PROBLEM SOLVINGCOGNITIVE 2012

Lecture overview Types of problems

Theories Gestalt Representational Change Theory Progress Monitoring Theory

Transfer of Training

Factors to be considered It is the evening before an exam, the text book you

need is unavailable in the library.There is not one obvious solution

You have upgraded your computer from Windows 2000 to Windows Vista and want to perform certain operations as beforeLearning (helpful and harmful)

You wish to avoid stale-mate in chessExpertise

You wish to become a better footballerIs it clear when the objective has been achieved

Problem SolvingDefining problem-solving activity:

1) It is purposeful, goal directed action2) It does not involve automatic processes,

but relies on cognitive processes3) It is only a ‘problem’ if the solution is not

available immediately.

‘h i j k l m n o’

Problem SolvingWell defined problem: All aspects of the

problem are clearly laid out. We know the initial state, the rules, and the goal state.e.g. a maze

ILL defined problem: None of these things are as clear. “It is the evening before an exam, the text book you need is unavailable in the library and the bookshop is closed”Starting point? Potential solutions? End point?

Problem SolvingGestalt Psychology: A theory of mind that

emerged from Germany in the early 20th century

Concerned with entities/experience as a whole rather than consisting of parts

Problem Solving (Gestalt approach)

They drew a distinction between reproductive thinking, involving re-use of previous experience, and productive thinking involving a novel restructuring of the problem

Problem Solving (Gestalt approach)

Insight occurs during productive thinking when the problem is suddenly restructured and the solution becomes clear.

Kohler (1925) observed insight with apes

Problem Solving (Gestalt approach)

Novick & Sherman (2003) highlighted the difference between subjective experience and the underlying process

In a series of experiments, expert and non-expert anagram solvers were presented with a series of anagrams.

Problem Solving (Gestalt approach)

Evidence that insight is unique: Novick & Sherman found that when rating the experience of solving anagrams both groups often reported ‘pop out’ solutions. ‘The solution came suddenly, seemingly out of nowhere’

Evidence that insight does not work like this: In a different experiment participants had to indicate after brief exposure (469ms) if the word was an anagram or not. Both groups performed better than chance

Problem Solving (Gestalt approach)

Problem Solving (Gestalt approach)

Representational ChangeRepresentational change theory is an attempt to

incorporate some Gestalt ideas into a working theory (Ohlsson, 1992)

It is based on the following assumptions:

A problem is represented in a certain way in the person’s mind and this serves as a probe for information from long-term memory

The retrieval process spreads activation over ‘relevant’ long term memory items

Representational ChangeRepresentational change theory is an attempt to

incorporate some Gestalt ideas into a working theory (Ohlsson, 1992).

It is based on the following assumptions:

A block occurs if the way a problem is represented does not lead to a helpful memory search

The way the problem is represented changes and the memory search is extended, making new information available

Representational ChangeRepresentational change theory is an attempt to

incorporate some Gestalt ideas into a working theory (Ohlsson, 1992).

It is based on the following assumptions:

Representational change can occur due to ‘elaboration’ (addition of new information) ‘constraint relaxation’ (rules are reinterpreted) or ‘re-encoding’ (functional fixedness is removed)

Insight occurs when a block is broken and retrieved knowledge results in solution

Representational ChangeExample: Can the 62 squares on this mutilated

draught-board be covered with 31 dominoes

Representational ChangeMutilated draught-board:Kaplan & Simon (1990) had participants think aloud

as they tried to solve this problem

All started by mentally covering the squares with dominoes (758,148 possibilities!)

Those who solved the problem reported a ‘representational change’ such as this…

Representational ChangeMutilated draught-board:If each domino is represented as an object covering

one black and one red square (re-encoding)

And represent the draught-board as having lost 2 black squares (elaboration)

It becomes clear that no arrangement will allow 31 dominoes to cover the 62 spaces

Representational ChangeDraw four straight lines to join all the dots without

taking the pen off the page

Representational ChangeThis problem was given to employees at Disney as is

reportedly the origin of the expression ‘thinking outside the box’

Representational ChangeParticipants who did not solve the 9 dot problem

usually failed to consider extending the lines beyond the grid

Constraint relaxation mentioned earlier allows someone to consider the correct solution

Representational ChangeKnoblich et al. (1999) showed the importance of

constraints in reducing the likelihood of insight

Problem: Reposition one match to make this equation correct

Representational ChangeKnoblich et al. (1999) showed the importance of

constraints in reducing the likelihood of insight

Problem: Reposition one match to make this equation correct

Representational ChangeOur experience of equations often involves changing

numerical values as in

But not changing operators (+, -, =)

Representational ChangeInsight is more difficult in the second example

because re-encoding operators is more advanced than re-encoding numerical values.

