Week 8 - Problem solving

Behaviourist approach

Trial and error - reproduction of previously learned experiences

Thorndicke 1911 - observation of cats in cages, over trials learned to produce an initially accidental response faster until eventually knock pole over immediately upon being put in the cage

Gestalt approach

Mental representation of problem as a whole

Two types of process

– Reproductive processes involving previously learnt responses. Often impede solution (e.g. Einstellung or mental
set and functional fixedness)
– Productive processes in which the problem as a whole is successively restructured (alternative ways of representing
the problem are tried out)
▪ Insight often occurs suddenly rather than gradually developing via trial and error
– Kohler (1927) - problem solving apes
– Maier (1931) - pendulum problem
– Luchins (1942) - water jugs problem
– Scheerer (1963) - nine dot problem
Mostly demonstrating barriers to solution from reproductive processes.

Newell and Simon 1956 general problem solver

▪ Gap between an initial state and a goal state.
▪ Problem solving: Applying mental operators (“if-then” rules) to move from current state towards the goal
state.
▪ The total number of possible paths between the initial and goal state constitutes the problem space.
▪ Problem-solving consists of a search for a path between initial and goal state.
▪ Search is guided by heuristic strategies designed to reduce the length of search.
▪ Takes place within a limited capacity cognitive system.

Means-end heuristic

Identify differences between goal state and initial state, set these as goals, select most important difference and search for operator to satisfy the goal, if the operator wont apply identify difference between condition for it to apply and the sub-goal and try eliminate it

Expertise - the return of reproductive processes

Newell and Simon's work concentrated on well- defined, toy problems ('knowledge poor') and on general strategies like means-end analysis ('weak procedures').
▪ In real life, problems are ill-defined and depend on a vast network of prior knowledge.
▪ Current work employs their basic concepts to study expertise at solving 'knowledge rich' problems.

Chess expertise

Two conflicting theories - experts have better strategies for searching a problem space, practice enables experts to build up a rich knowledge base enabling rapid pattern recognition

Template vs search theories

Template theory (Gobet & Simon, 1996) claims that expertise should be associated
with differences in memory and pattern recognition, but not in depth of search.
▪ Search theories (Holding, 1982) claims that it is associated with deeper search of the problem space (i.e. looking ahead

Pattern recognition in chess

de Groot (1965)
– (i) Compared expert and novice chess players.
• Experts looked no deeper than novices, but their moves were rated better.
• Difference lay in their stored knowledge of different board positions.
– (ii) Experts and novices 5 secs to look at board.
Knocked over and asked to reconstruct it
• Masters 90% correct
• Novices 40% correct
• When pieces were randomly arranged both equally bad.
▪ Chase & Simon (1973)
• experts can store bigger 'chunks‘, faster
• experts divide board into better chunks

Speed and cognitive load - Gobet and simon 1996

Eye movement studies show that experts identify the best moves extremely rapidly. Experts performance is not affected by playing simultaneous matches (does not depend on WM capacity)

Objections

▪ Lassiter (2000)
– Experts’ performance, though still better, is reduced when playing simultaneous
matches
– Computers, which do rely on search, do better at speed chess
▪ Campitelli & Gobet (2004)
– Used wider range of more complex positions
– Experts search much deeper than novices

Anderson’s ACT-R model (Adaptive control of thought - rational)

Declarative memory (knowing that)
– Semantic network of interconnected concepts
– Consciously accessible, widely applicable
▪ Procedural memory (knowing how)
– Production system consisting of “if-then” rules
– Automatically cued, context specific
▪ Working memory
– Workspace in which information is manipulated

Skill acquisition in ACT-R

Knowledge compilation
– Declarative knowledge becomes proceduralised and is applied automatically
– Proceduralisation builds specific rules from examples so that extensive search of LTM is no longer necessary
– Composition reduces strings of actions to simpler sequences

Long-term working memory and deliberate practice - Ericsson & Kintsch 1995

▪ Apparent working memory capacity can be increased enormously by developing the structure of info in LTM
▪ Deliberate practice involves building patterns relating to LTM
▪ Ericsson claims this is all that is involved in expertise

Expert performance and deliberate practice

▪ Increasing digit span from 7 to 80 digits
(Ericsson & Chase, 1982)
▪ Chess expertise correlates with deliberate practice rather than amount of playing
(Charness et al,1996)
▪ More expert violinists did 7500 hrs of deliberate practice compared to 5300 hrs for less expert
(Ericsson et al, 1993)