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Complex Problem Solving: What It Is and What It Is Not

Dietrich dörner.

1 Department of Psychology, University of Bamberg, Bamberg, Germany

Joachim Funke

2 Department of Psychology, Heidelberg University, Heidelberg, Germany

Computer-simulated scenarios have been part of psychological research on problem solving for more than 40 years. The shift in emphasis from simple toy problems to complex, more real-life oriented problems has been accompanied by discussions about the best ways to assess the process of solving complex problems. Psychometric issues such as reliable assessments and addressing correlations with other instruments have been in the foreground of these discussions and have left the content validity of complex problem solving in the background. In this paper, we return the focus to content issues and address the important features that define complex problems.

Succeeding in the 21st century requires many competencies, including creativity, life-long learning, and collaboration skills (e.g., National Research Council, 2011 ; Griffin and Care, 2015 ), to name only a few. One competence that seems to be of central importance is the ability to solve complex problems ( Mainzer, 2009 ). Mainzer quotes the Nobel prize winner Simon (1957) who wrote as early as 1957:

The capacity of the human mind for formulating and solving complex problems is very small compared with the size of the problem whose solution is required for objectively rational behavior in the real world or even for a reasonable approximation to such objective rationality. (p. 198)

The shift from well-defined to ill-defined problems came about as a result of a disillusion with the “general problem solver” ( Newell et al., 1959 ): The general problem solver was a computer software intended to solve all kind of problems that can be expressed through well-formed formulas. However, it soon became clear that this procedure was in fact a “special problem solver” that could only solve well-defined problems in a closed space. But real-world problems feature open boundaries and have no well-determined solution. In fact, the world is full of wicked problems and clumsy solutions ( Verweij and Thompson, 2006 ). As a result, solving well-defined problems and solving ill-defined problems requires different cognitive processes ( Schraw et al., 1995 ; but see Funke, 2010 ).

Well-defined problems have a clear set of means for reaching a precisely described goal state. For example: in a match-stick arithmetic problem, a person receives a false arithmetic expression constructed out of matchsticks (e.g., IV = III + III). According to the instructions, moving one of the matchsticks will make the equations true. Here, both the problem (find the appropriate stick to move) and the goal state (true arithmetic expression; solution is: VI = III + III) are defined clearly.

Ill-defined problems have no clear problem definition, their goal state is not defined clearly, and the means of moving towards the (diffusely described) goal state are not clear. For example: The goal state for solving the political conflict in the near-east conflict between Israel and Palestine is not clearly defined (living in peaceful harmony with each other?) and even if the conflict parties would agree on a two-state solution, this goal again leaves many issues unresolved. This type of problem is called a “complex problem” and is of central importance to this paper. All psychological processes that occur within individual persons and deal with the handling of such ill-defined complex problems will be subsumed under the umbrella term “complex problem solving” (CPS).

Systematic research on CPS started in the 1970s with observations of the behavior of participants who were confronted with computer simulated microworlds. For example, in one of those microworlds participants assumed the role of executives who were tasked to manage a company over a certain period of time (see Brehmer and Dörner, 1993 , for a discussion of this methodology). Today, CPS is an established concept and has even influenced large-scale assessments such as PISA (“Programme for International Student Assessment”), organized by the Organization for Economic Cooperation and Development ( OECD, 2014 ). According to the World Economic Forum, CPS is one of the most important competencies required in the future ( World Economic Forum, 2015 ). Numerous articles on the subject have been published in recent years, documenting the increasing research activity relating to this field. In the following collection of papers we list only those published in 2010 and later: theoretical papers ( Blech and Funke, 2010 ; Funke, 2010 ; Knauff and Wolf, 2010 ; Leutner et al., 2012 ; Selten et al., 2012 ; Wüstenberg et al., 2012 ; Greiff et al., 2013b ; Fischer and Neubert, 2015 ; Schoppek and Fischer, 2015 ), papers about measurement issues ( Danner et al., 2011a ; Greiff et al., 2012 , 2015a ; Alison et al., 2013 ; Gobert et al., 2015 ; Greiff and Fischer, 2013 ; Herde et al., 2016 ; Stadler et al., 2016 ), papers about applications ( Fischer and Neubert, 2015 ; Ederer et al., 2016 ; Tremblay et al., 2017 ), papers about differential effects ( Barth and Funke, 2010 ; Danner et al., 2011b ; Beckmann and Goode, 2014 ; Greiff and Neubert, 2014 ; Scherer et al., 2015 ; Meißner et al., 2016 ; Wüstenberg et al., 2016 ), one paper about developmental effects ( Frischkorn et al., 2014 ), one paper with a neuroscience background ( Osman, 2012 ) 1 , papers about cultural differences ( Güss and Dörner, 2011 ; Sonnleitner et al., 2014 ; Güss et al., 2015 ), papers about validity issues ( Goode and Beckmann, 2010 ; Greiff et al., 2013c ; Schweizer et al., 2013 ; Mainert et al., 2015 ; Funke et al., 2017 ; Greiff et al., 2017 , 2015b ; Kretzschmar et al., 2016 ; Kretzschmar, 2017 ), review papers and meta-analyses ( Osman, 2010 ; Stadler et al., 2015 ), and finally books ( Qudrat-Ullah, 2015 ; Csapó and Funke, 2017b ) and book chapters ( Funke, 2012 ; Hotaling et al., 2015 ; Funke and Greiff, 2017 ; Greiff and Funke, 2017 ; Csapó and Funke, 2017a ; Fischer et al., 2017 ; Molnàr et al., 2017 ; Tobinski and Fritz, 2017 ; Viehrig et al., 2017 ). In addition, a new “Journal of Dynamic Decision Making” (JDDM) has been launched ( Fischer et al., 2015 , 2016 ) to give the field an open-access outlet for research and discussion.

This paper aims to clarify aspects of validity: what should be meant by the term CPS and what not? This clarification seems necessary because misunderstandings in recent publications provide – from our point of view – a potentially misleading picture of the construct. We start this article with a historical review before attempting to systematize different positions. We conclude with a working definition.

Historical Review

The concept behind CPS goes back to the German phrase “komplexes Problemlösen” (CPS; the term “komplexes Problemlösen” was used as a book title by Funke, 1986 ). The concept was introduced in Germany by Dörner and colleagues in the mid-1970s (see Dörner et al., 1975 ; Dörner, 1975 ) for the first time. The German phrase was later translated to CPS in the titles of two edited volumes by Sternberg and Frensch (1991) and Frensch and Funke (1995a) that collected papers from different research traditions. Even though it looks as though the term was coined in the 1970s, Edwards (1962) used the term “dynamic decision making” to describe decisions that come in a sequence. He compared static with dynamic decision making, writing:

  • simple  In dynamic situations, a new complication not found in the static situations arises. The environment in which the decision is set may be changing, either as a function of the sequence of decisions, or independently of them, or both. It is this possibility of an environment which changes while you collect information about it which makes the task of dynamic decision theory so difficult and so much fun. (p. 60)

The ability to solve complex problems is typically measured via dynamic systems that contain several interrelated variables that participants need to alter. Early work (see, e.g., Dörner, 1980 ) used a simulation scenario called “Lohhausen” that contained more than 2000 variables that represented the activities of a small town: Participants had to take over the role of a mayor for a simulated period of 10 years. The simulation condensed these ten years to ten hours in real time. Later, researchers used smaller dynamic systems as scenarios either based on linear equations (see, e.g., Funke, 1993 ) or on finite state automata (see, e.g., Buchner and Funke, 1993 ). In these contexts, CPS consisted of the identification and control of dynamic task environments that were previously unknown to the participants. Different task environments came along with different degrees of fidelity ( Gray, 2002 ).

According to Funke (2012) , the typical attributes of complex systems are (a) complexity of the problem situation which is usually represented by the sheer number of involved variables; (b) connectivity and mutual dependencies between involved variables; (c) dynamics of the situation, which reflects the role of time and developments within a system; (d) intransparency (in part or full) about the involved variables and their current values; and (e) polytely (greek term for “many goals”), representing goal conflicts on different levels of analysis. This mixture of features is similar to what is called VUCA (volatility, uncertainty, complexity, ambiguity) in modern approaches to management (e.g., Mack et al., 2016 ).

In his evaluation of the CPS movement, Sternberg (1995) compared (young) European approaches to CPS with (older) American research on expertise. His analysis of the differences between the European and American traditions shows advantages but also potential drawbacks for each side. He states (p. 301): “I believe that although there are problems with the European approach, it deals with some fundamental questions that American research scarcely addresses.” So, even though the echo of the European approach did not enjoy strong resonance in the US at that time, it was valued by scholars like Sternberg and others. Before attending to validity issues, we will first present a short review of different streams.

