Complex Problem Solving

The European Perspective

Peter A. Frensch,Joachim Funke

• Publisher: Psychology Press
• Year: 2014
• ISBN:
  9781317781394
• Edition: 1
• Topic: Psychology
• Subtopic: History & Theory in Psychology
• Index: Psychology

This volume presents a state-of-the-science review of the most promising current European research -- and its historic roots of research -- on complex problem solving (CPS) in Europe. It is an attempt to close the knowledge gap among American scholars regarding the European approach to understanding CPS. Although most of the American researchers are well aware of the fact that CPS has been a very active research area in Europe for quite some time, they do not know any specifics about even the most important research. Part of the reason for this lack of knowledge is undoubtedly the fact that European researchers -- for the most part -- have been rather reluctant to publish their work in English-language journals. The book concentrates on European research because the basic approach European scholars have taken to studying CPS is very different from one taken by North American researchers. Traditionally, American scholars have been studying CPS in "natural" domains -- physics, reading, writing, and chess playing -- concentrating primarily on exploring novice-expert differences and the acquisition of a complex skill. European scholars, in contrast, have been primarily concerned with problem solving behavior in artificially generated, mostly computerized, complex systems. While the American approach has the advantage of high external validity, the European approach has the advantage of system variables that can be systematically manipulated to reveal the effects of system parameters on CPS behavior. The two approaches are thus best viewed as complementing each other. This volume contains contributions from four European countries -- Sweden, Switzerland, Great Britain, and Germany. As such, it accurately represents the bulk of empirical research on CPS which has been conducted in Europe. An international cooperation started two years ago with the goal of bringing the European research on complex problem solving to the awareness of American scholars. A direct result of that effort, the contributions to this book are both informative and comprehensive.

PART ONE

INTRODUCTION

CHAPTER ONE

Definitions, Traditions, and a General Framework for Understanding Complex Problem Solving

Peter A. Frensch*

University of Missouri at Columbia, USA

Joachim Funke

University of Missouri at Columbia, USA

Introduction

Definitions of Problem Solving

Explicit Definitions

Explicit Versus Implicit Definitions

Why Do Definitions Differ?

The Perceived Usefulness of a Definition

Can We Ever Agree on a Universal Definition of Problem Solving?

Definitions of Problem Solving: The European Approach

The Contributors’ View

Historical Roots

The European Situation

An Integrated View

Summary

A Theoretical Framework for Complex Problem Solving

Internal Subject Factors

External Factors

The Components of a Theory of CPS

Summary

INTRODUCTION

Many of our daily activities involve problem solving of some sort. For example, we decide what to wear in the morning, which route to take to get to our office, which job-related duties to perform in which sequence once we arrive at our office, what to have for lunch, and so on. Of course, not all problem solving is alike. There are problems that can be solved with a few mental steps, and there are problems that require extensive thinking. There are problems that we have never encountered before, and there are problems we are familiar with. There are problems that have very clear goals, and there are problems where the goals are far from clear. Problems, then, can be distinguished on any number of meaningful dimensions, and the solution processes, the mental steps we engage in when solving a problem, may differ widely for different types of problems.

Given the multidimensionality of a problem, it may not come as a surprise to discover that different researchers, all claiming to study the phenomenon of problem solving, have on more than one occasion wholeheartedly disagreed with each other’s conclusions. For example, many of those studying expert problem solving have maintained that experts typically use a forward-working (from the givens to the goal) approach to problem solving, whereas others have argued that experts work backward (from the goal to the givens). This apparent contradiction can be resolved if one considers the type of task that has been studied by the different researchers. It turns out that those claiming that experts prefer a forward-working approach have used problems that their experts were relatively familiar with, whereas those claiming the opposite tended to use tasks that were relatively novel for their experts (Smith, 1991). Thus, any general conclusion regarding expert problem solving, and indeed any conclusion regarding problem solving in general, can only be meaningful if we can all agree on what constitutes a problem and what constitutes problem solving.

In the first section of this introductory chapter, therefore, we present definitions of the terms problem and problem solving that have been offered in the past, and discuss why these definitions differ. In the second section, we discuss the main differences between the current North American and European mainstream approaches to studying problem solving, and argue that the differences between the two approaches are at least partially due to differences in how problem solving is defined. Finally, in the third section, we discuss how selecting a definition of problem solving constrains a theory of problem solving, and describe how a general theoretical framework for understanding problem solving that is based on the definition adopted within the European tradition, might look like.

DEFINITIONS OF PROBLEM SOLVING

“When I use a word,” Humpty Dumpty said in a rather scornful tone, “it means just what I choose it to mean—neither more nor less.” (Lewis Carroll, 1935, p. 119)

According to Webster’s New Twentieth Century Dictionary (1983), a definition is “an explanation or statement of what a word or word phrase means or has meant.” In the first section of this chapter, we present and compare various statements of the meaning of problem solving that have been offered in the past. We ask why we need an explicit definition of problem solving at all, and discuss why existing definitions differ. Finally, we present our thoughts on whether we can ever agree on a general definition of problem solving.

