Problem Solving: Definition, terminology, and patterns Problem Solving Terminology

Problem solving

 

Problem Solving: Definition, terminology, and patterns Problem Solving Terminology

Problem solving consists in using generic or ad hoc methods, in an orderly manner, for finding solutions to problems. Some of the problem-solving techniques developed and used in artificial intelligence, computer science, engineering, mathematics, medicine, etc. are related to mental problem-solving techniques studied in psychology.

Definition

The term problem solving is used in many disciplines, sometimes with different perspectives, and often with different terminologies. For instance, it is a mental process in psychology and a computerized process in computer science.

Psychology

In psychology, problem solving refers to a state of desire for reaching a definite goal from a present condition that either is not directly moving toward the goal, is far from it, or needs more complex logic for finding a missing description of conditions or steps toward the goal. In psychology, problem solving is the concluding part of a larger process that also includes problem findingand problem shaping.

Considered the most complex of all intellectual functions, problem solving has been defined as a higher-order cognitive process that requires the modulation and control of more routine or fundamental skills. Problem solving has two major domains: mathematical problem solving and personal problem solving where, in the second, some difficulty or barrier is encountered. Further problem solving occurs when moving from a given state to a desired goal state is needed for either living organisms or an artificial intelligence system.

While problem solving accompanies the very beginning of human evolution and especially the history of mathematics,^[3] the nature of human problem solving processes and methods has been studied by psychologists over the past hundred years. Methods of studying problem solving include introspection, behaviorism, simulation, computer modeling, and experiment. Social psychologists have recently distinguished between independent and interdependent problem-solving (see more).

Clinical Psychology

Simple laboratory-based tasks can be useful in explicating the steps of logic and reasoning that underlie problem solving; however, they usually omit the complexity and emotional valence of “real-world” problems. In clinical psychology, researchers have focused on the role of emotions in problem solving (D’Zurilla & Goldfried, 1971; D’Zurilla & Nezu, 1982), demonstrating that poor emotional control can disrupt focus on the target task and impede problem resolution (Rath, Langenbahn, Simon, Sherr, & Diller, 2004). In this conceptualization, human problem solving consists of two related processes: problem orientation, the motivational/attitudinal/affective approach to problematic situations and problem-solving skills. Working with individuals with frontal lobe injuries,neuropsychologists have discovered that deficits in emotional control and reasoning can be remedied, improving the capacity of injured persons to resolve everyday problems successfully (Rath, Simon, Langenbahn, Sherr, & Diller, 2003).

Cognitive Sciences

The early experimental work of the Gestaltists in Germany placed the beginning of problem solving study (e.g., Karl Duncker in 1935 with his book The psychology of productive thinking). Later this experimental work continued through the 1960s and early 1970s with research conducted on relatively simple (but novel for participants) laboratory tasks of problem solving. Choosing simple novel tasks was based on the clearly defined optimal solutions and their short time for solving, which made possible for the researchers to trace participants’ steps in problem-solving process. Researchers’ underlying assumption was that simple tasks such as the Tower of Hanoi correspond to the main properties of “real world” problems and thus the characteristiccognitive processes within participants’ attempts to solve simple problems are the same for “real world” problems too; simple problems were used for reasons of convenience and with the expectation that thought generalizations to more complex problems would become possible. Perhaps the best-known and most impressive example of this line of research is the work by Allen Newell and Herbert A. Simon. Other experts have shown that the principle of decomposition improves the ability of the problem solver to make good judgment.

Computer Science and Algorithmics

In computer science and in the part of artificial intelligence that deals with algorithms (“algorithmics”), problem solving encompasses a number of techniques known as algorithms, heuristics, root cause analysis, etc. In these disciplines, problem solving is part of a larger process that encompasses problem determination, de-duplication, analysis, diagnosis, repair, etc.

Engineering

Problem solving is used in engineering when products or processes fail, so corrective action can be taken to prevent further failures. It can also be applied to a product or process prior to an actual fail event, i.e., when a potential problem can be predicted and analyzed, and mitigation applied so the problem never actually occurs. Techniques such as Failure Mode Effects Analysiscan be used to proactively reduce the likelihood of problems occurring.

