Solve problem

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Problem solving (noun: problem solving ) is a key skill of people that aims to eliminate recognized problems through intelligent action through conscious thought processes .


Problems arise in everyday life with all economic subjects ( private households , companies , the state and its subdivisions such as public administration ). Problems in this sense are tasks or issues , the solution of which is associated with difficulties or obstacles. They have to be solved in order to be able to meet personal goals , corporate goals or national goals . As a task that can be organized in a targeted manner, initiative ensures that there is a permanent search for problems, precise and documented problem articulation takes place, problem management with minimal sanctions is in place, existing resistance to information is reduced and personal responsibility is strengthened.

Based on the actual state , the specified goal results in a target state that must be achieved by problem solving. More complex problems need to be structured before they can be brought closer to a solution. For this purpose, the causes of the problem must be researched.

G. H. Wheatley gave the humorous definition “Problem solving is what you do when you don't know what to do”. Dissatisfaction is seen as a condition that can lead someone to view an actual situation as a problem. The sequence of different partial activities in the context of such a process is also referred to as a problem-solving process . The fundamentals of problem-solving as an object of knowledge are researched by thought psychology , cognitive science and decision theory .

According to Thomas Samuel Kuhn , normal science consists of problem solving. Scientists are socialized to carry on a particular tradition of problem-solving.


Problem solving is required for interpersonal personal problems ( information asymmetry , conflicts , rivalry , disputes in interpersonal communication ) or for factual problems . The latter include, for example, errors , financial risks , legal risks , legal disputes , organizational weaknesses , operational adjustments or job stoppers in the organization .

Problems can also be categorized in terms of their complexity, the clarity of their goals and means, their time scale, the area from which they originate, their time pressure and the motivation attached to the problem.

Problem-solving phases

The process of problem-solving requires a certain chronological sequence of cognitive activities. These range from the identification of the problem to a precise analysis of the situation and determination of goals to the creation of a plan as well as its execution and evaluation . In the following, the universal phases of problem solving and their characteristic properties are explained in more detail.

Phase 1
Problem identification

First, a problem must be recognized as such. This is particularly important when dealing with complex issues . A problem is identified when it is recognized that a set goal cannot be achieved without further reflection.

Phase 2
Goal and situation analysis

The second phase of problem solving consists of two sub-phases, the goal and the situation analysis.

Phase 2a: goal analysis

This phase is about a precise definition of the target state set in phase one. It is examined by which features the target state to be achieved is characterized.

Phase 2b: situation analysis

The situation analysis phase includes an inventory of the current situation. In contrast to target analysis and problem identification, the desired target state is not the focus here. Instead, it examines why a problem cannot be solved at the moment (conflict). In addition, it is checked what material is available and what of it could be important in the course of problem solving.

Phase 3
Plan creation

The third phase deals with the preparation of a concrete procedure for problem solving. After both the initial and the target state have been defined, work on a solution plan can begin. When creating a plan, certain aspects are of particular importance. First of all, the chronological sequence must be recognized; the actions must therefore be carried out in a logically meaningful sequence. In addition, the framework conditions must be recognized and properly assessed. The creation of intermediate goals also makes it easier to create a solution plan. For a successful plan implementation, it is very important to consider available alternatives in the event of malfunctions. It is also important to be able to correctly assess the appropriateness of the resolution.

Phase 4
Plan execution

This phase includes the concrete implementation of the solution plan. During the implementation, the process is constantly monitored and checked for errors. In this way, it is possible to react quickly in the event of a fault and plan changes or a plan cancellation can be initiated. The phase of plan execution is closely linked to the phase of plan creation. Often, steps in the solution plan are created and carried out before the further course of the plan has been determined.

Phase 5

In the last phase of problem-solving, the result is assessed. The evaluation is based on the (sub) goals formulated in the goal analysis. The more of these partial goals are achieved, the better the overall result is to be assessed. In the case of a rather negative evaluation of the result, the attempt to achieve the goal is terminated or a new attempt at a solution is made.