Explicit Definitions

Researchers in the area of problem solving have long been troubled by the absence of agreement on the exact meaning of many of the basic terms used (e.g., Smith, 1991). Among these basic terms are expert, novice, heuristic, problem, and even problem solving itself. Consider, for example, some of the better known definitions of problem solving that have been offered in the past:

• Prhoblem solving is defined as any goal-directed sequence of cognitive operations. (Anderson, 1980, p. 257)

• …problem solving is defined here as a goal-directed sequence of cognitive and affective operations as well as behavioral responses for the purpose of adapting to internal or external demands or challenges. (Heppner & Krauskopf, 1987, p. 375)

• What you do, when you don’t know what to do. (Wheatley, 1984, p. 1)

These definitions are examples of literally dozens and dozens of definitions that continue to be offered in the literature. Most of the definitions that one encounters in the literature differ primarily on three dimensions. First, they differ in terms of their semantic content, that is, in which actions and thoughts are classified as problem solving. To take two examples from the aforementioned, affectively coping with the loss of a close relative, for instance, would be considered problem solving by Heppner and Krauskopf, but would not be considered problem solving by Anderson. Second, the definitions differ in how fuzzy their boundaries are. The boundary of Anderson’s definition is clearly more precise, or less fuzzy, than the boundaries of the definitions presented by Heppner and Krauskopf or Wheatley. What exactly is meant, for instance, by Heppner and Krauskopf’s “internal or external demands or challenges?” And what exactly does Wheatley’s “what you do” include and exclude? And finally, the definitions differ in terms of their category size, that is, in how many events are classified as problem solving.

If we find it difficult to define problem solving, then perhaps we can at least agree on a definition of the more basic term problem. The following are some of the commonly cited definitions of problem:

• A problem exists when the goal that is sought is not directly attainable by the performance of a simple act available in the animal’s repertory; the solution calls for either a novel action or a new integration of available actions. (Thorndike, 1898, cited by Sheerer, 1963, p. 118)

• A problem occurs … if an organism follows a goal and does not know how to reach it. Whenever a given state cannot be converted into the desired state directly through the activation of obvious operations, thinking is needed to construct mediating actions. (Duncker, 1935, p. 1; translated by the authors)

• A question for which there is at the moment no answer is a problem. (Skinner, 1966, p. 225)

• A problem is a stimulus situation for which an organism does not have a ready response. (Davis, 1973, p. 12)

• A problem is a “stimulus situation for which an organism does not have a response,” … a problem arises “when the individual cannot immediately and effectively respond to the situation.” (Woods, Crow, Hoffman, & Wright, 1985, p. 1)

• A person is confronted with a problem when he wants something and does not know immediately what series of actions he can perform to get it. (Newell & Simon, 1972, p. 72)

• Whenever there is a gap between where you are now and where you want to be, and you don’t know how to find a way to cross that gap, you have a problem. (Hayes, 1980, p. i)

As in the case of problem solving, it should be readily apparent that the one and only, universally accepted definition of what constitutes a problem does not exist. Most of the definitions in the literature appear to differ again on primarily three dimensions: (a) their semantic content, or more precisely, a focus on either the absence of a task-relevant response or the absence of a task-relevant thought that would lead to a solution for the task at hand, (b) the fuzziness of their boundaries, and (c) their category size, that is, in how many tasks are classified as problems.

For example, the definitions provided by Thorndike, Davis, and Woods et al., respectively, focus on the absence of an observable response, whereas most of the remaining definitions focus on the absence of a nonobservable thought or cognition. Thus, a known, yet complicated mathematical equation that requires hours to be solved and thus may not lead to an observable response for a long time, may be classified as a problem according to some definitions, but may not constitute a problem according to other definitions.

On the other hand, however, most, if not all, of the definitions just given do appear to share an important component, namely a focus on the distance between the task and the solver, rather than a focus on the nature of the task itself. That is, a problem is said to exist only if there is a gap between task and solver, or a barrier between the state given in the actual situation and the goal state in the head of the problem solver. A problem is not defined by task features, but rather by the interaction between task requirements and solver, that is, by the interaction between task characteristics and person characteristics. In general, gap definitions imply that the same task may constitute a problem for one solver, but not for another, whereas task definitions assume that a given task either constitutes, or does not constitute, a problem for all solvers.

Explicit Versus Implicit Definitions

The impression that all definitions of problem share a common aspect, namely a focus on the task-person interaction, quickly disappears, however, when we consider implicit, in addition to, explicit definitions of a problem. By an explicit definition, we mean a definition that is articulated in writing, or is at least stated verbally. Thus, all of the examples given previously constitute explicit definitions of problem and problem solving, respectively. By an implicit definition, in contrast, we mean an operational definition that one uses in one’s research. Ideally, the implicit definition is accompanied by, and consistent with, an explicit definition. However, frequently the implicit definition is the only definition a researcher uses, and worse, on occasion, the implicit definition used may not be consistent with the explicit definition that one subscribes to.

By their very nature, implicit definitions are hidden and can be discovered only if one carefully examines the details of the research performed under the heading of problem solving. For instance, historically, much of what is generally considered problem-solving research has been concerned with subjects’ performances on classroom tasks that are well-structured (e.g., “what does 15 × 16 equal?”). For these tasks, subjects typically do not immediately know the correct answer, although they know how to get the answers, that is, how to solve the task. Such tasks would not be considered problems according to any of the explicit definitions previously discussed. However, by using these tasks in what is labeled as problem-solving research, one implicitly defines problem in terms of task characteristics.

Thus, explicitly, problems have been defined in terms of the interaction between task and individual; implicitly, however, problems frequently have been defined in terms of their task properties. If we accept the explicit definitions of problem solving, then research that has used exerciselike tasks cannot be relevant to our understanding of problem solving. The extensive literature on routin...