain up to 2,000 highly interconnected variables (e.g., Dörner, Kreuzig, Reither, & Stäudel's, 1983, LOHHAUSEN project; Ringelband, Misiak, & Kluwe, 1990). The two traditions are described in detail by Buchner (1995).

To sum up, researchers' realization that problem solving processes differ across knowledge domains and across levels of expertise (e.g., Sternberg, 1995) and that, consequently, findings obtained in the laboratory cannot necessarily be generalized to problem solving situations outside the laboratory, has during the past two decades, led to an emphasis on real-world problem solving. This emphasis has been expressed quite differently in North America and Europe, however. Whereas North American research has typically concentrated on studying problem solving in separate, natural knowledge domains, much of the European research has focused on novel, complex problems, and has been performed with computerized scenarios (see Funke, 1991, for an overview).

Complex Problem Solving: A Definition

With the above discussion in mind, it might not come as a surprise to find that there exists a wide variety of definitions of the term complex problem solving that all have little in common (e.g., Frensch & Funke, 1995). Indeed, researchers in the area of problem solving have long been troubled by the absence of agreement on the exact meaning of many of the basic terms in the area (e.g., Smith, 1991). Any general conclusion regarding complex problem solving, however, and any theoretical model of complex problem solving can only be meaningful if we can all agree on what constitutes a problem and what constitutes complex problem solving. Below we therefore offer our own definition of CPS, a definition that is firmly rooted in the European tradition of Donald Broadbent and Dietrich Dörner. The definition has the advantage that it incorporates many aspects of the definitions provided by the contributors to the volume edited by Frensch and Funke (1995), and thus is rooted in a rather broad theoretical basis. According to our definition,

CPS occurs to overcome barriers between a given state and a desired goal state by means of behavioral and/or cognitive, multi-step activities. The given state, goal state, and barriers between given state and goal state are complex, change dynamically during problem solving, and are intransparent. The exact properties of the given state, goal state, and barriers are unknown to the solver at the outset. CPS implies the efficient interaction between a solver and the situational requirements of the task, and involves a solver's cognitive, emotional, personal, and social abilities and knowledge.

Notice that this definition differs rather substantially from definitions that feature prominent in the North American tradition. John Anderson, for the North American approach, for example, has defined problem solving as "any goal-directed sequence of cognitive operations” (Anderson, 1980, p. 257), regardless of whether the task is novel or familiar to the solver, regardless of whether or not the task is complex, and regardless of whether or not a single barrier or multiple barriers exist between given state and goal state. Our definition, in contrast, constrains potential problems by requiring that they be (a) novel tasks that subjects are unfamiliar with, (b) complex, (c) dynamically changing over time, and (d) intransparent. In order to solve these problems, a solver has to be able to anticipate what will happen over time, and has to consider side effects of potential actions.

Note that the definition given above has an important component, namely a focus on the distance between the task and the solver, rather than a focus on the nature of the task itself. That is, a complex problem is said to exist only if there is a "gap” between task and solver, or a "barrier” between the state given in the actual situation and the goal state in the head of the problem solver. Therefore, our definition can be called a "gap" definition. A complex problem is not defined by task features, but rather by the interaction between task requirements and solver, that is, by the interaction between task characteristics and person characteristics. Gap definitions, in general, imply that the same task may constitute a problem for one solver, but not for another, whereas "task” oriented definitions assume that a given task either constitutes, or does not constitute, a problem for all solvers.

Also, note that according to our definition CPS is not simply an extension of "simple” problem solving (henceforth SPS), that is, problem solving involving relatively simple laboratory problems. CPS and SPS are qualitatively different. For example, whereas in SPS typically a single barrier needs to be overcome, in CPS a large number of barriers exists. Because there are multiple barriers, a single cognitive or behavioral activity may not be sufficient to reach the goal state. Rather, a well-planned, prioritized, set of cognitions and actions needs to be performed in order to get closer to the goal state.