Motivation / emotion criterion

With regard to the motivation / emotion associated with a problem, these can be divided into “ high-stakes ” and “low-stakes” problems. While the “high-stakes” problem has a high level of motivation and intense emotional involvement on the part of the actor, a “low-stakes” problem has few emotions and only a low level of motivation . One speaks of “high-stakes” problems when the problem is solved with great importance. An example of this would be the spaceship "Odyssey", which during the Apollo 13 mission had to record explosions in the oxygen tank when it exited the earth's atmosphere. It was imperative for the crew to solve this unprecedented problem in some way in order not to suffer human losses. The actors' motivation and their emotional involvement were of course correspondingly high. "Low-stakes" problems are problems of a rather unimportant kind. The actor would find a solution to the problem nice, but would not be further disappointed in the event of a failure.

Criterion of clarity of the goals and means

Problems also differ in the clarity of their ends and means. We distinguish here between well-defined problems ( well-defined ) and poorly defined problems ( ill-defined ). Well-defined problems have clear starting and target situations, and it is also known which means (operators) are available for the problem-solving process. While the well-defined problems can be counted among the "pleasant" problems, the poorly defined problems represent a greater challenge for the problem solver. Neither the starting nor the target conditions are clearly defined here. It is questionable which sub-goals are to be striven for and which features actually make up the desired target situation. In addition, little or no information is available about the operants present. The Middle East conflict with all of its intransparent, networked and confusing processes is an example of a poorly defined problem .

Complexity criterion

A distinction between problems can also be made according to the criterion of complexity . This differentiation concerns the difference between complex and simple problems. In the case of simple problems, a known, singular gap in the action plan must be filled. An example of this type of problem would be a puzzle with a single piece missing to complete. Simple problems are always well defined. Complex problems, on the other hand, are more difficult to solve. A large number of gaps in the course of action, some of which are not precisely defined, have to be closed, which often only open up in the course of the problem-solving process. Complex problems are always poorly defined, so it is not easy to see whether the chosen solution is actually effective. The protection of a nuclear power plant against terrorist attacks and environmental disasters is a complex, poorly defined problem. Numerous options have to be considered here, the risk of having overlooked a gap or not closing it completely is always present.

Time scale criterion

Also measured on a time scale, there are clear differences between the individual problems. While short-term problems can be solved quickly, long-term problems can be solved with a long-term solution process with various sub-goals. An example of a long-term problem is the determination to achieve a better work-life balance . This goal cannot be achieved without further ado, but requires a long-term solution plan that includes various intermediate goals.

Criterion of time pressure

Problems can also be differentiated according to the intensity of their inherent time pressure. While some problems can be solved without any time limit, others require extremely fast action by the actor. For example, if a child walks in front of a car on the street, the driver only has a fraction of a second to solve the problem by braking or swerving. A chess player, on the other hand, can think about his next move as long as he wants, which gives him the opportunity to make a lot of thought.

Criterion of the area

The area or domain from which a problem originates is also a criterion for categorization. For example, a distinction is made between academic and non-academic problems, problems from the field of nature and problems from the field of technology, etc. Depending on its domain, a problem requires specific problem-solving strategies or knowledge of the properties of the respective field.

Objective description of the problem

Since cognitive problem-solving processes are always based on a subjective problem representation, it is necessary for the systematic investigation of problem-solving to define what characterizes a problem at all. In a complex space that can assume an infinite number of different states, a problem can be seen as the difference between an existing initial state and a target state. The goal of a problem-solving process is to minimize this difference step-by-step using intermediate states that are generated through the targeted use of operators. In this sense, an operator is defined as an action that transforms one problem state into another. Thus, a problem can be exhaustively described by its target state and the operator inventory with which it is to be achieved. According to Dietrich Dörner (1981), every problem can be classified using these two components:

  • a problem with a closed, i.e. precisely delimited, target state and operator inventory is characterized by an interpolation barrier (e.g. chess),
  • a problem with a closed target state and an open operator inventory is characterized by a synthesis barrier (e.g. research in medicine),
  • a problem with an open target state and a closed operator inventory is characterized by a dialectical barrier (e.g. vacation planning),
  • an open target state and operator inventory problem is characterized by both a synthesis and a dialectical barrier .

The formalized forms of operators are called productions , which are characterized by conditionality, modularity, goal decomposition and abstraction. They are made up of two components:

  1. an IF component that contains the application condition and thus implicitly the target state,
  2. a THEN component that contains the specific operator that leads either to the goal or to an intermediate state.

