Why is problem solving a complex mental process

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. One competence that seems to be of central importance is the ability to solve complex problems Mainzer, Mainzer quotes the Nobel prize winner Simon who wrote as early as 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.

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, As a result, solving well-defined problems and solving ill-defined problems requires different cognitive processes Schraw et al. 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. According to the instructions, moving one of the matchsticks will make the equations true.

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?

Systematic research on CPS started in the s with observations of the behavior of participants who were confronted with computer simulated microworlds. 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 and later: theoretical papers Blech and Funke, ; Funke, ; Knauff and Wolf, ; Leutner et al. 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. The German phrase was later translated to CPS in the titles of two edited volumes by Sternberg and Frensch and Frensch and Funke a that collected papers from different research traditions.

He compared static with dynamic decision making, writing:. 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.

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. 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.

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, This mixture of features is similar to what is called VUCA volatility, uncertainty, complexity, ambiguity in modern approaches to management e.

His analysis of the differences between the European and American traditions shows advantages but also potential drawbacks for each side. He states p. Before attending to validity issues, we will first present a short review of different streams.

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

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. He found, for example, that solution quality decreases as the number of systems relations increases.

These authors demonstrated that a small improvement in predicting school grade point average beyond reasoning is possible with MicroDYN tests.

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.

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 idea behind this concept was that whereas the upper limits of complexity are unbound, the lower limits might be identifiable. 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.

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 that measure new aspects of problem solving, namely interactive problems besides static problem solving Greiff and Funke, PISA 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 — 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, a ; Greiff and Martin, ; Funke et al. In the words of Funke b , p. 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.

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. 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. These phenomena require theories for explaining them and they require assessment instruments eliciting them in a reliable way.

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. The third phenomenon relates to failures that occur during the planning and acting stages Jansson, ; Ramnarayan et al.

Jansson 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.

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. 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. Dealing with partly unknown complex systems requires courage, wisdom, knowledge, grit, and creativity. Everyday creativity is important for solving everyday problems e. 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?

Even if the experimental approach has been successful for testing hypotheses for an overview of older work, see Funke, , 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. 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. 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. 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. Even though a growing number of references claiming to deal with complex problems exist e. The dynamics behind on-off-switches Thimbleby, 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.

This type of simple systems is used frequently. 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. 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, ; Hundertmark et al.

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 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. In real-life, it is hard to imagine a business manager trying to solve her or his problems by means of VOTAT. In the current decade, for example, the World Economic Forum attempts to identify the complexities and risks of our modern world.

Ramnarayan et al. 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. 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. 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, ; Lee and Cho, , 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.

Schweizer et al. 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, ; Bennett, , CPS should not be reduced to the mere outcome of a solution 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.

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. 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. 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:. 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 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. 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. 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! In war, that is impossible. If you decide to attack, you cannot know whether the necessary conditions are met for you to succeed. Solving a problem is reaching a goal state; there are many things that can stand in the way of solving a problem, but many strategies that can help.

The human mind is a problem-solving machine. It is considered the most complex of all intellectual functions, since it is a higher-order cognitive process that requires the modulation and control of basic skills.

There are considered to be two major domains in problem solving: mathematical problem solving, which involves problems capable of being represented by symbols, and personal problem solving, where some difficulty or barrier is encountered.

There are many common mental constructs that impede our ability to correctly solve problems in the most efficient manner possible.

A mental set is an unconscious tendency to approach a problem in a particular way. Our mental sets are shaped by our past experiences and habits. For example, if the last time your computer froze you restarted it and it worked, that might be the only solution you can think of the next time it freezes. So for example, say you need to open a can of broth but you only have a hammer. You might not realize that you could use the pointy, two-pronged end of the hammer to puncture the top of the can, since you are so accustomed to using the hammer as simply a pounding tool.

The dot problem : In the dot problem, described below, solvers must attempt to connect all nine dots with no more than four lines, without lifting their pen from the paper.

This is a barrier that shows up in problem solving that causes people to unconsciously place boundaries on the task at hand. A famous example of this barrier to problem solving is the dot problem. In this problem, there are nine dots arranged in a 3 x 3 square. The solver is asked to draw no more than four lines, without lifting their pen or pencil from the paper, that connect all of the dots. What often happens is that the solver creates an assumption in their mind that they must connect the dots without letting the lines go outside the square of dots.

The solvers are literally unable to think outside the box. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals.

The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. In order to make good decisions, we use our knowledge and our reasoning.

Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An anchoring bias occurs when you focus on one piece of information when making a decision or solving a problem. The confirmation bias is the tendency to focus on information that confirms your existing beliefs.

For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis.

In other words, you knew all along that things would turn out the way they did. Representative bias describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision. These biases are summarized in [link]. Please visit this site to see a clever music video that a high school teacher made to explain these and other cognitive biases to his AP psychology students. Were you able to determine how many marbles are needed to balance the scales in [link]?

You need nine. Were you able to solve the problems in [link] and [link]? Here are the answers [link]. Many different strategies exist for solving problems. Typical strategies include trial and error, applying algorithms, and using heuristics. To solve a large, complicated problem, it often helps to break the problem into smaller steps that can be accomplished individually, leading to an overall solution.

Roadblocks to problem solving include a mental set, functional fixedness, and various biases that can cloud decision making skills. What is functional fixedness and how can overcoming it help you solve problems? Which type of bias do you recognize in your own decision making processes?

Functional fixedness occurs when you cannot see a use for an object other than the use for which it was intended. For example, if you need something to hold up a tarp in the rain, but only have a pitchfork, you must overcome your expectation that a pitchfork can only be used for garden chores before you realize that you could stick it in the ground and drape the tarp on top of it to hold it up.

An algorithm is a proven formula for achieving a desired outcome. It saves time because if you follow it exactly, you will solve the problem without having to figure out how to solve the problem. It is a bit like not reinventing the wheel. Skip to main content. Thinking and Intelligence.

Search for:. Problem Solving Learning Objectives By the end of this section, you will be able to: Describe problem solving strategies Define algorithm and heuristic Explain some common roadblocks to effective problem solving. Everyday Connections: Solving Puzzles.