In addition, note that in contrast to earlier, often implicit views, CPS is not viewed as deterministic in the sense that any problem solving activity will always lead to the solution of a problem. Rather, CPS may lead to an approximate solution that may advance the solver but may not lead to actually solving the problem. For example, subjects performing the duties of the mayor of a computer-simulated town, may, even after some practice, still not be able to generate the best possible solution to a given problem. In fact, many, often computerized, tasks exist for which -due to the complex nonlinear relations among the task variables- the optimal solution is unknown. Of course, the absence of an optimal solution, while theoretically reasonable and even desirable, poses a problem to experimenters who want to determine the quality of subjects' performances, and to those who use microworlds for personnel selection purposes (e.g., U. Funke, 1995).

Finally, because both the given state and goal state and also the barriers are intransparent in CPS, it is difficult for a solver to evaluate her progress toward problem solution. This makes it necessary for the solver to select and structure the interactions with the task such that information that is helpful for the evaluation of progress can be extracted.

A Theoretical Framework for Complex Problem Solving

Adopting any definition has consequences not only for how an area is studied but also for how empirical findings are theoretically interpreted. For example, if problem solving is defined in terms of cognitive, rather than neurophysiological, biological, or behavioral, processes, then it makes little sense to construct a theory of problem solving at a neurophysiological, biological, or behavioral level. In the following, we present our thoughts on how a general theoretical framework for understanding problem solving that is based on our definition of CPS might look like. Our framework is based on the assumptions that (a) the theoretical goal of CPS research is to understand the interplay among cognitive, motivational, personal, and social factors when complex, novel, dynamic, intransparent tasks are solved, and (b) the interplay among the various components can best be understood within an Information Processing model. The framework is constrained, of course, by what is known already about CPS as it is defined above. Below, we therefore present a brief, non-exhaustive list of the main empirical phenomena that have been demonstrated in recent years, thereby summarizing many of the findings presented in the various chapters of Frensch and Funke (1995).

Internal Subject Factors

(1) Experience. CPS appears to vary with the amount of experience an individual has in the task domain at hand (e.g., Krems, 1995). Experience affects the likelihood of successful problem solving, but more importantly, it affects which strategies are employed. It influences, for instance, whether or not a person experiments with a task, that is, whether or not the person exhaustively tests hypotheses about task relations and tries to falsify the assumptions.

(2) Cognitive Variables. There is considerable evidence that cognitive variables, such as background knowledge, monitoring and evaluation strategies, and cognitive style affect CPS. There is even evidence indicating that general intelligence, when measured appropriately, affects at least some aspects of CPS (e.g., Beckmann & Guthke, 1995). Also, it appears that at least under certain conditions, CPS performance and explicit task knowledge may be dissociable. That is, performance improvements can be found even in the absence of explicit knowledge about the task (e.g., Berry & Broadbent, 1995), although the interpretation of these dissociations is not clear (see Buchner, Funke, & Berry, 1995).

(3) Non-cognitive Variables. CPS appears to be enhanced by some non-cognitive factors such as self-confidence, perseverance, motivation, and enjoyment. In general, both personality and social factors appear to influence CPS (e.g., Dörner & Wearing, 1995). All these factors are included in theories of action regulation which explain behavior as result of a complex interaction between different modules. The modules deal not only with cognitive processes but also with emotional states. Thus, the type of information processing is influenced by non-cognitive variables.

External Factors

(1) Problem Structure. CPS appears to vary with the structure of the task including the semantics of the task, the complexity of the task, the transparency of the task, and with other structural task features (e.g., J. Funke, 1995). Such structural variables appear to set up a frame within which the problem solver makes certain "moves" that depend on formal task characteristics.

(2) Problem Context. The likelihood of successful CPS performance seems to vary with the semantic embeddedness of a task, that is, with whether or not the task is couched within a well understood and familiar context (e.g., Huber, 1995). In a way, this external factor reflects the influence of the internal factor experience mentioned above. The important role of contextual embedding, known fairly well from deduction tasks and from cognitive illusions, is also found in CPS.

(3) Environmental Factors. Successful CPS performance is influenced by the environment within which a solver operates. This includes feedback and feedback delay, expectations, cooperation, peer pressure, and so on (e.g., Brehmer, 1995). Even if the task at hand is kept constant, changes in the environment like a shift from individual to group problem solving or from direct to delayed feedback shows drastic effects on problem solving performance.

