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This research paper reviews developments in the psychology of everyday problem solving. The adjective ‘everyday’ is interpreted by contrast with the puzzles and academic tasks that have been the main focus of psychological problem solving research. This leads to an emphasis on the relation between planning and action, and between the mental representation of the problem and the physical situation in which problem solving takes place. The role of artifacts in support of everyday problem solving is discussed, and the idea that problem solving can be understood as an adaptation to environmental constraints is reviewed.
The psychology of human problem solving was transformed by the work of Newell and Simon (1972) and all subsequent theorizing has used their work as a platform. Newell and Simon (1972) developed a very general abstract conception of problem solving as search through a problem space. A problem is deﬁned by a goal state, a start state, and a set of operators, and the problem solver must achieve the goal state by applying a sequence of operators so as to transform the start state into the goal state. The set of states that are generatively deﬁned by the start state and the operators is called the ‘problem space,’ and problem solving can be viewed as a search of this problem space for the goal state.
Newell and Simon’s early empirical work within this framework concentrated on discovering the heuristics that people use to direct search through the problem space. This led them and their followers initially to concentrate on well-deﬁned puzzles, with a predetermined set of operators and a completely speciﬁed problem space. This program of research was very eﬀective, leading at least one prominent reviewer (VanLehn 1989) to claim that the psychology of human problem solving had been ‘solved’ (leaving as a residual mystery the question of what is learned from problem-solving experience).
But however valuable puzzles like the Tower of Hanoi or letter-arithmetic might be for the study of human problem solving, they are clearly not ‘everyday’ problems. There is no doubt that the problem space theory and search heuristics such as means–ends analysis and hill-climbing are vital to a full understanding of everyday human problem solving. But equally, the salient and manifold diﬀerences between many everyday problems and well-deﬁned, self-contained puzzles raise important issues for the problem solver and for the psychologist.
Consider the following examples of everyday problems (from Anderson 1990, p. 193, given by his students as answers to the question ‘name a problem that you tried to solve in the last 24 hours’).
Finding a route from a hotel to a restaurant
Debugging someone else’s code
Getting subjects to sign up for my experiment
Getting two Diet Cokes from a Coke machine
Getting my car registered
Perhaps the most obvious special property of puzzles like Tower of Hanoi compared to these problems is that all the knowledge needed for a solution is provided in the problem statement. (This is not quite true of letter-arithmetic, of course, but even then the additional knowledge required, that is, arithmetic, is well-deﬁned and strictly demarcated.) In particular the set of applicable operators is constrained and pre- determined.
An extensive literature has extended the study of human problem solving to ‘knowledge-intensive’ domains, in which the application of the solver’s experience (in particular by choosing operators from long-term memory) is the critical issue. The most extensively studied domains have been academic domains like mathematics, physics, and computer programming (as well as chess, which is self-contained in principle, but reliant on long-term memory in practice), and the most extensively used methodology has been a comparison of expert and novice problem solving. The classic established ﬁnding of this research is that experts are better problem solvers than novices not because they are better able to use search heuristics, but rather because their knowledge of the domain allows them to identify and classify problems in terms of the methods that will be useful to solve them, thereby obviating the need for extensive search of the problem space. Experts tend to work forwards from problem statements to solutions, whereas novices tend to work backwards from the goal, searching memory for applicable knowledge (Larkin et al. 1980).
Most everyday problems are even less well-deﬁned than academic problems in terms of the applicable operators. If you want to register your car and you don’t know how, the problem is discovering the applicable operators, not merely ordering them. Furthermore, in contrast to puzzles and to academic problems, most everyday problem solving involves interacting with (so as to change) the everyday physical and social environment.
2. The Problem Of Everyday Problems
Perhaps the single most important issue that the study of everyday problem solving prioritizes is the nature of the interplay between mental activity and physical activity, or between the mental problem space and the physical setting in which problem solving takes place. Within the traditional domains of problem solving research noted above, this has seldom been treated as a serious issue (although it should be noted that Newell and Simon recognized its importance, and have contributed some important analyses of the relation between external and internal representations, e.g., Simon 1975). Search of a problem space is primarily a mental activity: the current state is mentally represented, operators are considered, and imagined next-states are evaluated. Perhaps hierarchies and sequences of operators are mentally considered (‘planning’ or ‘look-ahead’). Eventually an operator or sequence of operators is chosen, and then enacted. Many computational models of human problem solving gloss any distinction between mental and physical application of an operator. And early AI planning systems, building on Newell and Simon’s analyses of search, computed entire sequences of operators from start state to goal state before acting on the world. People are seldom so patient. Instead they iteratively interleave planning and action. Since the early 1980s a body of literature has shown that in many everyday problem-solving situations the speciﬁcs of the physical situation and the problem solver’s management of the relation between planning, perception, and action are crucial determinants of problem-solving success.
Consider one observation from some very inﬂuential empirical studies by the cognitive anthropologist Jean Lave and her colleagues (1984). A supermarket shopper picked up one slab of cheese from a shelf of similar cheeses to be surprised by its price. She guessed that it had been wrongly labeled but wanted to check. She might have used mental division to compute its price per unit weight and then performed the same computation on one of the other slabs (as usual the cheeses varied somewhat in weight and therefore price). Instead she searched the shelf for a cheese of very similar weight and directly compared the prices of the two cheeses.
A similar observation of in-situ problem solving was made by Scribner (1984). She observed dairy workers completing orders for partially full crates of milk bottles. For example, a packer might receive an order of 1-6, meaning one crate-six bottles. Instead of completing this order by taking a full crate (16 bottles) and removing six bottles, the packer might ﬁnd a crate has eight bottles in it and add two. This ‘nonliteral’ strategy involves mental eﬀort, using arithmetic to recode the original order, but saves physical eﬀort. (Scribner found that nonliteral strategies were common among skilled packers, and could almost always be accounted for by the saving of physical eﬀort.)