Different Approaches to CPS

In the short history of CPS research, different approaches can be identified ( Buchner, 1995 ; Fischer et al., 2017 ). To systematize, we differentiate between the following five lines of research:

  • simple (a) The search for individual differences comprises studies identifying interindividual differences that affect the ability to solve complex problems. This line of research is reflected, for example, in the early work by Dörner et al. (1983) and their “Lohhausen” study. Here, naïve student participants took over the role of the mayor of a small simulated town named Lohhausen for a simulation period of ten years. According to the results of the authors, it is not intelligence (as measured by conventional IQ tests) that predicts performance, but it is the ability to stay calm in the face of a challenging situation and the ability to switch easily between an analytic mode of processing and a more holistic one.
  • simple (b) The search for cognitive processes deals with the processes behind understanding complex dynamic systems. Representative of this line of research is, for example, Berry and Broadbent’s (1984) work on implicit and explicit learning processes when people interact with a dynamic system called “Sugar Production”. They found that those who perform best in controlling a dynamic system can do so implicitly, without explicit knowledge of details regarding the systems’ relations.
  • simple (c) The search for system factors seeks to identify the aspects of dynamic systems that determine the difficulty of complex problems and make some problems harder than others. Representative of this line of research is, for example, work by Funke (1985) , who systematically varied the number of causal effects within a dynamic system or the presence/absence of eigendynamics. He found, for example, that solution quality decreases as the number of systems relations increases.
  • simple (d) The psychometric approach develops measurement instruments that can be used as an alternative to classical IQ tests, as something that goes “beyond IQ”. The MicroDYN approach ( Wüstenberg et al., 2012 ) is representative for this line of research that presents an alternative to reasoning tests (like Raven matrices). These authors demonstrated that a small improvement in predicting school grade point average beyond reasoning is possible with MicroDYN tests.
  • simple (e) The experimental approach explores CPS under different experimental conditions. This approach uses CPS assessment instruments to test hypotheses derived from psychological theories and is sometimes used in research about cognitive processes (see above). Exemplary for this line of research is the work by Rohe et al. (2016) , who test the usefulness of “motto goals” in the context of complex problems compared to more traditional learning and performance goals. Motto goals differ from pure performance goals by activating positive affect and should lead to better goal attainment especially in complex situations (the mentioned study found no effect).

To be clear: these five approaches are not mutually exclusive and do overlap. But the differentiation helps to identify different research communities and different traditions. These communities had different opinions about scaling complexity.

The Race for Complexity: Use of More and More Complex Systems

In the early years of CPS research, microworlds started with systems containing about 20 variables (“Tailorshop”), soon reached 60 variables (“Moro”), and culminated in systems with about 2000 variables (“Lohhausen”). This race for complexity ended with the introduction of the concept of “minimal complex systems” (MCS; Greiff and Funke, 2009 ; Funke and Greiff, 2017 ), which ushered in a search for the lower bound of complexity instead of the higher bound, which could not be defined as easily. The idea behind this concept was that whereas the upper limits of complexity are unbound, the lower limits might be identifiable. Imagine starting with a simple system containing two variables with a simple linear connection between them; then, step by step, increase the number of variables and/or the type of connections. One soon reaches a point where the system can no longer be considered simple and has become a “complex system”. This point represents a minimal complex system. Despite some research having been conducted in this direction, the point of transition from simple to complex has not been identified clearly as of yet.

Some years later, the original “minimal complex systems” approach ( Greiff and Funke, 2009 ) shifted to the “multiple complex systems” approach ( Greiff et al., 2013a ). This shift is more than a slight change in wording: it is important because it taps into the issue of validity directly. Minimal complex systems have been introduced in the context of challenges from large-scale assessments like PISA 2012 that measure new aspects of problem solving, namely interactive problems besides static problem solving ( Greiff and Funke, 2017 ). PISA 2012 required test developers to remain within testing time constraints (given by the school class schedule). Also, test developers needed a large item pool for the construction of a broad class of problem solving items. It was clear from the beginning that MCS deal with simple dynamic situations that require controlled interaction: the exploration and control of simple ticket machines, simple mobile phones, or simple MP3 players (all of these example domains were developed within PISA 2012) – rather than really complex situations like managerial or political decision making.

As a consequence of this subtle but important shift in interpreting the letters MCS, the definition of CPS became a subject of debate recently ( Funke, 2014a ; Greiff and Martin, 2014 ; Funke et al., 2017 ). In the words of Funke (2014b , p. 495):

  • simple  It is funny that problems that nowadays come under the term ‘CPS’, are less complex (in terms of the previously described attributes of complex situations) than at the beginning of this new research tradition. The emphasis on psychometric qualities has led to a loss of variety. Systems thinking requires more than analyzing models with two or three linear equations – nonlinearity, cyclicity, rebound effects, etc. are inherent features of complex problems and should show up at least in some of the problems used for research and assessment purposes. Minimal complex systems run the danger of becoming minimal valid systems.

Searching for minimal complex systems is not the same as gaining insight into the way how humans deal with complexity and uncertainty. For psychometric purposes, it is appropriate to reduce complexity to a minimum; for understanding problem solving under conditions of overload, intransparency, and dynamics, it is necessary to realize those attributes with reasonable strength. This aspect is illustrated in the next section.

Importance of the Validity Issue

The most important reason for discussing the question of what complex problem solving is and what it is not stems from its phenomenology: if we lose sight of our phenomena, we are no longer doing good psychology. The relevant phenomena in the context of complex problems encompass many important aspects. In this section, we discuss four phenomena that are specific to complex problems. We consider these phenomena as critical for theory development and for the construction of assessment instruments (i.e., microworlds). These phenomena require theories for explaining them and they require assessment instruments eliciting them in a reliable way.

The first phenomenon is the emergency reaction of the intellectual system ( Dörner, 1980 ): When dealing with complex systems, actors tend to (a) reduce their intellectual level by decreasing self-reflections, by decreasing their intentions, by stereotyping, and by reducing their realization of intentions, (b) they show a tendency for fast action with increased readiness for risk, with increased violations of rules, and with increased tendency to escape the situation, and (c) they degenerate their hypotheses formation by construction of more global hypotheses and reduced tests of hypotheses, by increasing entrenchment, and by decontextualizing their goals. This phenomenon illustrates the strong connection between cognition, emotion, and motivation that has been emphasized by Dörner (see, e.g., Dörner and Güss, 2013 ) from the beginning of his research tradition; the emergency reaction reveals a shift in the mode of information processing under the pressure of complexity.

The second phenomenon comprises cross-cultural differences with respect to strategy use ( Strohschneider and Güss, 1999 ; Güss and Wiley, 2007 ; Güss et al., 2015 ). Results from complex task environments illustrate the strong influence of context and background knowledge to an extent that cannot be found for knowledge-poor problems. For example, in a comparison between Brazilian and German participants, it turned out that Brazilians accept the given problem descriptions and are more optimistic about the results of their efforts, whereas Germans tend to inquire more about the background of the problems and take a more active approach but are less optimistic (according to Strohschneider and Güss, 1998 , p. 695).

The third phenomenon relates to failures that occur during the planning and acting stages ( Jansson, 1994 ; Ramnarayan et al., 1997 ), illustrating that rational procedures seem to be unlikely to be used in complex situations. The potential for failures ( Dörner, 1996 ) rises with the complexity of the problem. Jansson (1994) presents seven major areas for failures with complex situations: acting directly on current feedback; insufficient systematization; insufficient control of hypotheses and strategies; lack of self-reflection; selective information gathering; selective decision making; and thematic vagabonding.

The fourth phenomenon describes (a lack of) training and transfer effects ( Kretzschmar and Süß, 2015 ), which again illustrates the context dependency of strategies and knowledge (i.e., there is no strategy that is so universal that it can be used in many different problem situations). In their own experiment, the authors could show training effects only for knowledge acquisition, not for knowledge application. Only with specific feedback, performance in complex environments can be increased ( Engelhart et al., 2017 ).

These four phenomena illustrate why the type of complexity (or degree of simplicity) used in research really matters. Furthermore, they demonstrate effects that are specific for complex problems, but not for toy problems. These phenomena direct the attention to the important question: does the stimulus material used (i.e., the computer-simulated microworld) tap and elicit the manifold of phenomena described above?

Dealing with partly unknown complex systems requires courage, wisdom, knowledge, grit, and creativity. In creativity research, “little c” and “BIG C” are used to differentiate between everyday creativity and eminent creativity ( Beghetto and Kaufman, 2007 ; Kaufman and Beghetto, 2009 ). Everyday creativity is important for solving everyday problems (e.g., finding a clever fix for a broken spoke on my bicycle), eminent creativity changes the world (e.g., inventing solar cells for energy production). Maybe problem solving research should use a similar differentiation between “little p” and “BIG P” to mark toy problems on the one side and big societal challenges on the other. The question then remains: what can we learn about BIG P by studying little p? What phenomena are present in both types, and what phenomena are unique to each of the two extremes?

Discussing research on CPS requires reflecting on the field’s research methods. Even if the experimental approach has been successful for testing hypotheses (for an overview of older work, see Funke, 1995 ), other methods might provide additional and novel insights. Complex phenomena require complex approaches to understand them. The complex nature of complex systems imposes limitations on psychological experiments: The more complex the environments, the more difficult is it to keep conditions under experimental control. And if experiments have to be run in labs one should bring enough complexity into the lab to establish the phenomena mentioned, at least in part.