The Components of a Theory of CPS

These empirical findings have led us to construct a simple theoretical framework for understanding CPS that is depicted in Figure 1. The figure summarizes the basic components of our framework and the interrelations among the components. As can be seen, the framework contains three separate components, the problem solver, the task, and the environment.


Figure 1. CPS is viewed as the interaction between a problem solver and a task in the context of an environment. The figure shows only static aspects of the interaction. For additional information see text.


Within the problem solver, we distinguish between static memory content and dynamic information processing. Memory is divided further into domain-general and domain-specific knowledge both of which affect CPS performance. Information processing includes the task strategies that are selected and the processes of task monitoring and progress evaluation. In addition, non-cognitive problem solver variables such as motivation and personality also factor into CPS performance.

The task itself is depicted in terms of the barriers that exist between a given state and a goal state (see our remarks on the "gap” definition). As noted above, the barriers are assumed to be complex, dynamically changing, and intransparent; the transition from given to goal state is constrained by the problem solver's memory content and information processing, and by the tools that are available to the solver.

The environment includes the resources that are available for problem solving, as well as feedback, expectations, cooperation, peer pressure, disturbances etc. The environment affects both the problem solver and the task. It affects the problem solver by constraining the information processes that can be used and by influencing which knowledge is accessible. The environment affects the task by offering additional information, constraining which tools may be used, and so on. In addition, the environment can be changed actively by the problem solver but not by the task.

From this relatively simple view of CPS, it should become clear that two of the main questions that will need to be addressed by future research are: (a) which components within the problem solver, task, and environment affect CPS in which way, and (b) how do the various components, the person, task, and environment interact in affecting CPS performance? Clearly, much more research will need to be conducted before we can attempt to answer these questions.

Methodological Approaches to Studying Complex Problem Solving

Of the many different methods that could potentially be used to study CPS, two approaches have become favorites in recent years, the experimental method and single-case studies (cf. Eyferth, Schömann, & Widowski, 1986; Kluwe, 1993). Although some researchers have argued that complex problem solving cannot be fruitfully approached with classical experimental techniques (e.g., Brehmer & Dörner, 1993; Dörner, 1992; Dörner & Wearing, 1995; Schaub, 1993; Strohschneider, 1991), others have demonstrated rather convincingly that experimental techniques can be used to further our understanding of CPS (e.g., Funke, 1991, 1993; Hussy, 1985; Kluwe, 1995; Müller, 1993; Putz-Osterloh, 1993; Strauß, 1993). It now appears that the controversy between supporters and opponents of the use of experimental methodology may, at least in part, be based on a false conception of what experimental methods really are. The experimental method is a set of techniques, at least in our view, that can be employed not only to test a set of static assumptions, but also to test dynamic process models. Proponents of the experimentally oriented research strategy argue that false theoretical models can be identified only with the experimental method, that is, only experiments allow one to make ultimate decisions about scientific hypotheses. Thus, the experimental method may be most fruitfully employed for the purpose of theory testing.

The phenomenologically oriented research strategy, on the other hand, relies strongly on the precise reconstruction of single cases of complex problem solving. Cognitive modeling is then used to reconstruct certain aspects of an individual's behavior. The procedure is described in detail by Kluwe (1995), who also highlights some of the problematic features of this methodological approach. In general, it appears to be rather difficult with this approach to identify false theoretical assumptions. Proponents of the single case methodology therefore frequently argue that single cases are useful primarily for explorative purposes, i.e., for the development of scientific hypotheses.

We consider the two approaches, the experimental method and single case studies, to be complementary. Single case studies may be employed most fruitfully during theory development; the strength of the experimental method in contrast, is that it provides a strong test of proposed assumptions. While both of these approaches are helpful and both have the potential to advance our understanding of CPS, the effectiveness of the two approaches is critically affected by some general problems of the research domain. Addressing these problems is of critical importance before both the experimental method and single case studies can be employed. We list four of these general problems below:

(1) The first general problem concerns the measurement of CPS knowledge and performance. The adequate measurement of subjects' knowledge and performance in CPS situations represents a major hurdle that needs to be addressed and resolved before we can make any real progress toward understanding CPS. To this end, Hübner (1989), for instance, has proposed mathematical procedures for the operationalization of certain aspects of task performance. Kolb, Petzing, and Stumpf (1992) propose the use of operations research methods for the same purpose. We believe that real progress will not come from these propositions but will only come from theoretical advances. Any good theory of CPS must prescribe the dependent variables and must outline how these variables can be measured. Additionally, a theory of the formal system itself may help to select important and reliable indicators of system performance.