Both the packer and the shopper are evidently managing a tradeoﬀ between physical and perceptual activities (such as searching a display for relevant items) and mental activities (arithmetic operations). To fully understand their problem-solving behavior it is necessary to understand the opportunities for this tradeoﬀ that are provided by the situation, and the cognitive mechanisms by which the tradeoﬀ is managed.
3. Cognitive Artifacts
The ﬁrst issue becomes particularly salient when coupled with the observation that much everyday problem solving is supported by ‘cognitive artifacts’ or tools of thought, ranging from pencil-and-paper through conventional representations like diagrams and graphs to computational systems. How can we understand the role of such artifacts in problem solving?
One theoretical approach is to simply redraw the boundaries of the cognitive agent away from the human problem solver to include the artifacts being used (Hutchins 1995). This approach has led to some insightful descriptions of how various human– machine systems perform their speciﬁc tasks (e.g., how a cockpit remembers its speeds). In the work of Zhang and Norman (1994) it has been developed into a general framework for the understanding of distributed cognitive tasks, in which the relation between external and internal representations is the primary focus. Zhang and Norman (1994) argue that when aspects of the representation of a problem can be oﬄoaded into the physical environment, problem solving becomes easier.
A second approach focuses on how the artifact changes the cognitive task of its user. For example, Larkin and Simon (1987) have analyzed how diagrams facilitate certain problem-solving strategies by allowing simple perceptual judgments (such as whether two lines intersect) to replace more demanding mental computations.
Diagrams might be referred to as ‘read only’ cognitive artifacts. Artifacts that are ‘read-write’ can have more complex mediating eﬀects on cognition. Consider the use of a simple appointment diary (Payne 1993). Recording an appointment in a diary changes the task of remembering that appointment in several ways. First, the fact that the appointment has been named and written will aﬀect the internal memory trace for the appointment. And of course, the diary can act as an external memory, allowing its user to retrieve the appointment by reading. Furthermore, in conventional paper diaries the act of writing a new appointment leads to the inevitable rehearsal of already noted appointments.
A third approach to understanding cognitive artifacts is to focus on the properties of the artifact itself as an information system, and to ask how readily it allows certain information-processing operations. This approach has been pioneered in the ﬁeld of human–computer interaction by Green (1989) under the banner ‘cognitive dimensions of notations.’ Green’s enterprise is to deﬁne a limited number of widely applicable dimensions on which cognitive artifacts can be compared in terms of the extent to which they support ﬂexible patterns of use. (Green has been particularly concerned with artifacts that are used in design tasks, such as spreadsheets, programming languages, document processors, and musical notations, and with supporting opportunistic design, in which initial drafts are iteratively revised.) One cognitive dimension is ‘role expressiveness,’ the extent to which a notation exposes meaningful structure. As a simple example, the use of meaningful variable names in a program will tend to increase role expressiveness. Another dimension is ‘viscosity,’ the extent to which a notation is resistant to local change. Consider a text with section numbers. Insert a section and all subsequent numbers must be changed.
All these approaches are set to continue in various guises. Understanding the cognitive eﬀects of artifacts is one of the most important open problems for the theory of human problem solving.
4. Rational Approaches To Problem Solving
Let us now turn to the second crucial issue raised above, that is, how the tradeoﬀ between mental and physical activity is managed. Scribner (1984) in her analysis of milk crate packing, suggested that packers might be explicitly trading mental and physical costs and beneﬁts. More recently this basic idea has been developed, particularly in the work of John Anderson (1990) on what he has called the rational analysis of cognition. The general idea is to analyze cognition as an optimal adaptation to the probabilistic structure of the environment. Such an analysis asks why cognitive behavior is the way it is, and may help structure the subsequent investigation of how cognition approximates the optimal solution.
This approach has already thrown some light on the critical characteristics of everyday problem solving. First, consider the interplay between planning and acting. From a rational perspective, a problem solver should plan before acting to the extent that the estimated beneﬁts of planning outweigh the costs. The beneﬁts of planning will relate to a reduction in the number of actions required and the individual costs of those actions. We might suppose that Scribner’s dairy workers would have been less inclined to transform their orders arithmetically if moving bottles around had been somehow much easier. This idea has been tested in a series of experiments by O’Hara and Payne (1998) who showed that clumsy user interfaces to puzzles (i.e., interfaces that made each move more costly in terms of keystrokes or time) produced fewer move solutions to puzzles than did more eﬃcient interfaces.
The use of cognitive artifacts has also been illuminated by an adaptive analysis. A simple case is the electronic calculator. There are many problems that can be computed either mentally or by calculator. An experiment by Siegler and Lemaire (1997) showed that people are able to make this choice adaptively according to an accurate model of their own capabilities: that is, they reliably choose to do a task mentally when that is indeed the quickest way to do it, and to use the calculator instead when that has real beneﬁts.
Finally, Pirolli and Card (1999) have shown that aspects of people’s use of complex computer-based information retrieval systems can be well modeled by equations based on optimal foraging theory. In other words, people behave as if they could compute and use accurate estimates of their current and previous rates of information gain (cf. an animal’s intake of energy from a food supply) and of the costs of searching diﬀerent information resources (cf. an animal’s journey to a new food supply).
Some theorists have argued that the situational contingencies of everyday problem solving render the abstract cognitive theory of Newell and Simon useless. However, an alternative view is that instead these complexities simply emphasize certain theoretical questions over others, and the required reworking is best considered as an elaboration of aspects of Newell and Simon’s framework. This second approach has the advantage of allowing incremental development in our understanding of the psychology of human problem solving.
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