There are interesting options to be explored (again): think-aloud protocols , which have been discredited for many years ( Nisbett and Wilson, 1977 ) and yet are a valuable source for theory testing ( Ericsson and Simon, 1983 ); introspection ( Jäkel and Schreiber, 2013 ), which seems to be banned from psychological methods but nevertheless offers insights into thought processes; the use of life-streaming ( Wendt, 2017 ), a medium in which streamers generate a video stream of think-aloud data in computer-gaming; political decision-making ( Dhami et al., 2015 ) that demonstrates error-proneness in groups; historical case studies ( Dörner and Güss, 2011 ) that give insights into the thinking styles of political leaders; the use of the critical incident technique ( Reuschenbach, 2008 ) to construct complex scenarios; and simulations with different degrees of fidelity ( Gray, 2002 ).

The methods tool box is full of instruments that have to be explored more carefully before any individual instrument receives a ban or research narrows its focus to only one paradigm for data collection. Brehmer and Dörner (1993) discussed the tensions between “research in the laboratory and research in the field”, optimistically concluding “that the new methodology of computer-simulated microworlds will provide us with the means to bridge the gap between the laboratory and the field” (p. 183). The idea behind this optimism was that computer-simulated scenarios would bring more complexity from the outside world into the controlled lab environment. But this is not true for all simulated scenarios. In his paper on simulated environments, Gray (2002) differentiated computer-simulated environments with respect to three dimensions: (1) tractability (“the more training subjects require before they can use a simulated task environment, the less tractable it is”, p. 211), correspondence (“High correspondence simulated task environments simulate many aspects of one task environment. Low correspondence simulated task environments simulate one aspect of many task environments”, p. 214), and engagement (“A simulated task environment is engaging to the degree to which it involves and occupies the participants; that is, the degree to which they agree to take it seriously”, p. 217). But the mere fact that a task is called a “computer-simulated task environment” does not mean anything specific in terms of these three dimensions. This is one of several reasons why we should differentiate between those studies that do not address the core features of CPS and those that do.

What is not CPS?

Even though a growing number of references claiming to deal with complex problems exist (e.g., Greiff and Wüstenberg, 2015 ; Greiff et al., 2016 ), it would be better to label the requirements within these tasks “dynamic problem solving,” as it has been done adequately in earlier work ( Greiff et al., 2012 ). The dynamics behind on-off-switches ( Thimbleby, 2007 ) are remarkable but not really complex. Small nonlinear systems that exhibit stunningly complex and unstable behavior do exist – but they are not used in psychometric assessments of so-called CPS. There are other small systems (like MicroDYN scenarios: Greiff and Wüstenberg, 2014 ) that exhibit simple forms of system behavior that are completely predictable and stable. This type of simple systems is used frequently. It is even offered commercially as a complex problem-solving test called COMPRO ( Greiff and Wüstenberg, 2015 ) for business applications. But a closer look reveals that the label is not used correctly; within COMPRO, the used linear equations are far from being complex and the system can be handled properly by using only one strategy (see for more details Funke et al., 2017 ).

Why do simple linear systems not fall within CPS? At the surface, nonlinear and linear systems might appear similar because both only include 3–5 variables. But the difference is in terms of systems behavior as well as strategies and learning. If the behavior is simple (as in linear systems where more input is related to more output and vice versa), the system can be easily understood (participants in the MicroDYN world have 3 minutes to explore a complex system). If the behavior is complex (as in systems that contain strange attractors or negative feedback loops), things become more complicated and much more observation is needed to identify the hidden structure of the unknown system ( Berry and Broadbent, 1984 ; Hundertmark et al., 2015 ).

Another issue is learning. If tasks can be solved using a single (and not so complicated) strategy, steep learning curves are to be expected. The shift from problem solving to learned routine behavior occurs rapidly, as was demonstrated by Luchins (1942) . In his water jar experiments, participants quickly acquired a specific strategy (a mental set) for solving certain measurement problems that they later continued applying to problems that would have allowed for easier approaches. In the case of complex systems, learning can occur only on very general, abstract levels because it is difficult for human observers to make specific predictions. Routines dealing with complex systems are quite different from routines relating to linear systems.

What should not be studied under the label of CPS are pure learning effects, multiple-cue probability learning, or tasks that can be solved using a single strategy. This last issue is a problem for MicroDYN tasks that rely strongly on the VOTAT strategy (“vary one thing at a time”; see Tschirgi, 1980 ). In real-life, it is hard to imagine a business manager trying to solve her or his problems by means of VOTAT.

What is CPS?

In the early days of CPS research, planet Earth’s dynamics and complexities gained attention through such books as “The limits to growth” ( Meadows et al., 1972 ) and “Beyond the limits” ( Meadows et al., 1992 ). In the current decade, for example, the World Economic Forum (2016) attempts to identify the complexities and risks of our modern world. In order to understand the meaning of complexity and uncertainty, taking a look at the worlds’ most pressing issues is helpful. Searching for strategies to cope with these problems is a difficult task: surely there is no place for the simple principle of “vary-one-thing-at-a-time” (VOTAT) when it comes to global problems. The VOTAT strategy is helpful in the context of simple problems ( Wüstenberg et al., 2014 ); therefore, whether or not VOTAT is helpful in a given problem situation helps us distinguish simple from complex problems.

Because there exist no clear-cut strategies for complex problems, typical failures occur when dealing with uncertainty ( Dörner, 1996 ; Güss et al., 2015 ). Ramnarayan et al. (1997) put together a list of generic errors (e.g., not developing adequate action plans; lack of background control; learning from experience blocked by stereotype knowledge; reactive instead of proactive action) that are typical of knowledge-rich complex systems but cannot be found in simple problems.

Complex problem solving is not a one-dimensional, low-level construct. On the contrary, CPS is a multi-dimensional bundle of competencies existing at a high level of abstraction, similar to intelligence (but going beyond IQ). As Funke et al. (2018) state: “Assessment of transversal (in educational contexts: cross-curricular) competencies cannot be done with one or two types of assessment. The plurality of skills and competencies requires a plurality of assessment instruments.”

There are at least three different aspects of complex systems that are part of our understanding of a complex system: (1) a complex system can be described at different levels of abstraction; (2) a complex system develops over time, has a history, a current state, and a (potentially unpredictable) future; (3) a complex system is knowledge-rich and activates a large semantic network, together with a broad list of potential strategies (domain-specific as well as domain-general).

Complex problem solving is not only a cognitive process but is also an emotional one ( Spering et al., 2005 ; Barth and Funke, 2010 ) and strongly dependent on motivation (low-stakes versus high-stakes testing; see Hermes and Stelling, 2016 ).

Furthermore, CPS is a dynamic process unfolding over time, with different phases and with more differentiation than simply knowledge acquisition and knowledge application. Ideally, the process should entail identifying problems (see Dillon, 1982 ; Lee and Cho, 2007 ), even if in experimental settings, problems are provided to participants a priori . The more complex and open a given situation, the more options can be generated (T. S. Schweizer et al., 2016 ). In closed problems, these processes do not occur in the same way.

In analogy to the difference between formative (process-oriented) and summative (result-oriented) assessment ( Wiliam and Black, 1996 ; Bennett, 2011 ), CPS should not be reduced to the mere outcome of a solution process. The process leading up to the solution, including detours and errors made along the way, might provide a more differentiated impression of a person’s problem-solving abilities and competencies than the final result of such a process. This is one of the reasons why CPS environments are not, in fact, complex intelligence tests: research on CPS is not only about the outcome of the decision process, but it is also about the problem-solving process itself.

Complex problem solving is part of our daily life: finding the right person to share one’s life with, choosing a career that not only makes money, but that also makes us happy. Of course, CPS is not restricted to personal problems – life on Earth gives us many hard nuts to crack: climate change, population growth, the threat of war, the use and distribution of natural resources. In sum, many societal challenges can be seen as complex problems. To reduce that complexity to a one-hour lab activity on a random Friday afternoon puts it out of context and does not address CPS issues.

Theories about CPS should specify which populations they apply to. Across populations, one thing to consider is prior knowledge. CPS research with experts (e.g., Dew et al., 2009 ) is quite different from problem solving research using tasks that intentionally do not require any specific prior knowledge (see, e.g., Beckmann and Goode, 2014 ).

More than 20 years ago, Frensch and Funke (1995b) defined CPS as follows:

  • simple  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. (p. 18)

The above definition is rather formal and does not account for content or relations between the simulation and the real world. In a sense, we need a new definition of CPS that addresses these issues. Based on our previous arguments, we propose the following working definition:

  • simple  Complex problem solving is a collection of self-regulated psychological processes and activities necessary in dynamic environments to achieve ill-defined goals that cannot be reached by routine actions. Creative combinations of knowledge and a broad set of strategies are needed. Solutions are often more bricolage than perfect or optimal. The problem-solving process combines cognitive, emotional, and motivational aspects, particularly in high-stakes situations. Complex problems usually involve knowledge-rich requirements and collaboration among different persons.

The main differences to the older definition lie in the emphasis on (a) the self-regulation of processes, (b) creativity (as opposed to routine behavior), (c) the bricolage type of solution, and (d) the role of high-stakes challenges. Our new definition incorporates some aspects that have been discussed in this review but were not reflected in the 1995 definition, which focused on attributes of complex problems like dynamics or intransparency.

This leads us to the final reflection about the role of CPS for dealing with uncertainty and complexity in real life. We will distinguish thinking from reasoning and introduce the sense of possibility as an important aspect of validity.