Newell and Simon's Problem Solving Theory

With their theory of problem solving (1972) Allen Newell and Herbert A. Simon represent the basis of many approaches in psychology to this day. Newell and Simon regard humans as information processing systems with limited capabilities that interact with their environment. They developed a detailed account of the problem-solving process in the human brain. According to their theory ( information processing approach , 1972), two cooperating sub-processes are of central importance for solving problems: the understanding and the search process.

In the process of understanding (understanding) it comes to generating an internal representation of the problem. This is intended to provide three important pieces of information: First of all, the initial state must be determined. Then it should be worked out which operators can be used to change the actual state. In addition, it must be precisely defined how it can be recognized that an achieved state can be designated as a goal. These three components constitute the so-called problem space . The problem area is not a fixed construct, but can change further in the course of the solution process.

The partial process of searching (search) is concerned with the creation of a solution to the problem. This process is closely linked to the process of understanding. A search is now made for the discrepancy between the initial state and the target state and for operators that could contribute to reaching the target state. A distinction is made between weak and specific methods. While specific methods have a lot of power but can rarely be used ("Use a hammer to hit the nail in the wall!"), Weak methods are less powerful but can be used more often ("Use a tool to get ahead." ! ").

The process of understanding and searching do not follow a chronological order; rather, they are often mixed up and mixed up by the problem-solver.

Newell and Simon's problem-solving theory involves a multi-step problem-solving process:

  1. The first step is to create a mental representation of the problem in the problem-solver.
  2. A suitable method is then selected from an internal memory for solution methods.
  3. In the third step, the method is applied. It ends either by itself or due to metacognitive processes.
  4. Depending on the end result of the method, the internal representation is changed, a different solution method is used or the attempted solution is canceled.
  5. Problems that arise while using a method are treated as subgoals in the same way as the original problem. The solution process can be influenced and changed by newly arriving information.

Various factors influence the problem space as well as the solution program of a problem-solving person. Among other things, the instruction that provides a description of the initial and target state is to be mentioned. Furthermore, Newell and Simon see the previous experience of the problem-solver with the task in question or a similar task as an effective quantity. The solution spaces stored in the long-term memory, which can be used for a large number of tasks, as well as the stored programs for the construction of problem spaces and new programs, also play a not insignificant role. The course of the current problem-solving process, which enriches, changes or even radically modifies the problem space, can also be described as an influencing factor.

Heuristics and strategies

Problem solving usually proceeds according to the following scheme:

  1. At the beginning there is the problem, a cognitive conflict, an unsatisfactory actual state ,
  2. It now takes epistemic curiosity to overcome the current situation
  3. The search for tools, information and solutions begins,
  4. Once we have found the right solution, we experience an aha effect (if not: back to 3.),
  5. At the end there is relaxation, the desired target state .

The fact that the process of problem-solving is anything but trivial is shown by a large number of heuristics that allow individuals or groups (see also problem-solving technique (group) ) to work on problems despite limited resources (time, energy, etc.) in such a way that they can be dealt with in find an adequate solution in most cases.

Central mechanisms that have proven useful for this in the course of evolution are so-called heuristics. However, in some situations they cause systematic errors to be made in solving complex problems .

The use of different solution strategies is based on the fact that a person can have several possible solutions stored in memory for a problem situation . She observes the situation, evaluates it based on her experience-based or differently learned solution strategies and looks for a way to solve the situation adequately.

The various creativity techniques and special problem-solving techniques designed for groups offer specific strategies for problem- solving . The two cannot be strictly separated, as different techniques work through both internal and external dialogue.

Problem solving happens between two possible extremes:

  1. Trial and error ( english trial and error ) and other heuristics or
  2. Learning through insight ( English insight learning ).

The distinction between the terms heuristics and strategies is not uniform in problem solving. In the following, no differentiation is made and various problem-solving strategies / heuristics are presented as examples.

Trial and error

The "trial and error" method was investigated by Edward Lee Thorndike on rats. It does not require any intelligence. To illustrate: A caged dog will only make itself noticeable by making loud sounds. The barking is probably followed by door scratching. If that doesn't help, he'll probably jump up on the door and eventually manage to pull the handle down by accident. If he is successful, he will repeatedly apply what he has " experienced " through trial and error . Something similar can be observed in children. Once they have learned that they could cope with a situation with a certain behavior, they repeat this in the future.