Forensic engineering is an important technique of failure analysis that involves tracing product defects and flaws. Corrective action can then be taken to prevent further failures.

Reverse engineering attempts to discover the original problem-solving logic used in developing a product by taking it apart.

Europe

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

North America

In North America, initiated by the work of Herbert A. Simon on “learning by doing” in semantically rich domains (e.g. Anzai & Simon, 1979; Bhaskar & Simon, 1977), researchers began to investigate problem solving separately in different natural knowledge domains – such as physics, writing, or chess playing – thus relinquishing their attempts to extract a global theory of problem solving (e.g. Sternberg & Frensch, 1991). Instead, these researchers have frequently focused on the development of problem solving within a certain domain, that is on the development ofexpertise (e.g. Anderson, Boyle & Reiser, 1985; Chase & Simon, 1973; Chi, Feltovich & Glaser, 1981).

Areas that have attracted rather intensive attention in North America include:

·                     Reading (Stanovich & Cunningham, 1991)

·                     Writing (Bryson, Bereiter, Scardamalia & Joram, 1991)

·                     Calculation (Sokol & McCloskey, 1991)

·                     Political decision making (Voss, Wolfe, Lawrence & Engle, 1991)

·                     Problem Solving for Business (Cornell, 2010)

·                     Managerial problem solving (Wagner, 1991)

·                     Lawyers’ reasoning (Amsel, Langer & Loutzenhiser, 1991)

·                     Mechanical problem solving (Hegarty, 1991)

·                     Problem solving in electronics (Lesgold & Lajoie, 1991)

·                     Computer skills (Kay, 1991)

·                     Game playing (Frensch & Sternberg, 1991)

·                     Personal problem solving (Heppner & Krauskopf, 1987)

·                     Mathematical problem solving (Pólya, 1945; Schoenfeld, 1985)

·                     Social problem solving (D’Zurilla & Goldfreid, 1971; D’Zurilla & Nezu, 1982)

·                     Problem solving for innovations and inventions: TRIZ (Altshuller, 1973, 1984, 1994)

As elucidated by Dietrich Dörner and later expanded upon by Joachim Funke, difficult problems have some typical characteristics that can be summarized as follows:

·                     Intransparency (lack of clarity of the situation)

·                      commencement opacity

·                      continuation opacity

·                     Polytely (multiple goals)

·                      inexpressiveness

·                      opposition

·                      transience

·                     Complexity (large numbers of items, interrelations and decisions)

·                      enumerability

·                      connectivity (hierarchy relation, communication relation, allocation relation)

·                      heterogeneity

·                     Dynamics (time considerations)

·                      temporal constraints

·                      temporal sensitivity

·                      phase effects

·                      dynamic unpredictability

The resolution of difficult problems requires a direct attack on each of these characteristics that are encountered.

Problem solving strategies are the steps that one would use to find the problem(s) that in are in the way to getting to one’s own goal. Some would refer to this as the ‘problem-solving cycle’. (Bransford & Stein, 1993) In this cycle one will recognize the problem, define the problem, develop a strategy to fix the problem, organize the knowledge of the problem, figure-out the resources at the user’s disposal, monitor one’s progress, and evaluate the solution for accuracy. Although called a cycle, one does not have to do each step in order to fix the problem, in fact those who don’t are usually better at problem solving.^{[citatioeeded]} The reason it is called a cycle is that once one is completed with a problem another usually will pop up. Blanchard-Fields (2007) looks at problem solving from one of two facets. The first looking at those problems that only have one solution (like math problems, or fact based questions) which are grounded in psychometric intelligence. The other that is socioemotional iature and are unpredictable with answers that are constantly changing (like what’s your favorite color or what you should get someone for Christmas).