CPS as Combining Reasoning and Thinking in an Uncertain Reality

Leading up to the Battle of Borodino in Leo Tolstoy’s novel “War and Peace”, Prince Andrei Bolkonsky explains the concept of war to his friend Pierre. Pierre expects war to resemble a game of chess: You position the troops and attempt to defeat your opponent by moving them in different directions.

“Far from it!”, Andrei responds. “In chess, you know the knight and his moves, you know the pawn and his combat strength. While in war, a battalion is sometimes stronger than a division and sometimes weaker than a company; it all depends on circumstances that can never be known. In war, you do not know the position of your enemy; some things you might be able to observe, some things you have to divine (but that depends on your ability to do so!) and many things cannot even be guessed at. In chess, you can see all of your opponent’s possible moves. In war, that is impossible. If you decide to attack, you cannot know whether the necessary conditions are met for you to succeed. Many a time, you cannot even know whether your troops will follow your orders…”

In essence, war is characterized by a high degree of uncertainty. A good commander (or politician) can add to that what he or she sees, tentatively fill in the blanks – and not just by means of logical deduction but also by intelligently bridging missing links. A bad commander extrapolates from what he sees and thus arrives at improper conclusions.

Many languages differentiate between two modes of mentalizing; for instance, the English language distinguishes between ‘thinking’ and ‘reasoning’. Reasoning denotes acute and exact mentalizing involving logical deductions. Such deductions are usually based on evidence and counterevidence. Thinking, however, is what is required to write novels. It is the construction of an initially unknown reality. But it is not a pipe dream, an unfounded process of fabrication. Rather, thinking asks us to imagine reality (“Wirklichkeitsfantasie”). In other words, a novelist has to possess a “sense of possibility” (“Möglichkeitssinn”, Robert Musil; in German, sense of possibility is often used synonymously with imagination even though imagination is not the same as sense of possibility, for imagination also encapsulates the impossible). This sense of possibility entails knowing the whole (or several wholes) or being able to construe an unknown whole that could accommodate a known part. The whole has to align with sociological and geographical givens, with the mentality of certain peoples or groups, and with the laws of physics and chemistry. Otherwise, the entire venture is ill-founded. A sense of possibility does not aim for the moon but imagines something that might be possible but has not been considered possible or even potentially possible so far.

Thinking is a means to eliminate uncertainty. This process requires both of the modes of thinking we have discussed thus far. Economic, political, or ecological decisions require us to first consider the situation at hand. Though certain situational aspects can be known, but many cannot. In fact, von Clausewitz (1832) posits that only about 25% of the necessary information is available when a military decision needs to be made. Even then, there is no way to guarantee that whatever information is available is also correct: Even if a piece of information was completely accurate yesterday, it might no longer apply today.

Once our sense of possibility has helped grasping a situation, problem solvers need to call on their reasoning skills. Not every situation requires the same action, and we may want to act this way or another to reach this or that goal. This appears logical, but it is a logic based on constantly shifting grounds: We cannot know whether necessary conditions are met, sometimes the assumptions we have made later turn out to be incorrect, and sometimes we have to revise our assumptions or make completely new ones. It is necessary to constantly switch between our sense of possibility and our sense of reality, that is, to switch between thinking and reasoning. It is an arduous process, and some people handle it well, while others do not.

If we are to believe Tuchman’s (1984) book, “The March of Folly”, most politicians and commanders are fools. According to Tuchman, not much has changed in the 3300 years that have elapsed since the misguided Trojans decided to welcome the left-behind wooden horse into their city that would end up dismantling Troy’s defensive walls. The Trojans, too, had been warned, but decided not to heed the warning. Although Laocoön had revealed the horse’s true nature to them by attacking it with a spear, making the weapons inside the horse ring, the Trojans refused to see the forest for the trees. They did not want to listen, they wanted the war to be over, and this desire ended up shaping their perception.

The objective of psychology is to predict and explain human actions and behavior as accurately as possible. However, thinking cannot be investigated by limiting its study to neatly confined fractions of reality such as the realms of propositional logic, chess, Go tasks, the Tower of Hanoi, and so forth. Within these systems, there is little need for a sense of possibility. But a sense of possibility – the ability to divine and construe an unknown reality – is at least as important as logical reasoning skills. Not researching the sense of possibility limits the validity of psychological research. All economic and political decision making draws upon this sense of possibility. By not exploring it, psychological research dedicated to the study of thinking cannot further the understanding of politicians’ competence and the reasons that underlie political mistakes. Christopher Clark identifies European diplomats’, politicians’, and commanders’ inability to form an accurate representation of reality as a reason for the outbreak of World War I. According to Clark’s (2012) book, “The Sleepwalkers”, the politicians of the time lived in their own make-believe world, wrongfully assuming that it was the same world everyone else inhabited. If CPS research wants to make significant contributions to the world, it has to acknowledge complexity and uncertainty as important aspects of it.

For more than 40 years, CPS has been a new subject of psychological research. During this time period, the initial emphasis on analyzing how humans deal with complex, dynamic, and uncertain situations has been lost. What is subsumed under the heading of CPS in modern research has lost the original complexities of real-life problems. From our point of view, the challenges of the 21st century require a return to the origins of this research tradition. We would encourage researchers in the field of problem solving to come back to the original ideas. There is enough complexity and uncertainty in the world to be studied. Improving our understanding of how humans deal with these global and pressing problems would be a worthwhile enterprise.

Author Contributions

JF drafted a first version of the manuscript, DD added further text and commented on the draft. JF finalized the manuscript.

Authors Note

After more than 40 years of controversial discussions between both authors, this is the first joint paper. We are happy to have done this now! We have found common ground!

Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


The authors thank the Deutsche Forschungsgemeinschaft (DFG) for the continuous support of their research over many years. Thanks to Daniel Holt for his comments on validity issues, thanks to Julia Nolte who helped us by translating German text excerpts into readable English and helped us, together with Keri Hartman, to improve our style and grammar – thanks for that! We also thank the two reviewers for their helpful critical comments on earlier versions of this manuscript. Finally, we acknowledge financial support by Deutsche Forschungsgemeinschaft and Ruprecht-Karls-Universität Heidelberg within their funding programme Open Access Publishing .

1 The fMRI-paper from Anderson (2012) uses the term “complex problem solving” for tasks that do not fall in our understanding of CPS and is therefore excluded from this list.

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Encyclopedia of the Sciences of Learning pp 682–685 Cite as

Complex Problem Solving

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Dealing with uncertainty ; Dynamic decision making ; Problem solving in dynamic microworlds

Complex problem solving takes place for reducing the barrier between a given start state and an intended goal state with the help of cognitive activities and behavior. Start state, intended goal state, and barriers prove complexity, change dynamically over time, and can be partially intransparent. In contrast to solving simple problems, with complex problems at the beginning of a problem solution the exact features of the start state, of the intended goal state, and of the barriers are unknown. Complex problem solving expects the efficient interaction between the problem-solving person and situational conditions that depend on the task. It demands the use of cognitive, emotional, and social resources as well as knowledge (see Frensch and Funke 1995 ).

Theoretical Background

Since 1975 there has been started a new movement in the psychology of thinking that is engaged in complex...

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Brehmer, B., & Dörner, D. (1993). Experiments with computer-simulated microworlds: Escaping both the narrow straits of the laboratory and the deep blue sea of the field study. Computers in Human Behavior, 9 , 171–184.

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Frensch, P. A., & Funke, J. (Eds.). (1995). Complex problem solving: The European perspective . Hillsdale: Lawrence Erlbaum Associates.

Funke, J. (2003). Problemlösendes Denken . Stuttgart: Kohlhammer.

Osman, M. (2010). Controlling uncertainty: A review of human behavior in complex dynamic environments. Psychological Bulletin, 136 , 65–86.

Wenke, D., Frensch, P. A., & Funke, J. (2005). Complex problem solving and intelligence: Empirical relation and causal direction. In R. J. Sternberg & J. E. Pretz (Eds.), Cognition and intelligence: Identifying the mechanisms of the mind (pp. 160–187). New York: Cambridge University Press.

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Bryan Lindsley

How To Solve Complex Problems

In today’s increasingly complex world, we are constantly faced with ill-defined problems that don’t have a clear solution. From poverty and climate change to crime and addiction, complex situations surround us. Unlike simple problems with a pre-defined or “right” answer, complex problems share several basic characteristics that make them hard to solve. While these problems can be frustrating and overwhelming, they also offer an opportunity for growth and creativity. Complex problem-solving skills are the key to addressing these tough issues.

In this article, I will discuss simple versus complex problems, define complex problem solving, and describe why it is so important in complex dynamic environments. I will also explain how to develop problem-solving skills and share some tips for effectively solving complex problems.

How is simple problem-solving different from complex problem-solving?

Solving problems is about getting from a currently undesirable state to an intended goal state. In other words, about bridging the gap between “what is” and “what ought to be”. However, the challenge of reaching a solution varies based on the kind of problem that is being solved. There are generally three different kinds of problems you should consider.

Simple problems have one problem solution. The goal is to find that answer as quickly and efficiently as possible. Puzzles are classic examples of simple problem solving. The objective is to find the one correct solution out of many possibilities.