An essential prerequisite for the trial-and-error strategy is the ability to remember , which prevents repeated attempts by chance that are unsuccessful. The creative change of already successfully applied problem solving strategies for mastering similar problems, the so-called "restructuring" of what has been learned is an important step away from random actions and toward einsichtigem problem solving. Schemas already present in the brain are adapted to the circumstances of the respective situation through generalization services. Restructuring what has been learned therefore requires a capacity for abstraction . With creativity , however, refers to the possibilities of an intelligent being, new and as yet unseen behaviors or ideas involve them in the problem solving process.

Difference reduction

As already mentioned above, the difference reduction means that an effective problem solution is usually possible by gradually approaching the target state. This principle is also called the mountaineering method and has the disadvantage that intermediate states may be reached in complex problem-solving processes, from which it is no longer possible, and one therefore has to fall back on earlier intermediate steps.

One problem that can be used to demonstrate the method of difference reduction is the so-called missionaries-and-cannibals task. Three missionaries and three cannibals (in other versions hobbits and orcs or similar) want to cross over to the other side of a river in a boat that can hold a maximum of two people. However, the number of cannibals must never exceed that of missionaries. When trying to solve the problem, there are always two possible moves, one of which leads back to an earlier state.

Means-goal analysis

With more complex problems, however, the mountaineering method can end in dead ends or endless loops. An effective problem-solving strategy that avoids such difficulties is the means-goal analysis formulated by Simon & Newell (1972). It is based on the fact that the operators relevant to the solution but not available are made available. This is done by means of recursion , in which the target state is broken down into subgoals that are fulfilled using other available operators. This was modeled as an information processing process with the help of a computer: the General Problem Solver.

Analogy building

Another relevant heuristic is the formation of analogies, in which elements from a basic domain, a problem whose solution was already known, is transferred to a target domain. An example of this is the transfer of the elements of the heliocentric model to an atomic model by Rutherford. However, so that the elements can be transferred, it is necessary to know about the existence of relevant domains from which operators can be derived. According to Dörner (1981), however, an abstraction is necessary for this, which in many cases does not have to be obvious, since the base domains are represented differently than the target domain. Possible difficulties arise here, for example, from the functional fixation (you can use a hare's skin as a tinder , even if this is not obvious) or from setting effects.

Other strategies

  • Means-end analysis: Is my solution the right one (means) to achieve the target state (purpose)? Is the expected new state closer to the goal (target state)?
  • Think from the goal
  • Overcoming barriers: restructuring a stuck solution strategy

Strategy selection from a system-theoretical point of view

When thinking in terms of systems , the problem is classified in a very specific paradigmatic system and the solution strategy is selected from known strategies that are adapted to this paradigm.

  • If, for example, a person reports stressful fears and dreams, an appropriately trained psychologist is most likely to approach this phenomenon from a psychoanalytic point of view. However, if it is reported about this person from his environment that he z. B. becomes aggressive in different situations for no apparent reason, the psychologist will probably argue from the behaviorist point of view that this behavior has been learned and can be unlearned again. The Gestalt psychology considers the human being in himself and his environment and trying in this way to apply problem-solving techniques.
  • When a team of civil engineers specializing in bridge construction is commissioned to run a new railway line through hilly terrain, it will look for a high-altitude route and span valleys with bridges. Civil engineers with a focus on tunneling will look for and find a lower-lying route that traverses the valleys and crosses mountains with tunnels.

Experience and learning in problem solving

Setting effect

An attitude effect is when a certain pattern of solving problems becomes routine for similar problems or a series of problems. The pattern is often carried out even if there were simpler and shorter solutions.

Due to the difficulties that have already been mentioned in the section on “building analogies”, the attitude effect is often spoken of in a negative way. Because despite simpler solutions, more ineffective variants are often chosen. But the attitude effect can also show that you learn quickly when solving problems and that stable routines can be formed in the process. In addition, the cognitive economy speaks for the attitude effect. Because for the problem-solver, this is the most economical and certainly the most successful way to solve a problem or, above all, many successive problems as quickly as possible.