The following techniques are usually called problem-solving strategies:

·                     Abstraction: solving the problem in a model of the system before applying it to the real system

·                     Analogy: using a solution that solves an analogous problem

·                     Brainstorming: (especially among groups of people) suggesting a large number of solutions or ideas and combining and developing them until an optimum is found

·                     Divide and conquer: breaking down a large, complex problem into smaller, solvable problems

·                     Hypothesis testing: assuming a possible explanation to the problem and trying to prove (or, in some contexts, disprove) the assumption

·                     Lateral thinking: approaching solutions indirectly and creatively

·                     Means-ends analysis: choosing an action at each step to move closer to the goal

·                     Method of focal objects: synthesizing seemingly non-matching characteristics of different objects into something new

·                     Morphological analysis: assessing the output and interactions of an entire system

·                     Proof: try to prove that the problem cannot be solved. The point where the proof fails will be the starting point for solving it

·                     Reduction: transforming the problem into another problem for which solutions exist

·                     Research: employing existing ideas or adapting existing solutions to similar problems

·                     Root cause analysis: identifying the cause of a problem

·                     Trial-and-error: testing possible solutions until the right one is found

·                     Eight Disciplines Problem Solving

·                     GROW model

·                     How to solve it

·                     KEPNER and FOURIE Incident and Problem Investigation

·                     Kepner-Tregoe Problem Solving and Decision Making

·                     PDCA (plan–do–check–act)

·                     Productive Thinking Model

·                     RPR Problem Diagnosis (rapid problem resolution)

·                     Thinking Dimensions – Problem Solving

·                     TRIZ (in Russian: Teoriya Resheniya Izobretatelskikh Zadatch, “theory of solving inventor’s problems”)

Systems Thinking

Problem Solving is very important but problem solvers often misunderstand it. This report proposes the definition of problems, terminology for Problem Solving and useful Problem Solving patterns.

We should define what is the problem as the first step of Problem Solving. Yet problem solvers often forget this first step.

Further, we should recognize common terminology such as Purpose, Situation, Problem, Cause, Solvable Cause, Issue, and Solution. Even Consultants, who should be professional problem solvers, are often confused with the terminology of Problem Solving. For example, some consultants may think of issues as problems, or some of them think of problems as causes. But issues must be the proposal to solve problems and problems should be negative expressions while issues should be a positive expression. Some consultants do not mind this type of minute terminology, but clear terminology is helpful to increase the efficiency of Problem Solving. Third, there are several useful thinking patterns such as strategic thinking, emotional thinking, realistic thinking, empirical thinking and so on. The thinking pattern means how we think. So far, I recognized fourteen thinking patterns. If we choose an appropriate pattern at each step in Problem Solving, we can improve the efficiency of Problem Solving.

This report will explain the above three points such as the definition of problems, the terminology of Problem Solving, and useful thinking patterns.

Definition of problem

A problem is decided by purposes. If someone wants money and when he or she has little money, he or she has a problem. But if someone does not want money, little money is not a problem.

For example, manufacturing managers are usually evaluated with line-operation rate, which is shown as a percentage of operated hours to potential total operation hours. Therefore manufacturing managers sometimes operate lines without orders from their sales division. This operation may produce more than demand and make excessive inventories. The excessive inventories may be a problem for general managers. But for the manufacturing managers, the excessive inventories may not be a problem.

If a purpose is different between managers, they see the identical situation in different ways. One may see a problem but the others may not see the problem. Therefore, in order to identify a problem, problem solvers such as consultants must clarify the differences of purposes. But oftentimes, problem solvers frequently forget to clarify the differences of purposes and incur confusion among their problem solving projects. Therefore problem solvers should start their problem solving projects from the definition of purposes and problems

Terminology of Problem Solving

We should know the basic terminology for Problem Solving. This report proposes seven terms such as Purpose, Situation, Problem, Cause, Solvable Cause, Issue, and Solution.

 Purpose

Purpose is what we want to do or what we want to be. Purpose is an easy term to understand. But problem solvers frequently forget to confirm Purpose, at the first step of Problem Solving. Without clear purposes, we caot think about problems.

Situation

Situation is just what a circumstance is. Situation is neither good nor bad. We should recognize situations objectively as much as we can. Usually almost all situations are not problems. But some problem solvers think of all situations as problems. Before we recognize a problem, we should capture situations clearly without recognizing them as problems or non-problems. Without recognizing situations objectively, Problem Solving is likely to be narrow sighted, because problem solvers recognize problems with their prejudice.

