1. Lecture 13 – Problem Solving 1 Two points for this lecture: 1.Role of problem solving in history of cognition. 2. Cognitive theories of the problem, the solver, and the process.

2. Lecture 13 – Problem Solving 2 Role of problem solving in history of Cognition 1.Young turks vs. behaviourist establishment 2.Challenge to model some high level behaviour 3.Availability of computers as a metaphor 4.Virtue of programme as model Explicit You can tell whether it works

3. Lecture 13 – Problem Solving 3 Newell & Simon – developed GPS 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.

4. Lecture 13 – Problem Solving 4 Lachman, Lachman, & Butterfield (1979) said: (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)

5. Lecture 13 – Problem Solving 5 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? Most cognitive psychologists chose the former. But Newell, Simon, and some others continued to study problem solving. This is what they learned…

6. Lecture 13 – Problem Solving 6 The problem, the solver, the process Types of problems (Greeno, 1978): 1.Inducing structure (e.g., analogies) Discovery of a pattern relating elements of a problem to each other. 2.Transformation (e.g., water jar problem) Manipulation of objects or symbols while following certain rules.

7. Lecture 13 – Problem Solving 7 3.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

8. Lecture 13 – Problem Solving 8 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

9. Lecture 13 – Problem Solving 9 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.

10. Lecture 13 – Problem Solving 10 The problem, the solver, the process XXXG G G G G G G XXX XXXG 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.

11. Lecture 13 – Problem Solving 11 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… A table A candle A box of matches A box of tacks.

12. Lecture 13 – Problem Solving 12 The problem, the solver, the process Subjects are better at this 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… water in a car radiator can be drunk…

13. Lecture 13 – Problem Solving 13 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

14. Lecture 13 – Problem Solving 14 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

15. Lecture 13 – Problem Solving 15 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).

16. Lecture 13 – Problem Solving 16 Q: What do you need when you have 500 lawyers buried up to their necks in sand? A: More sand. Point – the solution you devise depends upon how you represent the problem – rescuing the lawyers or finishing the job of burying them.

17. Lecture 13 – Problem Solving 17 The problem, the solver, the process 2.Generating solutions. There are a # of ways to do this, depending upon type of problem: Generate all possible solutions (e.g., chess) Generate solutions randomly Use a strategy – such as a heuristic

18. Lecture 13 – Problem Solving 18 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.) A. Generate-test method can be very slow if there are lots of possible solutions Some heuristics for producing solutions:

19. Lecture 13 – Problem Solving 19 Some heuristics for producing solutions: B. Means-ends analysis must know what the ends are you seek must know the means available N & S: representation makes clear the current state, the goal, the differences between them, available operators which can be used to reduce difference.

20. Lecture 13 – Problem Solving 20 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

21. Lecture 13 – Problem Solving 21 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?

22. Lecture 13 – Problem Solving 22 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.

23. Lecture 13 – Problem Solving 23 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.

24. Lecture 13 – Problem Solving 24 The problem, the solver, the process General Problem Solver (GPS) For complex problems, 2 ways GPS can go wrong: If you can’t figure out most important difference If you don’t have a relevant operator.

25. Lecture 13 – Problem Solving 25 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’).

26. Lecture 13 – Problem Solving 26 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).

27. Lecture 13 – Problem Solving 27 The problem, the solver, the process Finding 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.