The attitude effect can be explained by two theories, one not excluding the other.

On the one hand, a setting can be traced back to the sequence effect. This means that it is easier to learn with increasing levels of difficulty than with decreasing levels. If there is a break in the increase in difficulty, the hiring effect can occur, since an easier task is simply not taken into account as the difficulty increases.

On the other hand, the hypothesis theory says that problems that suddenly appear from another hypothesis space also support an attitude effect. Because continuing a problem-solving strategy from the previous hypothesis space is more convenient and uncomplicated than adapting to a new one. If there is a break in the increasing difficulty and / or a change in the hypothesis space, an attitude effect can arise.

Scheme induction

If one learns from experience in dealing with problems, the knowledge induced in this way can be divided into four sub-areas:

  1. The ability to recognize a certain type of problem ( English identification ). Example: "This task looks like a three- rule problem".
  2. Knowing what the problems identified in 1 have in common structurally, which other examples also fit this type, etc. ( English elaboration ).
  3. Knowing what steps to take to solve the problem at hand, what tools are needed, how resources are to be allocated, etc. ( English planning ).
  4. The ability to execute the planned 3 steps ( English execution ).

The first three types of knowledge are declarative , the fourth is procedural .

Problem representation

When it comes to problems, a distinction is made between simple and complex problems. In order to be able to solve problems of any kind better or faster, it is important to choose the most suitable form of representation.

Internal representation

Internal representation is understood to mean all internal ideas (e.g. one imagines which movements one carried out shortly before the key was misplaced). The most important thing is to be able to imagine the goal (= final state) exactly or to know exactly WHAT the goal is. Furthermore, the initial situation must be known, as well as the operators to be used and their restrictions. Such internal representations are constructed by adding or removing information about the problem or interpreting this information. The internal representation is sufficient for simple problems.

External representation

For more complex problems, an external representation must also take place. External representations are all forms of representation that take place outside the mental imagination, for example counting on the fingers, reading out loud, recording, etc. External representation can only take place if an internal representation is already available and helps to show relationships between problem aspects.

Development and change of representation

Forms of representation can evolve in the course of the problem-solving process. These advancements are considered improvements. The changes take place because at the beginning of the problem-solving process one may have left out important aspects or did not recognize them or, for example, did not understand restrictions. From this it becomes clear once again how important it is to select a favorable form of representation as a solution strategy. This makes problem solving easier.

Emergency response of the cognitive system

The emergency response of the cognitive system, or NRK for short, is a response to unspecific dangerous situations and is genetically predetermined. It is helpful for a quick response. This means that both stressful situations and stress-like symptoms can trigger the NRK. So the NRK is more of a reactive, spontaneous than a planned action.

There are three effects of the NRK:

  1. The first effect is that there can be a decrease in the intellectual level. This means that the self-reflection and intentions of the problem-solving person are lowered.
  2. Second, there is a tendency to act quickly. This increases the willingness to take risks and to violate rules, but at the same time the tendency to flee.
  3. Finally, a degeneration of the hypothesis formation can set in, which leads to the de-concretization of goals. Hypotheses are formulated in a more general way and no detailed troubleshooting is required.

Methodical problem solving

An approach to methodical problem solving developed by the Institute for Product Development (IPEK) at the Karlsruhe Institute of Technology (formerly University of Karlsruhe ) is described by the acronym SPALTEN. Its individual steps are:

  • S ituationsanalyse
  • P roblemeingrenzung
  • A lternativen show
  • L ösungsauswahl
  • T ragweite analyze - assess opportunities and risks
  • E ECISION and implementation - measures and processes
  • N achbereitung and learning

This sequence can be understood as a guideline for the methodical solution of any problem.

In 1999, the British Open University divided a structured problem-solving process into the Creativity, Innovation and Change course as follows:

  • Exploration (mapping / enriching understanding of the problem)
  • Definition (sharpening / adjusting the focus on the problem)
  • Collecting (... information about the current status)
  • Generation (generating / collecting ideas / views / opinions, etc.)
  • Grouping (categorizing / roughly assigning related ideas / views / opinions, etc.)
  • Preselect (compress a large amount of material into a short list)
  • Prioritize (evaluation / selection / development within the short list)
  • Planning (turning the concept into a workable, acceptable plan)

If the problem environment is viewed as a system , various problem-solving methods from the system engineering concept can be used to solve it. This approach is particularly useful for problem solving in complex socio-technical systems such as B. Suitable for companies.