Puzzles complex problem-solving

Problems are different from puzzles in that they don’t have a known problem solution. As such, many people may agree that there is an issue to be solved, but they may not agree on the intended goal state or how to get there. In this type of problem, people spend a lot of time debating the best solution and the optimal way to achieve it.

Messes are collections of interrelated problems where many stakeholders may not even agree on what the issue is. Unlike problems where there is agreement about what the problem is, in messes, there isn’t agreement amongst stakeholders. In other words, even “what is” can’t be taken for granted. Most complex social problems are messes, made up of interrelated social issues with ill-defined boundaries and goals.

Problems and messes can be complicated or complex

Puzzles are simple, but problems and messes exist on a continuum between complicated and complex. Complicated problems are technical in nature. There may be many involved variables, but the relationships are linear. As a result, complicated problems have step-by-step, systematic solutions. Repairing an engine or building a rocket may be difficult because of the many parts involved, but it is a technical problem we call complicated.

On the other hand, solving a complex problem is entirely different. Unlike complicated problems that may have many variables with linear relationships, a complex problem is characterized by connectivity patterns that are harder to understand and predict.

Characteristics of complex problems and messes

So what else makes a problem complex? Here are seven additional characteristics (from Funke and Hester and Adams ).

  • Lack of information. There is often a lack of data or information about the problem itself. In some cases, variables are unknown or cannot be measured.
  • Many goals. A complex problem has a mix of conflicting objectives. In some sense, every stakeholder involved with the problem may have their own goals. However, with limited resources, not all goals can be simultaneously satisfied.
  • Unpredictable feedback loops. In part due to many variables connected by a range of different relationships, a change in one variable is likely to have effects on other variables in the system. However, because we do not know all of the variables it will affect, small changes can have disproportionate system-wide effects. These unexpected events that have big, unpredictable effects are sometimes called Black Swans.
  • Dynamic. A complex problem changes over time and there is a significant impact based on when you act. In other words, because the problem and its parts and relationships are constantly changing, an action taken today won’t have the same effects as the same action taken tomorrow.
  • Time-delayed. It takes a while for cause and effect to be realized. Thus it is very hard to know if any given intervention is working.
  • Unknown unknowns. Building off the previous point about a lack of information, in a complex problem you may not even know what you don’t know. In other words, there may be very important variables that you are not even aware of.
  • Affected by (error-prone) humans. Simply put, human behavior tends to be illogical and unpredictable. When humans are involved in a problem, avoiding error may be impossible.

What is complex problem-solving?

“Complex problem solving” is the term for how to address a complex problem or messes that have the characteristics listed above.

Since a complex problem is a different phenomenon than a simple or complicated problem, solving them requires a different approach. Methods designed for simple problems, like systematic organization, deductive logic, and linear thinking don’t work well on their own for a complex problem.

And yet, despite its importance, there isn’t complete agreement about what exactly it is.

How is complex problem solving defined by experts?

Let’s look at what scientists, researchers, and system thinkers have come up with in terms of a definition for solving a complex problem. 

As a series of observations and informed decisions

For many employers, the focus is on making smart decisions. These must weigh the future effects to the company of any given solution. According to Indeed.com , it is defined as “a series of observations and informed decisions used to find and implement a solution to a problem. Beyond finding and implementing a solution, complex problem solving also involves considering future changes to circumstance, resources, and capabilities that may affect the trajectory of the process and success of the solution. Complex problem solving also involves considering the impact of the solution on the surrounding environment and individuals.”

As using information to review options and develop solutions

For others, it is more of a systematic way to consider a range of options. According to O*NET ,  the definition focuses on “identifying complex problems and reviewing related information to develop and evaluate options and implement solutions.”

As a self-regulated psychological process

Others emphasize the broad range of skills and emotions needed for change. In addition, they endorse an inspired kind of pragmatism. For example, Dietrich Dorner and Joachim Funke define it as “a collection of self-regulated psychological processes and activities necessary in dynamic environments to achieve ill-defined goals that cannot be reached by routine actions. Creative combinations of knowledge and a broad set of strategies are needed. Solutions are often more bricolage than perfect or optimal. The problem-solving process combines cognitive, emotional, and motivational aspects, particularly in high-stakes situations. Complex problems usually involve knowledge-rich requirements and collaboration among different persons.”

As a novel way of thinking and reasoning

Finally, some emphasize the multidisciplinary nature of knowledge and processes needed to tackle a complex problem. Patrick Hester and Kevin MacG. Adams have stated that “no single discipline can solve truly complex problems. Problems of real interest, those vexing ones that keep you up at night, require a discipline-agnostic approach…Simply they require us to think systemically about our problem…a novel way of thinking and reasoning about complex problems that encourages increased understanding and deliberate intervention.”

A synthesis definition

By pulling the main themes of these definitions together, we can get a sense of what complex problem-solvers must do:

Gain a better understanding of the phenomena of a complex problem or mess. Use a discipline-agnostic approach in order to develop deliberate interventions. Take into consideration future impacts on the surrounding environment.

Why is complex problem solving important?

Many efforts aimed at complex social problems like reducing homelessness and improving public health – despite good intentions giving more effort than ever before – are destined to fail because their approach is based on simple problem-solving. And some efforts might even unwittingly be contributing to the problems they’re trying to solve. 

Einstein said that “We can’t solve problems by using the same kind of thinking we used when we created them.” I think he could have easily been alluding to the need for more complex problem solvers who think differently. So what skills are required to do this?

What are complex problem-solving skills?

The skills required to solve a complex problem aren’t from one domain, nor are they an easily-packaged bundle. Rather, I like to think of them as a balancing act between a series of seemingly opposite approaches but synthesized. This brings a sort of cognitive dissonance into the process, which is itself informative.

It brings F. Scott Fitzgerald’s maxim to mind: 

“The test of a first-rate intelligence is the ability to hold two opposing ideas in mind at the same time and still retain the ability to function. One should, for example, be able to see that things are hopeless yet be determined to make them otherwise.” 

To see the problem situation clearly, for example, but also with a sense of optimism and possibility.

Here are the top three dialectics to keep in mind:

Thinking and reasoning

Reasoning is the ability to make logical deductions based on evidence and counterevidence. On the other hand, thinking is more about imagining an unknown reality based on thoughts about the whole picture and how the parts could fit together. By thinking clearly, one can have a sense of possibility that prepares the mind to deduce the right action in the unique moment at hand.

As Dorner and Funke explain: “Not every situation requires the same action,  and we may want to act this way or another to reach this or that goal. This appears logical, but it is a logic based on constantly shifting grounds: We cannot know whether necessary conditions are met, sometimes the assumptions we have made later turn out to be incorrect, and sometimes we have to revise our assumptions or make completely new ones. It is necessary to constantly switch between our sense of possibility and our sense of reality, that is, to switch between thinking and reasoning. It is an arduous process, and some people handle it well, while others do not.”

Analysis and reductionism combined with synthesis and holism

It’s important to be able to use scientific processes to break down a complex problem into its parts and analyze them. But at the same time, a complex problem is more than the sum of its parts. In most cases, the relationships between the parts are more important than the parts themselves. Therefore, decomposing problems with rigor isn’t enough. What’s needed, once problems are reduced and understood, is a way of understanding the relationships between various components as well as putting the pieces back together. However, synthesis and holism on their own without deductive analysis can often miss details and relationships that matter.  

What makes this balancing act more difficult is that certain professions tend to be trained in and prefer one domain over the other. Scientists prefer analysis and reductionism whereas most social scientists and practitioners default to synthesis and holism. Unfortunately, this divide of preferences results in people working in their silos at the expense of multi-disciplinary approaches that together can better “see” complexity.

seeing complex problem solving

Situational awareness and self-awareness 

Dual awareness is the ability to pay attention to two experiences simultaneously. In the case of complex problems, context really matters. In other words, problem-solving exists in an ecosystem of environmental factors that are not incidental. Personal and cultural preferences play a part as do current events unfolding over time. But as a problem solver, knowing the environment is only part of the equation. 

The other crucial part is the internal psychological process unique to every individual who also interacts with the problem and the environment. Problem solvers inevitably come into contact with others who may disagree with them, or be advancing seemingly counterproductive solutions, and these interactions result in emotions and motivations. Without self-awareness, we can become attached to our own subjective opinions, fall in love with “our” solutions, and generally be driven by the desire to be seen as problem solvers at the expense of actually solving the problem.

By balancing these three dialectics, practitioners can better deal with uncertainty as well as stay motivated despite setbacks. Self-regulation among these seemingly opposite approaches also reminds one to stay open-minded.

How do you develop complex problem-solving skills?

There is no one answer to this question, as the best way to develop them will vary depending on your strengths and weaknesses. However, there are a few general things that you can do to improve your ability to solve problems.

Ground yourself in theory and knowledge

First, it is important to learn about systems thinking and complexity theories. These frameworks will help you understand how complex systems work, and how different parts of a system interact with each other. This conceptual understanding will allow you to identify potential solutions to problems more quickly and effectively.

Practice switching between approaches

Second, practice switching between the dialectics mentioned above. For example, in your next meeting try to spend roughly half your time thinking and half your time reasoning. The important part is trying to get habituated to regularly switching lenses. It may seem disjointed at first, but after a while, it becomes second nature to simultaneously see how the parts interact and the big picture.