(2) The second general problem concerns generalizability and external validity. Although the artificial systems currently used in our labs are much more complex than they were 20 years ago, we cannot necessarily assume that increased complexity has also led to improved generalizability. Dörner's attempt to bring complexity into the labs of the scholars of thinking and problem solving was successful--but has the situation really changed with respect to our understanding of real-world phenomena? We agree with Hunt (1991, p. 391) who argues that "Geneticists have a theory that explains how one generalizes from inheritance in the fruit fly to inheritance in human beings. Cognitive psychology does not have a theory to explain how we move from game behaviors to behaviors in other situations.”

(3) The third general problem concerns the analysis of problem solving processes. It is of critical importance that we try to understand the process of complex problem solving, rather than the product. The experimental method has not been specifically designed for process analyses, although experimental treatments can help in testing assumptions about parameters and their assumed dependence on external factors (e.g., multinomial modeling; see Riefer & Batchelder, 1988). Thus, process models and experiments are not contradictory; they are complementary tools that help us understand CPS.

(4) And finally, the development of problem solving theories is in a rather desolate condition. Developing a theory, or multiple theories, is the most difficult job to achieve--and yet at the same time the most necessary prerequisite for additional experimental research. A good theory prescribes and determines experimental research. Theoretical assumptions can be derived from everyday experiences, from cognitive modeling, or from single-case or field studies. Most, if not all, of the assumptions can be tested experimentally--but neither the experimental method nor the single case approach prescribe the development of theories.

It is our view that the experimental method will remain one central method of choice for studying human CPS simply because no other method is as capable of providing decisive answers to clearly formulated questions. At the same time, however, it remains clear that progress in this difficult research area can be achieved only if different approaches work together to achieve insights into how people deal with complex problems.

In conclusion, we believe that research on CPS, despite its many shortcomings and despite the diverse approaches taken by North American and European researchers, carries the promise of a more realistic, real-life approach to the psychology of action control within complex environments than has been employed in the past. This is an exciting area of research, and as the old saying goes, "Nothing is as promising as a beginning."


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Authors' Note

The present manuscript is a condensed and revised version of Chapter 1 from Frensch and Funke (1995). A version of this paper appeared in Russian language under the title:

Funke, J. & Frensch, P. A. (1995). Complex problem solving research in North America and Europe: An integrative review. Foreign Psychology, 5, 42-47.

Send correspondence to Joachim Funke, Psychologisches Institut der Universität Heidelberg, Hauptstr. 47-51, D-69117 Heidelberg, Germany, or to Peter A. Frensch, Humboldt-University, Institut für Psychologie, Hausvogteiplatz 5-7, D-10117 Berlin, Germany. Electronic mail may be sent to: or


Joachim Funke was born in 1953, and studied psychology, philosophy, and German at the Universities of Duesseldorf, Basel (Switzerland), and Trier. He received his M.S. in psychology in 1980, and was awarded his Ph.D. in 1984 at the University of Trier. In 1985, he moved to the University of Bonn, where he was granted his habilitation in 1990. From 1991 until 1997 he was Associate Professor at Bonn University. He is now in the Department of Psychology at Heidelberg University as Full Professor. His research interests include all areas of Experimental Psychology, with a special interest in cognitive processes in memory and problem solving.

Peter A. Frensch was born in 1956, and studied electrical engineering, psychology, and philosophy at the Universities of Darmstadt and Trier, Germany, and at Yale University, USA. He received his M.S. in 1987, followed by his M.phil. in 1988, and his Ph.D. in 1989, and has been working as an Assistant Professor of Psychology in the Department of Psychology at the University of Missouri-Columbia, USA, from 1989 until 1995. After working for some years at the Max-Planck-Institute for Human Development and Education, he is now Full Professor at the Department of Psychology, Humboldt-University, Berlin, Germany. His research interests include learning, memory, and problem solving.

See also the Frensch and Funke Edition on Complex problem solving

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Last modified on 30.11.2001 by JF.