Knoblich et al also included eyetracking data which showed a great deal of attention was paid to the numerical symbols but not the operators.

‘Thinking outside the box’ allows us to see the operators as changeable also

Progress Monitoring TheoryMacGregor et al (2001) have put forward this theory.

There are two main features

Maximisation heuristic: Each move or decision is an attempt to make as much headway as possible towards the goal

Progress monitoring: The rate of progress is assessed constantly, and if it is deemed to be slow and inefficient criterion failure occurs. An alternative strategy is then sought.

Progress Monitoring TheoryMacGregor et al (2001) have put forward this theory.

There are two main features

Maximisation heuristic: Each move or decision is an attempt to make as much headway as possible towards the goal

Progress monitoring: The rate of progress is assessed constantly, and if it is deemed to be slow and inefficient criterion failure occurs. An alternative strategy is then sought.

Progress Monitoring TheoryMacGregor et al. version of nine dot problem

A

Progress Monitoring TheoryMacGregor et al. version of nine dot problem

B

Progress Monitoring TheoryIf ‘constraint relaxation’ is all that is required to think

outside the box, then participants should do better on A than B

If criterion failure is necessary then participants will do better on B, because they can cover fewer dots in the next two moves, and so will realise they are on the wrong path sooner.

MacGregor et al. found that only 31% of those given A were successful. Compared to 53% of those given B.

Progress Monitoring TheoryIf ‘constraint relaxation’ is all that is required to think

outside the box, then participants should do better on A than B

If criterion failure is necessary then participants will do better on B, because they can cover fewer dots in the next two moves, and so will realise they are on the wrong path sooner.

MacGregor et al. found that only 31% of those given A were successful. Compared to 53% of those given B.

Progress Monitoring TheoryOrmerod et al. (2002) 8 coin problem.

Moving only 2 coins, leave each coin touching 3 others

Progress Monitoring TheoryOrmerod et al. (2002) 8 coin problem.

Moving only 2 coins, leave each coin touching 3 others

Progress Monitoring TheoryOrmerod et al. (2002) 8 coin problem.

Moving only 2 coins, leave each coin touching 3 others

Progress Monitoring TheoryOrmerod et al. (2002) 8 coin problem.

If the strategy employed simply seeks to achieve a short term goal of bringing one particular coin to rest in contact with 3 others, then there is ‘no move available’ in the first condition, but 20 moves available in the second

92% solved the problem in the first condition, 67% in the second

Again, strong evidence for the importance of ‘criterion failure’

Progress Monitoring TheoryEvaluation:

The central claim being that insight is most likely to occur when constraint relaxation is combined with criterion failure. There is good evidence for this

Deals well with the motivation for changing strategy

Transfer of TrainingRefers to how our experience of past problems

influences our ability to solve new ones.

Not surprisingly there can be positive and negative transfer

Transfer of TrainingE.g of negative transfer: Luchins (1942) water jar

problems

Jars: 28L 76L 3LAim: 25L

Participants who had trained on a number of difficult 3 jar solutions requiring the same complicated process failed to see the simplicity of the solution here

Transfer of TrainingOther factors to be considered

Far transfer: Refers to transfer to a dissimilar context

E.g. Learning about experimental method in science class (control groups, confounding variables etc.) and using the same principles in real world settings (deciding how to make the nicest biscuits)

Near transfer: Transfer to a similar contextE.g. Learning Luchins’ water jar solutionsLab studies often limited to near transfer

ReadingEysenck & Keane, Chapter 13

Sternberg, Chapter 11

Article: Ormerod, T. MacGregor, J. Chronicle, E. (2002) Dynamics and Constraints in Insight Problem Solving. Journal of Experimental Psychology: Learning, Memory, and Cognition vol. 28 (4) pp 791-799