Focus on the specific problem phenomena

Third, it may sound obvious, but people often don’t spend very much time studying the problem itself and how it functions. In some sense, becoming a good problem-solver involves becoming a problem scientist. Your time should be spent regularly investigating the phenomena of “what is” rather than “what ought to be”. A holistic understanding of the problem is the required prerequisite to coming up with good solutions.

Stay curious

Finally, after we have worked on a problem for a while, we tend to think we know everything about it, including how to solve it. Even if we’re working on a problem, which may change dynamically from day to day, we start treating it more like a puzzle with a definite solution. When that happens, we can lose our motivation to continue learning about the problem. This is very risky because it closes the door to learning from others, regardless of whether we completely agree with them or not.

As Neils Bohr said, “Two different perspectives or models about a system will reveal truths regarding the system that are neither entirely independent nor entirely compatible.”

By staying curious, we can retain our ability to learn on a daily basis.

Tips for how to solve complex problems

Focus on processes over results.

It’s easy to get lost in utopian thinking. Many people spend so much time on “what ought to be” that they forget that problem solving is about the gap between “what is” and “what ought to be”. It is said that “life is a journey, not a destination.” The same is true for complex problem-solving. To do it well, a problem solver must focus on enjoying the process of gaining a holistic understanding of the problem. 

Adaptive and iterative methods and tools

A variety of adaptive and iterative methods have been developed to address complexity. They share a laser focus on gaining holistic understanding with tools that best match the phenomena of complexity. They are also non-ideological, trans-disciplinary, and flexible. In most cases, your journey through a set of steps won’t be linear. Rather, as you think and reason, analyze and synthesize, you’ll jump around to get a holistic picture.

adapting complex problem-solving

In my online course , we generally follow a seven-step method:

  • Get clear sight with a complex problem-solving frame
  • Establish a secure base of operation
  • Gain a deep understanding of the problem
  • Create an interactive model of the problem
  • Develop an impact strategy
  • Create an action plan and implement
  • Embed systemic solutions

Of course, each of these steps involves testing to see what works and consistently evaluating our process and progress.

Resolution is about systematically managing a problem over time

One last thing to keep in mind. Most social problems are not just solved one day, never to return. In reality,  most complex problems are managed, not solved. For all practical purposes, what this means is that “the solution” is a way of systematically dealing with the problem over time. Some find this disappointing, but it’s actually a pragmatic pointer to think about resolution – a way move problems in the right direction – rather than final solutions.

Problem solvers regularly train and practice

If you need help developing your complex problem-solving skills, I have an online class where you can learn everything you need to know. 

Sign up today and learn how to be successful at making a difference in the world!

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what does complex problem solving mean

Complex Problem Solving Skills

Complex problem solving skills are the developed capacities used to solve novel, ill-defined problems in complex, real-world settings (O*NET). Look below for specific complex problem solving skills and tools to help foster them in yourself or others!!  

Complex Problem Solving

Building upon solid critical think practices, one is able to look at a problem from different vantage points, develop alternative solutions, and select the best solution given their understanding of the problem, the environment influencing the problem, and those impacted by its solution.

  • The University of Kent provides information on "How to Develop and Demonstrate your Problem Solving Skills" 
  • Mind Tools presents an Introduction to Problem Solving Skills and the Basic Steps involved in problem solving
  • Skills You Need provides an introduction, definition, goals,barriers and stages of problem solving
  • Fast Company shares Einstein's Problem-Solving Formula

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what does complex problem solving mean

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Top 10 Future Skills: Complex Problem Solving

what does complex problem solving mean

With the rise of automation, comes the rise of soft skills. The landscape of work is shifting; and in order to keep up with the change, workers needs to develop competencies that machines won’t tackle. In this series we talk about the top 10 soft skills that will help you thrive in 2020. And today’s skill is complex problem solving or CPS.

What is complex problem solving?

Artificial intelligence has stepped up to solve many problems as well as humans can, with all their brains. AI can recognize emotions, predict crop yields, and spot cancer in tissue slides better than epidemiologists.  AI can solve problems that humans can’t – but that also goes the other way around. If a problem is not well-defined and the steps are not clear, people can reverse-engineer an action plan by taking the result apart.

what does complex problem solving mean

The complexity of a system can be defined as the number of elements and the relations within the system. The more complex something is, the more features are interdependent. When one has a goal but doesn’t know the steps required to reach it, that’s when a problem that needs solving arises. Problem solving can be defined as searching for steps that will lead to a successful outcome. Thus, complex problem solving includes the problem itself and a set of many highly interrelated elements

The concept behind CPS goes back to the German phrase “komplexes Problemlösen”. The concept was first introduced by Dietrich Dörner, a professor of general and theoretical psychology and his colleagues in the mid-1970s. American psychologist Ward Edwards also described CPS as “dynamic decision making” as decisions come in a sequence.

How is a complex problem different from a simple problem?

There are five features traditionally outlined by Joachim Funke, a researcher on CPS from Universität Heidelberg in Germany that define a complex problem.

what does complex problem solving mean

Complexity of the problem situation

This is defined based on the number of variables you need to take into consideration. A problem solver needs to simplify the problem by reducing it to the essential.

Connectivity between involved variables

In complex problems, the relationship between factors of the problem is not linear but rather radiant, connecting several factors together. If a problem had 50 variables and they were each connected exactly to only one other, the connectivity would be lower than if all the variables were connected to each other.

Dynamics of the situation

This feature explains that if a change is made to one interconnected aspect of the problem, it might activate unintended processes.

Intransparency of the system

Intransparency implies not having all the required information. In this situation, the problem solver needs to seek additional information about the variables to make the picture complete, and this must be pursued with focused initiative.

Polytely or having multiple simultaneous goals

When goals contradict each other or conflict with one another, such situation requires prioritizing the outcomes and compromising.

Four Steps to CPS

A simple step-by-step procedure to solving professional problems has four stages that are outlined below.

what does complex problem solving mean

Define a problem

What is the goal you are trying to achieve? What’s preventing you from getting the result you want?

Identify various solutions

Branch out and visualize several possible scenarios of how to tackle a problem. What are the possible outcomes?

Choose a plan

Evaluate your ideas against your resources and abilities and eliminate the steps that are least likely to bring you forward. Which option will solve your problem? Which option is the easiest? What should you prioritize?

Implement the idea

Apply the chosen solution and see whether intermediate results align with your final goal. If not, seek an alternative scenario.

In order to better identify solutions and find the root causes of the problems, there are techniques to help you guide your thinking process in the right direction. And one of them is the Hurson’s Productive Thinking Model.

Using Hurson’s Productive Thinking Model

Canadian writer Tim Hurson developed a problem-solving technique known as Hurson’s Productive Thinking Model, which he presented in his book “Think Better”. The model consists of six stages. In each stage you should ask a specific number of questions to emphasize the different sides of the problem in order to reach a better understanding for the best solution.

For designers and creative people, one of the advantages of using this model is that it provides room for creative thinking and allows stakeholders to arrive at creative ways to achieve the target at each stage.

The steps in his Productive Thinking Model

  • Ask, “What is going on? ” Define the problem and how it’s impacting your workflow, then clarify your vision for the future.
  • Ask, “What is success?” Define what the solution must do, what resources it needs, and the factors you will base your success on.
  • Ask, “What is the question?” Generate a long list of questions around the goal you are aiming to achieve. When answered, they will solve the problem.
  • Generate answers. Answer all the questions in Step 3.
  • Outline the solution. Evaluate potentially successful ideas based on the criteria for success from step 2.
  • Align resources. Identify people, their skills and additional resources to help you execute the solution.

To give you a better picture of the different stages in the process, use the Fishbone diagram to visualize the goal and the steps towards it.

Draw a Fishbone Diagram to See Cause & Effect

In order to solve a problem completely, you need to look into possible root causes. To better visualize the different steps of how, when, and why a problem occurred, use a Fishbone diagram. This method is also known as an Ishikawa diagram or a cause and effect diagram.

what does complex problem solving mean

You can either create a diagram using a Smartdraw website or by simply drawing it out on a whiteboard. First you need to agree on a problem statement (effect). Write it at the center right of the whiteboard. Draw a box around it and a long horizontal arrow running to it across the whiteboard. Then brainstorm the major categories of causes of the problem: methods, people, materials, measurement, environment, etc. and write down these categories as branches from the main arrow.

To add detail to each branch, ask “Why does this happen?” and make a note of the reason. Continue asking the ‘Why?’ questions to create more sub-causes to generate a deeper understanding of the processes.

Additional resources on CPS

Complex problem solving is a soft skill that requires a great deal of meticulousness as well as the ability to see a bigger picture. To practice this CPS muscle, here are some of the resources for both theoretical and practical techniques.

  • For more practical advice on problem solving techniques, refer to this article. The author breaks down techniques such as asking questions and using diagrams to help you find a solution.
  • The “Introduction to design thinking” course will demonstrate how you can use design as a way of thinking to provide strategic and innovative advantages within your profession. The course focuses on design thinking, design making, and design breaking to provide a better picture for CPS approaches.
  • Additionally, A Harvard innovation course CPS lecture by Prof. Ricketts will help you to navigate in the decision-making process of CPS.
  • For critical thinking and its applications to problem solving, watch this TED talk by Tom Wujec, who walks you through a simple design exercise devoted to making toast.