Problem

Problem is some portions of a situation, which cannot realize purposes. Since problem solvers ofteeglect the differences of purposes, they cannot capture the true problems. If the purpose is different, the identical situation may be a problem or may not be a problem.

Cause

Cause is what brings about a problem. Some problem solvers do not distinguish causes from problems. But since problems are some portions of a situation, problems are more general than causes are. In other words causes are more specific facts, which bring about problems. Without distinguishing causes from problems, Problem Solving caot be specific. Finding specific facts which causes problems is the essential step in Problem Solving.

Solvable Cause

Solvable cause is some portions of causes. When we solve a problem, we should focus on solvable causes. Finding solvable causes is another essential step in Problem Solving. But problem solvers frequently do not extract solvable causes among causes. If we try to solve unsolvable causes, we waste time. Extracting solvable causes is a useful step to make Problem Solving efficient.

Issue

Issue is the opposite expression of a problem. If a problem is that we do not have money, the issue is that we get money. Some problem splvers do not know what Issue is. They may think of “we do not have money” as an issue. At the worst case, they may mix the problems, which should be negative expressions, and the issues, which should be positive expressions.

Solution

Solution is a specific action to solve a problem, which is equal to a specific action to realize an issue. Some problem solvers do not break down issues into more specific actions. Issues are not solutions. Problem solvers must break down issues into specific action.

Thinking patterns

Thinking patterns for judgements

In order to create a value through thinking we need to judge whether what we think is right or wrong. This report lists four judging patterns such as strategic thinking, emotional thinking, realistic thinking, and empirical thinking.

Strategic thinking

Focus, or bias, is the criterion for strategic thinking. If you judge whether a situation is right or wrong based on whether the situation is focused or not, your judgement is strategic. A strategy is not necessarily strategic. Historically, many strategists such as Sonfucis in ancient China, Naplon, M. Porter proposed strategic thinking when they develop strategies.

Emotional thinking

In organizations, an emotional aspect is essential. Tactical leaders judge whether a situation is right or wrong based on the participantsЃf emotional commitment. They think that if participants can be positive to a situation, the situation is right.

Realistic thinking

·                     Start from what we can do

·                     Fix the essential problem first

These two criteria are very useful. “Starting” is very important, even if we do very little. We do not have to start from the essential part. Even if we start from an easier part, starting is a better judgement than a judgement of not-starting in terms of the first part of realistic thinking. Further, after we start, we should search key factors to make the Problem Solving more efficient. Usually, 80 % of the problems are caused by only 20 % of the causes. If we can find the essential 20 % of the causes, we can fix 80 % of problems very efficiently. Then if we try to find the essential problem, what we are doing is right in terms of the second part of realistic thinking.

Empirical thinking

When we use empirical thinking, we judge whether the situation is right or wrong based on our past experiences. Sometimes, this thinking pattern persists on the past criteria too much, even if a situation has changed. But when it comes to our daily lives, situations do not change frequently. Further, if we have the experience of the identical situation before, we can utilize the experience as a reliable knowledge data base.

Thinking patterns for thinking processes

If we can think systematically, we do not have to be frustrated when we think. In contrast, if we have no systematic method, Problem Solving frustrate us. This reports lists five systematic thinking processes such as rational thinking, systems thinking, cause & effect thinking, contingent thinking, and the ToyotaЃfs five times WHYs method .

Rational thinking

Rational thinking is one of the most common Problem Solving methods. This report will briefly show this Problem Solving method.

1.                Set the ideal situation

2.                Identify a current situation

3.                Compare the ideal situation and the current situation, and identify the problem situation

4.                Break down the problem to its causes

5.                Conceive the solution alternatives to the causes

6.                Evaluate and choose the reasonable solution alternatives

7.                Implement the solutions

We can use rational thinking as a Problem Solving method for almost all problems.

Systems thinking

Systems thinking is a more scientific Problem Solving approach than the rational thinking approach. We set the system, which causes problems and analyze them based on systemsЃf functions. The following arre the system and how the system works.

