Four points for this lecture • Role of problem solving in history of cognition. • Theories about problem • Theories about solver’s knowledge • Theories about process.
Role of problem solving in history of Cognition • Young turks vs. Behaviourist establishment • Challenge to model some high level behaviour • Availability of computers as a metaphor • Virtue of programme as model • Explicit • You can tell whether it works
GPS – Newell & Simon • Newell & Simon pointed out that... • Mental processes (MPs) are knowable • MPs can be seen as a sequence of steps • Computer programs show human-like behaviour • Computer programs make every step explicit • Programs are therefore ideal as models of human mental function.
“(Global modellers…) sometimes seem to be marching to a different drummer than scholars in psychology’s strong empirical tradition. Creative thinking about what would constitute an adequate comprehension theory is as important to most of them as doing experiments to devise one. Anderson (1976) for example, has argued convincingly for the value of “rational experiments,” in which the data are everyday facts of life and logical proofs rather than systematic observations from the laboratory. These strategies are an unanticipated, and sometimes unappealing, development for some strict laboratory scientists.” (p. 459) Lachman, Lachman, & Butterfield (1979)
The dilemma: • L, L, & B were saying that we may have to choose – do we want to do experimental work? Or do we want to study complex behaviours such as problem solving? • Cognitive psychologists split into 2 schools on these issues, one led by Herbert Simon and Alan Newell, one led by Daniel Kahneman and Amos Tversky…
The dilemma • Simon and colleagues came out of the battle with Behaviourism – both sides wanted convincing models of complex human behaviours (for Skinner, language; for Simon, problem-solving.) • Simon always argued that verbal reports were needed to study what really matters.
The dilemma • Kahneman and his colleagues were younger. They came out of cognitive psychology. They focused on the kinds of representations and processes that other cognitive psychologists worked on. These are not available to introspection, but are studied through ingenious experimental methods.
The dilemma: • Newell died in the early ’90s, Tversky in the mid ’90s, and Simon in 2002. Both Simon (1979) and Kahneman (2002) were awarded Nobel Prizes in Economics for their work on problem solving and decision making. • This is some of what they learned on the way…
The problem, the solver, the process • Types of problems (Greeno, 1978): • Inducing structure (e.g., analogies) • Discovery of a pattern relating elements of a problem to each other. • Transformation (e.g., water jar problem) • Manipulation of objects or symbols while following certain rules.
The problem, the solver, the process • Arrangement (e.g., anagrams, seating guests) • All the elements are given, and the task is to re-arrange them. • Any problem could be in more than one category.
The problem, the solver, the process • Some characteristics of the solver will be discussed in the chapter on expertise. • Here, we’ll talk about characteristics that interfere with problem-solving: • Functional fixedness • Negative set
The problem, the solver, the process • Gestalt psychology: Perception is in your head. • Tau effect & Kappa effect • Principles that govern perception in humans: • Good form, good continuation, proximity, similarity • Perception important in problem-solving.
The problem, the solver, the process • X X X G G G G G G G • X X X • X X X • X X X G G G G G G G • Are these columns or rows? • They’re both – but we see the Xs as columns and Gs as rows, because of Proximity.
The problem, the solver, the process • Gestalt psychologists studied how our biases as perceivers influenced our problem-solving. • Functional fixedness – fix a candle to the wall. You’re given… • A table • A candle • A box of matches • A box of tacks.
The problem, the solver, the process • Subjects are better at candle task if the matches and the tacks are on the table, not in the box. • It is easier to think of empty boxes as something other than containers – to overcome functional fixedness. • Other examples: panty-hose can be used to make a fan belt…
The problem, the solver, the process • Mental set • Set is a preference for certain operators (things you can do, actions you can take to solve a problem). • Luchins and the water jar problem: • Einstellung (mechanization of thought) – people kept using a strategy that worked even when a better one was available
The problem, the solver, the process • Humans are, nonetheless, very good at problem-solving. We are the great problem-solvers of the world. • We are good at solving individual problems. • Animals solve problems through evolution. • Humans solve problems much faster. • We keep solving new problems. • We go out of our way to find new problems
The problem, the solver, the process • 3 stages of problem solving (Hunt & Ellis, 1993). • 1. Understanding the problem • This is about representation – how do you represent the problem? • Gestalt psychologists said, this is a question of perception (see lawyer joke).
The problem, the solver, the process • 2. Generating solutions. You could: • Generate all possible solutions (e.g., chess) • Generate solutions randomly • Use a strategy – such as a heuristic
Some heuristics for producing solutions • A heuristic is a ‘rule of thumb,’ a simple strategy that works often, but not always. (In contrast, algorithms always work, but not always available, and can be unworkable when available.) • A. Generate-test method • very slow if lots of possible solutions exist
Some heuristics for producing solutions • B. Means-ends analysis • must know what the ends are you seek • must know the means available • Current state • Goal state • Difference between them • Operators
Some heuristics for producing solutions • C. Working backwards • Start by figuring out what the solution to your problem looks like. • Move backward from that goal to your current state. • This defines a path that leads to goal • E.g., “I want to get into a graduate programme in cognitive psychology.”
The problem, the solver, the process • 3. Evaluating solutions • How do you know when you’ve solved your problem? • A problem for psychotherapists – how do you know when you’re finished, when your client doesn’t need you any more?
The problem, the solver, the process • Hunt & Ellis suggested that there are general-purpose operations applicable to a variety of problems. • That invites an attempt to create a problem-solving program that uses general purpose operations. • Newell & Simon’s GPS is the most important such program.
The problem, the solver, the process • GPS used means-ends analysis. • Assess the difference between current state and goal state. • Find and apply an operator that can reduce that difference. • Assess the difference again. If no difference, exit; if difference still, find an operator.
The problem, the solver, the process • General Problem Solver (GPS) • For complex problems, GPS model suggests two ways we can go wrong: • If we can’t figure out most important difference • If we don’t have a relevant operator.
The problem, the solver, the process • Finding the most important difference: • Sub-goaling: set up a series of sub-goals before you begin the problem-solving process. • E.g., if you want to go to medical school, you’ll need some chemistry courses. Do you have a chemistry course? If not, look for an operator (‘take a chemistry course’).
The problem, the solver, the process • Finding a relevant operator • One way of obtaining new operators is through formal education or training. • A second way is through analogy – seeing how a different problem is similar to the current one. This may let you adapt operators that worked with that problem (Gick & Holyoak, 1980).
The problem, the solver, the process • Using analogy to find a relevant operator: • One thing that gets in the way of seeing analogies is focus on the surface form of a problem. • A major difference between novices and experts in any area is that experts are less likely to focus on the surface form. They see the underlying structure of problems in the domain. • We’ll come back to this point soon…