Read more on the importance of honing soft skills .

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What is a ‘complex problem’ anyway?

what does complex problem solving mean

  • By Rowan Barnes
  • Published  10 May 21
  • Read in 5 minutes

what does complex problem solving mean

Ask anyone in a consulting capacity if they solve complex problems for their clients and the answer will almost certainly be ‘yes’. It wouldn’t sound terribly compelling if they said they solved simple problems, would it?

It’s a line that is shared between many different organisations, across many different business sectors. Consider some of the following examples:

what does complex problem solving mean

They all say they solve complex problems. But when we start to analyse it, are the problems they solve truly complex ? Or are they just complicated ?

In this article, we look at some of the characteristics of complex problems and compare them with those that are merely complicated. The distinction matters, because a problem’s level of complexity drastically changes how you approach tackling it.

So, when is a problem complex , and when is it just complicated ?

Characteristics of a complex problem.

When thinking about the complexity of a problem, consider the following attributes:


Reducibility, predictability, solvability.

Let’s look at all four in detail.

Complicated problems are difficult to solve, but are easy to define. Building a car is a complicated problem – there are hundreds of structural, mechanical, and electrical components to construct to successfully build a car. But the problem/goal is very easily defined. We want the ability to get from A to B and to do that we will build a car.

With complex problems, however, it is often difficult to define what the problem actually is and therefore what needs to be achieved. There may be multiple interacting problems at play; some obvious and some less so. It may also be difficult for individuals or groups involved in a project to agree on the relative importance of these interacting problems. Worse still, there may be unknown unknowns – problems that exist but nobody can see.

For example, we recently assisted the Alzheimer Society of Canada by consulting on the development of their new website. One of the most time-consuming aspects of the project wasn’t the design and the build of the website, in fact, it was defining the problems that needed to be solved. With multiple opinions, from fundraising to programs and services, to education and advocacy, to research, to marketing… everyone had their own view of what the problems were and the goals that needed to be achieved. Separate groups, all with a different understanding of the problems at play. This means they all, understandably, approach these problems with a different lens and therefore develop goals from their own, unique perspective.

Working through these often competing priorities is of critical importance in projects, which is often overlooked. This causes projects to veer off track, or require substantial rework further down the line. The best approach in these projects, where there are multiple actors with competing or even conflicting priorities, is to seek to build a common understanding across groups and work to define whatever you can (bearing in mind that you may never achieve a ‘perfect’ definition). Also of critical importance in this situation is an outside opinion, to uncover those ‘unknown unknowns’. Talking to real-world users rather than making internal assumptions usually serves to uncover problems you had never even considered.

A complicated problem can usually be broken down into its constituent parts. Staying with our car analogy – a car is complicated because it has lots of components that work together, but it isn’t complex. You can literally break it down into its individual parts, put it back together again, and you have the same car. A complicated problem can often be referred to as existing in a ‘closed system’, that is, you can define where the system starts and where it ends.

Complex problems, however, exist within open systems – it is often hard to define where the system starts and where it ends, what is impacted by the system, and what, in turn, the system has an impact on. Complex problems are also non-linear. Not only is it hard to break down a complex problem into its constituent parts, it is also hard to understand how constituent parts interact with one another or with external factors.

An example of this is in the marketing world. When starting on a project, it may appear simple. Do X to achieve Y. However, it is important to think holistically if you want to understand the total impact of the project. For example, what other projects are running at the same time? How do those projects impact this one, and how does our project impact them? What has happened in the run-up to this project? And once this project is finished, what is likely to happen next?

With a complicated problem, it is usually easy to predict what is going to happen. The process of building a car is not easy, but we know how one component of a car should interact with another. Therefore, we can predict what is going to happen. We can do that from experience. If you have built a car several times before, you can draw upon your past experience to predict what will happen again. And you don’t even need to have built a car yourself, because lots of other people have done it before and you can feed off their experience. Have you ever done any complicated DIY after watching a few YouTube videos? You’ve just solved a complicated problem by feeding off someone else’s experience.

In a complex problem, it is often hard to predict what is going to happen. Just because something happened before in a previous project, doesn’t mean it will happen again in the same way. This could happen for many different reasons, for example, cultural/geographic differences, the use of novel technology, political differences, sketchy background data, or team stability, to name just a few.

If you want to learn more about predictability, check out Dave Snowden’s Cynefin framework which talks about the relationship between cause and effect. Raising children sits well within the complex domain, as does leadership. Sending a rocket to the moon, however? That’s complicated, but not complex. Think about that the next time someone quips, “it’s not rocket science”.

One of the major issues with predictability is unintended consequences. It is hard to predict what is going to happen. So, how you approach a problem can sometimes spawn other complex problems which then cause further instability within the original problem.

Covid-19 is the epitome of a complex problem, for all four reasons outlined in this article, but largely due to its unpredictability. For more than a year governments around the World have been reacting to a constantly moving beast – new variants, vaccine issues, sociopolitical issues, struggling economies, and the unintended consequences caused by decisions on how to handle the pandemic. It is hard to get more complex than this.

Dealing with unpredictability in a digital marketing world can be handled in a few ways:

  • Do the basics well. While reducibility is a challenge with complex problems there will often be agreed actions that are intended to move you toward a solution. It is important to focus on quality, thus minimising further instability in the system.
  • Seek multiple perspectives. Seek advice from people who have seen similar problems before. While they might not be able to help you predict what is going to happen, they will be able to give you additional perspectives that you may not have considered, helping to avoid unintended consequences.
  • Adopt an experimentation mindset. Because we can’t easily predict what is going to happen, it is important to keep testing – isolating individual components of the system, observing how they might react in a given environment, and adjusting our approach based on that feedback.
  • Build a tolerance for uncertainty. The phrase ‘make decisions based on data’ has been drilled into us for years. It’s a phrase that I agree with most of the time and I often find myself using it in meetings. When people disagree on something, my stock standard reply is “let’s measure it and let the data do the talking”. But over the years I’ve learned to not be so dogmatic about it because getting perfect data isn’t always possible. This is especially true when it comes to complex problems, and my tolerance for uncertainty has duly increased.

Because complicated problems can be easily defined, broken down into their individual parts, and are easy to predict, they are usually solvable.

‘We solve complex problems’, however, is often a bit of a misnomer, because many complex problems can rarely be solved , they can merely be addressed . For example, if you can’t easily define a problem, and you can’t set a concrete goal, how do you know when the problem has been solved?

Furthermore, the extent to which a complex problem can be solved is often influenced by several external factors. Do we have access to the right people? Is the project backed by people who can make decisions? Is the budget appropriate? Can you use that budget flexibly to allow for experimentation? Is the timeline adequate? Is the project reliant on the success of some other project, or on the success of a third party?

In a constantly moving and changing environment full of unpredictability, rather than trying to create a ‘definition of done’, it is often preferable to specify sub-goals – things that you are sure will improve your situation relating to the problem – and then aim for incrementally better with regards to those sub-goals, rather than to aim for solved .

So, next time you are faced with a tricky problem, consider whether it is truly complex or whether it is just complicated. Your approach to the problem should change depending on the nature of the problem and its complexity.

Start by trying to define the problem. If that’s tricky, you may need to pull other people in to help define, or to seek outside opinion. Once you’ve done that, think about whether you can reduce the problem down into its constituent parts. If you can’t, you may need to try mapping out externalities – things that sit outside the problem but may impact or be impacted by it. Next, can you easily predict what’s going to happen? If you can’t, you may need to adopt an experimentation mindset rather than coming up with a rigid plan of action. And, finally, is the end goal clear and obvious? If not, you may need to aim for incrementally better, rather than ‘solved’.

Further reading

  • https://blog.usejournal.com/7-differences-between-complex-and-complicated-fa44e0844606
  • https://aese.psu.edu/research/centers/cecd/engagement-toolbox/problems/complex-or-wicked-issues
  • https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2465602/
  • https://sustainingcommunity.wordpress.com/2014/11/06/complex-problems/
  • https://www.accenture.com/nl-en/blogs/insights/what-can-the-brain-teach-us-about-complex-problem-solving
  • https://www.frontiersin.org/articles/10.3389/fpsyg.2017.01153/full
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Complex vs Complicated Problems: What's the Difference?

what does complex problem solving mean

One of the best parts of the 2021 Cascade Strategy Fest was hearing speakers and participants share mental models that they used to cultivate strong strategic thinking. Often these models encoded some timeless business wisdom but did so in a way that was easy to remember and act. And once one of these clicks, it can completely transform the way you think about a particular concept or idea.

One of these particular moments came from Jessica Nordlander who shared with us a subtle but powerful distinction between what she calls complex and complicated problems.

This distinction was the catalyst for a change in our thinking when it comes to strategy – and it might just do the same for you.

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The Bridge Analogy

The best way to kickstart this is to run through an analogy that Jessica shared that perfectly illustrates the two different kinds of problems.

Jessica moved to a small mountain town in British Columbia, Canada because of the serene environment, great skiing conditions, and a generally great place to work remotely. In the middle of the town, there is a beautiful river that personifies the nature that is in the region.