System

·                     Purpose

·                     Input

·                     Output

·                     Function

·                     Inside cause (Solvable cause)

·                     Outside cause (Unsolvable cause)

·                     Result

In order to realize Purpose, we prepare Input and through Function we can get Output. But Output does not necessarily realize Purpose. Result of the Function may be different from Purpose. This difference is created by Outside Cause and Inside Cause. We can not solve Outside Cause but we can solve Inside Cause. For example, when we want to play golf, Purpose is to play golf. If we caot play golf, this situation is Output. If we caot play golf because of a bad weather, the bad weather is Outside Cause, because we caot change the weather. In contrast, if we cannot play golf because we left golf bags in our home, this cause is solvable. Then, that we left bags in our home is an Inside Cause.

Systems thinking is a very clear and useful method to solve problems.

Cause & effect thinking

Traditionally, we like to clarify cause and effect relations. We usually think of finding causes as solving problems. Finding a cause and effect relation is a conventional basic Problem Solving method.

Contingent thinking

Game Theory is a typical contingent thinking method. If we think about as many situations as possible, which may happen, and prepare solutions for each situation, this process is a contingent thinking approach.

Thinking patterns for efficient thinking

In order to think efficiently, there are several useful thinking patterns. This report lists five patterns for efficient thinking such as hypothesis thinking, conception thinking, structure thinking, convergence & divergence thinking, and time order thinking.

Hypothesis thinking

If we can collect all information quickly and easily, you can solve problems very efficiently. But actually, we caot collect every information. If we try to collect all information, we need so long time. Hypothesis thinking does not require collecting all information. We develop a hypothesis based on available information. After we developed a hypothesis, we collect minimum information to prove the hypothesis. If the first hypothesis is right, you do not have to collect any more information. If the first hypothesis is wrong, we will develop the next hypothesis based on available information. Hypothesis thinking is a very efficient problem-solving method, because we do not have to waste time to collect unnecessary information.

Conception thinking

Problem Solving is not necessarily logical or rational. Creativity and flexibility are other important aspects for Problem Solving. We caot recognize these aspects clearly. This report shows only what kinds of tips are useful for creative and flexible conception. Following are portions of tips.

·                     To be visual.

·                     To write down what we think.

·                     Use cards to draw, write and arrange ideas in many ways.

·                     Change positions, forms, and viewpoints, physically and mentally.

We can imagine without words and logic, but in order to communicate to others, we must explain by words and logic. Therefore after we create ideas, we must explain them literally. Creative conception must be translated into reasonable explanations. Without explanations, conception does not make sense.

Structure thinking

If we make a structure like a tree to grasp a complex situation, we can understand very clearly.

Upper level should be more abstract and lower level should be more concrete. Dividing abstract situations from concrete situations is helpful to clarify the complex situations. Very frequently, problem solvers cannot arrange a situation clearly. A clear recognition of a complex situation increases efficiency of Problem Solving.

Convergence & divergence thinking

When we should be creative we do not have to consider convergence of ideas. In contrast, when we should summarize ideas we must focus on convergence. If we do convergence and divergence simultaneously, Problem Solving becomes inefficient.

Time order thinking

Thinking based on a time order is very convenient, when we are confused with Problem Solving. We can think based on a time order from the past to the future and make a complex situation clear.

Across the tiers, the problem-solving method is used to match instructional resources to educational need. The problem-solving method is as follows:

1.                Define the problem by determining the discrepancy between what is expected and what is occurring. Ask, “What’s the problem?”

2.                Analyze the problem using data to determine why the discrepancy is occurring. Ask, “Why is it taking place?”

3.                Establish a student performance goal, develop an intervention plan to address the goal, and delineate how the student’s progress will be monitored and implementation integrity will be ensured. Ask, “What are we going to do about it?”

4.                Use progress monitoring data to evaluate the effectiveness of the intervention plan based on the student’s response to the intervention. Ask, “Is it working?” If not, how will the intervention plan be adjusted to better support the student’s progress?