Like others (e.g. Design Thinking or the 6-step model of the REFA Association), these models have fundamental similarities. All models have a three-tier structure in common:

  • Exploration of the problem with subsequent formulation of the work
  • Exploration of the possible solutions with subsequent narrowing down to promising solution strategies
  • Introduction of a few solutions with subsequent back control.

Even highly structured special strategies such as TRIZ or ARIZ (both primarily serve to solve technical problems) largely follow this structured plan.

As clear as these structured strategies appear, they are equally unsuitable in various situations. Simple problems (e.g. finding the next parking space) usually do not require complex structures. Highly complex problems (e.g. peace negotiations after a civil war) cannot be captured and described in their entirety. In such cases, the problem-solving process itself becomes part of the solution; z. B. Good Friday Agreement in Northern Ireland or the Middle East Peace Process . Structured processes are accordingly suitable for problems of the middle category.

Non-human problem solving


An algorithm is a solution process that leads in a clear way from an initial state to a solution. The Euclidean algorithm calculates the greatest natural number for two natural numbers, which is contained in both natural numbers as a divisor. Algorithms can be executed automatically and always lead to a solution. Therefore one can write algorithms as computer programs and delegate the automatic solution to a computer.

Heuristics in the narrower sense (i.e. heuristics that cannot be written as algorithms) cannot be easily converted into computer programs. For example, there is an algorithmic solution for the “ traveling salesman problem ” (a travel route between many places is to be optimized), but this is practically impossible to implement because of the time and resources required if the number of places to be visited is very large. Here you can get ahead with a heuristic that only seeks to find the best possible solution. In order to have a computer solve this suboptimal solution programmatically, one needs an algorithm that clearly makes the suboptimal solution effective. However, this procedure does not automatically solve the problem of the origin unambiguously.

Problem solving through artificial intelligence

This article is about problem-solving strategies used by natural beings. For the derived application area in Artificial Intelligence , in which attempts are made to use formalized conclusions to solve problems, see Automatic Problem Solving .


In business administration , problem solutions are also understood to be products or services geared to individual customer requirements (see solution ).


Individual evidence

  1. ^ Rolf Bronner: Initiative. In: Fritz Nieske / Markus Wiener (ed.): Management Lexicon. Volume II, 1968, p. 568.
  2. Original: "What you do when you don't know what to do"; in: GH Wheatley: Problem solving in school mathematics. In: MEPS Technical Report 84.01. Purdue University, School of Mathematics and Science Center, West Lafayette (Indiana) 1984, p. 1.
  3. ^ Thomas Samuel Kuhn: The Structure of Scientific Revolutions , 1963, p. 351.
  4. Tilmann Betsch / Joachim Funke / Henning Plessner: Thinking, Judging, Deciding, Problem Solving . S. 151 ff .
  5. Tilmann Betsch / Joachim Funke / Henning Plessner: Thinking, Judging, Deciding, Problem Solving . S. 146-150 .
  6. Tilmann Betsch / Joachim Funke / Henning Plessner: Thinking, Judging, Deciding, Problem Solving . S. 180 ff .
  7. ^ S. Ian Robertson: Problem Solving . Psychology Press, Hove (UK), 2001, p. 40 ff.
  8. a b Tilmann Betsch / Joachim Funke / Henning Plessner: Thinking, Judging, Deciding, Problem Solving . S. 164 .
  9. Funke: Problem-solving thinking . S. 115 .
  10. a b c Funke: Problem-solving thinking . S. 114 .
  11. ^ SP Marshall: Schemas in problem solving . Cambridge University Press 1995.
  12. a b Tilmann Betsch / Joachim Funke / Henning Plessner: Thinking, Judging, Deciding, Problem Solving . S. 171 .
  13. Funke: Problem-solving thinking . S. 182 .
  14. J. Martin, R. Bell (and a contribution by Eion Famer) B822 Technique Library; The Open University 2000;