Imagine that the mayor of the town has a strategic plan for its infrastructure and wants to build a new bridge over the river to unlock future economic benefits. In order to do so, the mayor and their team must solve a range of different problems, all of which can be separated into two different types.

The actual act of building the bridge is a complicated problem. It’s not easy to build a bridge, especially over a river of that size. You need a lot of engineers to work together and come up with the right plans. You need to select the right materials that fit the budget and the construction plans. You need to go through lots of checks and balances to ensure that the bridge is structurally sound and is going to hold the weight that you’re expecting. All of this is complicated.

But, with enough resources and the right people, you can solve this problem. It’s not going to be easy, but it is tractable. And we can be relatively confident that we can find a way to get this bridge built. It’s a complicated problem.

On the other side of the coin, you might find that one of the problems that this project faces is convincing the people in the town that the bridge is a good idea. Imagine that half of the town isn't buying into the project and they think that it will actually have detrimental effects by ruining the natural beauty and bringing more unwanted tourists into this small mountain town.

Dealing with these social dynamics is a complex problem. When you’re trying to come up with a viable solution here, there are no experts that you can turn to and outsource the work to. You can’t just throw money at the problem. You can’t even solve it necessarily.

Instead, you have to accept that this complex problem is one that you’re going to have to manage over time. The social disagreement is going to linger forever, and all you can do is try to make the best decision you can, and manage whatever conflict comes along with it.

With that example in mind, let’s now apply this mental model to business strategy.

Complicated Problems

In the world of business strategy, we like complicated problems. There’s a certain reward to tackling something complicated and coming up with our perfect plan to tackle it. We speak to the right people, we adjust the right budgets, and we arrive at a plan that’s going to solve everything.

A common example of a complicated problem in the space of strategy development is figuring out what the size of your total addressable market might be.

In these situations, we are able to use data, expertise, and experience to make good progress in the direction we’re aiming – and even if we don’t get it right immediately, we have the comfort of knowing that it is solvable if we just apply the right efforts and incentives.

We also have tools that can help us here. We have project management tools, Gantt charts, financial models, and a myriad of other resources that can help us think through these problems and solve them over time. We can work against expectations and make the necessary adjustments to move in the right direction.

This tight feedback loop makes for decisive action and it is a key part of any company’s strategy. This is the core of the stated objectives, it’s the goals we set for ourselves. But just because a problem is tractable, does not mean that it is easy to overcome. It takes a high level of skill, resourcefulness, and perseverance to execute the planned solution.

One of the most common obstacles we encounter when dealing with complicated problems is that we don’t have the right people on board. Without knowing it, we can often bang our heads against the wall time and time again because we just can’t see the right way to look at a particular problem. We have blind spots that impede our ability to make progress.

However, when we get the right person at the table that can bring their skills and expertise to bear on the problem, things can change dramatically. It can often just be a change in perspective that makes all the difference. And if we can get that sooner, rather than later, we’ll save ourselves a lot of time.

This doesn’t necessarily mean that we have to hire people. We can leverage knowledge in a myriad of ways including partnerships, advisors, mentors, trade exchanges, and so much more. All that matters is that we can bring the right expertise into play to solve the problem in front of us.

This requires us to put our ego aside for a bit and recognize that we probably don’t have all the answers. But when we do that, we can greatly improve our effectiveness and drive the company forward because we have the right people.

Your human resources are paramount for solving complicated problems.

Don’t take them for granted.

Complex Problems

Complex problems are much more insidious because they are often not tractable in the way we want them to be. It’s very common for companies to misdiagnose complex problems as complicated ones because we overestimate our abilities to change things that are actually out of our control.

It requires a dose of realism and a keen awareness to identify complex problems for what they are. These are the problems that you’re never truly going to have a handle on. These are the issues that will forever live in contradiction, and you need to come to terms with that.

Businesses get into trouble when they don’t make that realization and instead, they think that they can maneuver their way out of it by throwing resources or people at it.

“The more complex a problem is, the less likely it is that it will be solved by having a group of experts hacking away at it.”

Jessica Nordlander

As such, it’s crucial that we are always looking out for complex problems that need to be managed rather than solved. Because once we get to that point, we can take steps in the right direction. We can stop deluding ourselves with the perfect solution that we could find if we just had more time. Instead, we can start to put into action our plan to manage the situation over the long term.

“There's no way of really solving a complex problem, you can just manage it well or less well.”

The first thing we can do is to gather more information about the complex problem and try to understand both sides of the dilemma. As a business, you might think that you understand why people disagree with your proposed idea, but often your intuition is way off. You need to genuinely reach out to the detractors and spend time with them to understand why they feel what they feel.

Is there a point of view that you’re ignoring?

Is there an assumption of yours that is incorrect?

These discussions help to unearth the real reasons for the dilemma and when you do this effectively, you’re in a much better position to traverse the distance between the two sides. In fact, you’ll often find that a lot of the conflict stems simply from miscommunication and once you get that right – things are a lot more aligned. But you can never get to that point unless you are willing to hear the other side and take their point of view seriously.

In some cases, the mere act of listening is enough to bring people around and make them comfortable with the decision. If they feel that their objections have been heard and acknowledged, they are more likely to come on board, rather than shutting off completely.

After listening, you then need to take action and look for a compromise wherever possible.

If there are concerns that you come across that can be mitigated, then see what you can do in that regard. It’s often small things that you can improve on that show that you’re willing to compromise to try and reach a solution that works for everyone involved.

This back and forth is what managing a complex problem is all about. Keeping your stakeholders happy and content is what is going to give your project the time it needs to breathe. This is a continuous effort and requires regular maintenance, which is why so many decision-makers shy away from it. But it's part and parcel of what running a business is all about and it can be a significant factor in your overall success.

There is no manual or book that’s going to tell you how to solve these problems. There is no software tool that’s going to deliver the perfect solution. You have to be comfortable in the uncertainty. You have to acknowledge things for what they are and not let that get in the way of you taking it seriously.

It’s here in the depths of nuance, that companies can make their mark on the world, for good and for bad. This is because it deals with humanity at its core.

The Power of the Distinction 

The great companies are those who can make this distinction effectively. When you’re able to differentiate between those problems that can be solved with resources and expertise, and those that deal with much more nuanced human complexity, you’re in the best possible position to succeed.

“So, what you probably need to do is involve as many people as possible to tap into the collective intelligence, democratize the process, increase the understanding, and ensure ownership of the execution.”

Jessica’s main takeaway here is that we should leave the complicated problems to the experts, while we activate the whole organization to solve the complex problems. This common alignment and open-minded thinking make for more harmonious and sustainable solutions that perform well over time.

It’s the dichotomy between these two different responses that help us better prioritize how we make strategic decisions. Too often we assume that there are only complicated problems and so we end up throwing more and more resources at something that actually isn’t tractable in any meaningful way. We’ve seen it time and time again where companies are searching for a perfect solution that is going to appease everyone- but it never comes. And so instead of moving forward with a workable solution, they remain paralyzed in the research phase as they try to figure it out.

There is something to be said about working your problems out in the open, especially when they are complex in nature. Even though it can be tiring and difficult, there is magic to be found when you engage meaningfully with your stakeholders to understand why they’re against this or that.

It goes beyond the problem in front of you and gives you a tremendous level of insight into the people around you that you might not have had previously. It also helps to build relationships and rapport because you are genuinely trying to manage what can often be difficult circumstances. This small piece of humanity goes a long way and it can even be transformational in how your business is perceived.

If this mental model acts as a trojan horse that gets you closer to your stakeholders, then it’s well worth it. Don’t shy away from this. Embrace the distinction for what it is and your entire organization can shift.

Monitoring Progress

One last point that is worth mentioning here is that the way you track progress for each type of problem is going to vary. When you have a complicated problem, it's often quite easy to map out the step-by-step process to solve it, and you can track your progress according to that in order to stay accountable and on track. This is not the case with complex problems.

Complex problems are, by their nature, less tangible than their counterparts and so it’s more challenging to decipher whether you’re making progress or not. As such, you need to be a bit more creative with how you plan to monitor these issues. There may be some indirect ways in which you can quantify progress here but typically you’re going to rely on your intuition based on what reactions you’re getting from stakeholders.

What is key here is that you set up a time for regular reflection on these problems. Don’t let the lack of direct feedback mean you leave things to run as they are. As you’re managing complex problems over the medium and long term, you should be continually going back to the issue and evaluating how you’re doing. It’s only through forcing this internal feedback that you can adjust and adapt as you go along.

In summary, Jessica’s mental model in distinguishing between complicated and complex problems can prove incredibly useful when you take it seriously. Understanding the nuances of each type will serve you well in deploying the right resources and tools towards tackling each problem in your business setup.

In strategic decision-making, everything that we can do to better systematize these decisions is going to benefit us. So, it’s worth taking an internal inventory of all the problems you’re faced with right now as a business so you can categorize them accordingly. We think that if you take the time to work through this exercise, you’ll find that there are some complex problems that you’ve been treating as complicated ones. And when you realize that those issues can only be managed, rather than solved- you’ll take a big weight off of your shoulders.

Then, the remaining complicated problems can be handed off to the necessary experts while you seek to democratize the information for the complex ones. It might just radically shift how you view your business and its potential.

And the only way to find that out is to look inward. We certainly are.

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