Nature of Problem Solving

Content

Introduction
Logic Problems
Algorithms
Story (Word) Problems
Rule Using (Induction) Problems
Decision Making Problems
Troubleshooting Problems
Diagnosis-Solution Problems
Policy Analysis Problems
Design Problems
Dilemmas
References

Introduction

The most common intellectual activity that occupies people in everyday contexts (both work and personal lives) is problem solving. While many of us prefer not to admit that we have problems, the reality is that we solve problems constantly.  What shall I wear to work? Which is the best route to avoid this traffic jam? How do I prevent my boss from criticizing me?  How can I get that new contract? What shall we make for supper this evening?  How much should I add to inventory? How shall we market this new product to maximize cash flow?  What do I have to do in order to attract recognition in this agency? We are deluged with problems every day. Unfortunately, we have rarely been taught how to solve problems, especially the kinds of problems that plague us in our everyday lives.

We believe that the only legitimate goal of education is problem solving. Why?One, problem solving is the most authentic and therefore the most relevant learning activity that students can engage students.  Two, situated learning research has shown that knowledge constructed in the context of solving problems is better comprehended, retained, and therefore more transferable. Three, students construct better conceptual understanding while solving problems, because they must articulate an intention to solve the problem. Meaningful learning cannot occur until and unless learners manifest an intention to learn.  Four, life is short. Because time allocated to education is always limited, why not make the most of it?

What is problem solving?

Problem solving has three critical attributes.  One, a problem is an unknown value, process, method, position, or belief that is worth finding an answer to.  Two, in order to find the unknown, problem solving requires the mental representation of the problem. That is, human problem solvers individually construct or socially co-construct a representation of the problem, known as the problem space (Newell & Simon, 1972).  Three, problem solving engages cognitive and social activities that manipulate the problem space, such as model building, hypothesis generation, speculation, solution testing, information gathering, etc.

How do people solve problems?

Historically, problem solving has been conceived as a uniform process.  In traditional models of problem solving, all problems are solved essentially the same way. A typical model includes these processes:

Gick (1986) synthesized problem solving models into a simplified model of the problem-solving process, including the processes of

However, more contemporary research and theory asserts that problem solving is context-specific r domain-specific, that is, solving problems in one situation or discipline is different than solving problems in another situation or discipline.

How do problems vary?

In the Center for the Study of Problem Solving, we argue that problems and problem solving vary in several ways. Several authors (Jonassen, 1997; Simon, 1973, Voss & Post, 1988) have distinguished well-structured from ill-structured problems and recommended different learning approaches for each. Most problems encountered in schools and universities are well-structured problems. Well-structured problems typically present all elements of the problem; engage a limited number of rules and principles that are organized in a predictive and prescriptive arrangement; possess correct, convergent answers; and have a preferred, prescribed solution process.

Ill-structured problems, on the other hand, are the kinds of problems that are encountered in everyday practice. Ill-structured problems have many alternative solutions to problems; vaguely defined or unclear goals and constraints; multiple solution paths; and multiple criteria for evaluating solutions; so they are more difficult to solve.

Problems also vary in complexity. The complexity of a problem is a function of the number of issues, functions, or variables involved in the problem; the number of interactions among those issues, functions, or variables; and the predictability of the behavior of those issues, functions, or variables.  Ill-structured problems tend to be more complex, however, there are a number of highly complex well-structured problems, such as chess.

Dynamicity is another dimension of complexity. In dynamic problems, the relationships among variables or factors change over time. Changes in one factor may cause variable changes in other factors. The more intricate these interactions, the more difficult it is any solution. Ill-structured problems tend to be more dynamic.

A final dimension of problems and problem solving is domain specificity.  In contemporary psychology, there is a common belief that problems within a domain rely on cognitive strategies that are specific to that domain (Mayer, 1992; Smith, 1991; Sternberg &Frensch, 1991).  These are often referred to as strong methods, as opposed to domain-general strategies (weak methods). For example, Lehman, Lempert, and Nisbett (1988) concluded that different forms of reasoning are learned in different graduate disciplines. Graduate students in the probabilistic sciences of psychology and medicine perform better on statistical, methodological, and conditional reasoning problems than students in law and chemistry, who do not learn such forms of reasoning.  The cognitive operations are learned through the development of pragmatic reasoning schemas rather than exercises in formal logic.  Graduates in different domains develop reasoning skills through solving situated, ill-structured problems that require forms of logic that are domain-specific.

How do problems vary within these dimensions?  Jonassen (2000) described a typology of problems that vary primarily along a continuum from well-structured to ill-structured, including the following kinds of problems.

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Logic Problems

Outcome: efficient solution
Problem: logical manipulation
Solution: single, clear criteria

Examples of Logic Problems


Algorithms

Outcome: correct solution
Problem: procedural, algorithmic
Solution: single, clear criteria
Context: abstract, formulaic

Examples of Algorithms

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Story (Word) Problems

Outcome: correct solution
Problem: identify variables, insert & solve, practice
Solution: single, clear criteria
Context: constrained to predefined elements, shallow context; textbook problems

Examples of Story Problems


Rule Using (Induction) Problems

Outcome: information
Problem: procedural
Solution: productivity, relevance, correctness
Context: purposeful academic, real world, constrained

Examples of Rule Using Problems

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Decision Making Problems

Outcome: decision about alternatives and justification
Problem:  advantages, disadvantages, weighing options
Solution: selection of alternatives
Context: life decisions, information needs,  tactical decisions

Examples of Decision Making Problems


Troubleshooting Problems

Outcome: fault isolation
Problem: search & replace, serial elimination, space splitting
Solution: correct fault & replace, efficiency
Context: closed system, real world

Examples of Troubleshooting Problems

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Diagnosis-Solution Problems

Outcome: fault identification and treatment
Problem: serial elimination, problem schemas, management
Solution: optional, must be defended
Context: real world, technical, mostly closed system

Examples of Diagnosis-Solution Problems

Strategic Performance Problems

Applying tactics to meet strategy in real-time, complex environment
Maintaining situational awareness
Achieving mission objective

Examples of Strategic Performance Problems

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Policy Analysis Problems

Outcome:decision, action, argumentation
Problem: solution identification. Alternative actions, argue position
Solution: multiple, unclear
Context: real world, constrained

Examples of Policy Analysis Problems


Design Problems

Outcome: problem articulation,  options, design, justification
Problem: original, principle-based
Solution: multiple, undefined criteria
Context: complex, real world

Examples of Design Problems

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Dilemmas

Outcome: complex, nonpredictive: personal, social, & ethical dilemmas
Problem: vexing decision, no solutions, perspective irreconcilable
Solution: articulated preference, preferred decisions
Context: topical, complex, interdisciplinary

Examples of Dilemmas


References

Bransford, J. & Stein, B.S. (1983). The IDEAL problem solver: A guide for improving thinking, learning, and creativity. New York: W.H. Freeman.

Newell, A. & Simon, H. (1972). Human problem solving. Englewood Cliffs, NJ: Prentice Hall.