Problem solving - summary of chapter 9 of Cognitive Psychology by Gilhooly, K & Lyddy, F, M

Cognitive Psychology
Chapter 9
Problem solving

Problem: a situation in which you have a goal but do not know how to achieve it.
Thinking: a process of mental exploration of possible actions and states of the world.

Problems and problem types

Problems can be said to arise when a person or animal has a goal but does not have an immediately available way of reaching the goal.
Problems can be classified in terms of a few broad characteristics:

• Degree of definition
• Whether an adversary is involved or not
• Whether extensive knowledge is needed or not.
• Whether the time scale of the problem is long or short.

There are a number of ways we classify problems based on these characteristics which help us to group different types of problems together for understanding and research.

• Well defined
  A problem in which starting conditions, actions available and goals are all completely specified
• Ill-defined
  A problem in which starting conditions, or actions available or goals are not completely specified.

We then determine whether specialized knowledge is required to solve a problem. Making them:

• Knowledge rich
  Problems that require extensive specialist knowledge
• Knowledge lean
  Do not require specialist knowledge

Finally, we consider whether the type of problem involves a rational opponent.
Problems can be classified as:

• Non-adversary
  Problems in which the solver is dealing with inert problem materials with no rational opponent
• Adversary problems
  Problems in which the solver has to deal with a rational opponent (as in board games)

Some problems are large scale and require months or years of effort.
Some are small scale and can be tackled within minutes.

Brief history and background

Gestalt approach

Problem solving as much like perceiving a new pattern in an ambiguous drawing.
The key process was one of changing the way the problem was seen, in other words restructuring the way the problem was perceived.
Changing how one represents a problem.

Insight: a restructuring of a problem that makes the solution obvious and understandable.

No trial and error.

Barriers to insight

Two important barriers to insight

• Set
  A tendency to persist with one approach to a problem
• Functional fixity
  A difficulty in thinking of a novel use for a familiar object

Information processing approach

inspired by the development of programmable digital computers.
Strategies

Problem space

The problem space is an abstract representation of possible states of a problem.
Representing a problem as a graph, with points representing states of the problem and with lines connecting the points representing possible actions that lead from one state of the problem to other states.

Problem spaces in two sub-types

• State action spaces
  A representation of how problems can be transformed from starting state through intermediate states of the goal.
• Goal-subgoal spaces
  A representation of how an overall problem goal can be broken down into subgoals and sub-subgoals

State-action spaces

Representations problems may be solved by searching through a series of operations which will transform the stating state into intermediate states which in turn are transformed into further intermediate states until ultimately the goal state is reached.

Analysis of possible strategies indicates three main methods by which an state-action tree can searched systematically:

• Depth first search
  Involves a light load on memory in that only one possible move at a time is considered.
  Searching a state-action space by generating one state only form each intermediate state.
• Breath first search
  Searching a state-action space by generating all possible states form each intermediate state
  Involves a very heavy working memory load.
  An algorithm, is always reaches its goal.
• Progressive deepening
  Searching a state-action space by using depth first search to a limited depth, when depth limit is reached, search back up to start and repeats, avoiding previously explored branches and so on. If a solution is not found, increase the depth limit.

The above basic search methods involve a ‘blind’ search in that they only classify states as ‘goal’ or ‘not goal’.

Hill climbing.

Heuristic
A problem solving method that often finds a low effort solution but is not guaranteed to solve.

Goal-subgoal spaces

In this representation the problem is divided into goals and subgoals and each subgoal can be tackled by splitting it into subsubgoals and so on.
Often referred to as problem reduction or mean-ends analysis.

Detour problems: are problems in which the hill climbing method does not work well, as the solver has to move away from the goal at some stage.

Insight revisited

Understanding of how we solve problems which need a change in the way they are represented (insight problems).

Comparing insight and non-insight problems

Feeling of warmth: a rating of how close the solver feels to problem solution, taken at intervals during the solving process.
Sudden restructing in insight tasks.

Neuroscience approach to insight versus non-insight tasks

fMRI showed increased activity in one particular brain area, the right anterior superior temporal gyrus, for insight solutions compared to non-insight solutions.
EEG records also show increases in activity in the same area shortly before solution.
These findings suggest differences in neural processes between insight versus non-insight solving.

Think loud effects on insight versus non-insight problems

Thinking aloud impaired insight but non non-insight tasks.

Recent theories of insight

Representational change

The main stages and processes in representational change theory:

1. Problem perception
   The person encodes the problem
2. Problem solving
   Heuristic research processes based on initial representation. These processes draw on possible actions or operators from long-term memory which change the current state of problem into new states.
3. Impasse
   The initial representation is misleading and does not permit a solution. Hence, impasses arise in which the person experiences a blank mind and can think of no more actions to try.
4. Restructuring
   Anew encoding is derived through elaboration, re-encoding or constaint relaxation. Elaboration involves adding information to the initial representation by noticing previously ignored features.
   Re-encoding involves completely changing the encoding rather than just adding new features.
   Constraint relaxation. involves loosening constraints on what is required in the goal or what actions are permitted.
5. Partial insight
   Retrieval of possible actions following restructuring breaks the impasse and lead to a sequence of steps that achieve solution.
6. Full insight
   Retrieval of possible actions following restructuring leads immediately to a solution state or to a state close enough to the solution so that the solution can be anticipated within a limited metal look-ahead.

Process monitoring

The main source of difficulty in insight tasks is the use of inappropriate heuristics.
As people search for actions that would help them to reach a solution, they monitor their progress against some criterion.
Failure to meet a progress criterion restructuring.

• Maximization heuristic: in which 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 too slow and inefficient, then criterion failure occurs. An alternative strategy may then be sought.

Insight is most likely to occur when constraint relaxation follows criterion failure.

Knowledge-rich (or expert) problem solving

Expertise: the accumulated high level knowledge that allows outstanding performance in complex problem areas.

Expertise acquisition

Acquisition of domain expertise in many areas seems to require approximately 10 years of intensive study.
Strong motivation is required to maintain study over many years.
Deliberate practice of skill components, guided by a training schedule and by coaching, is needed for the best results.

Nature of expertise

Expertise typically seems to involve extensive memory for familiar patterns which cue appropriate actions.
Experts have built up extensive long-term memory of familiar patterns which helps them encode or chunk new positions into familiar sub-patterns.

Experts represent or ‘see’ problem situations differently from novices as they draw on a more elaborate set of schemata.

Experts can carry out wider, deeper and faster searches through possible sequences of chess moves than can novices.

In the case of expert problem solving, the emphasis is mainly on recognition of familiar problem patterns and application of previously acquired solutions as against extensive searching through possible action sequences.

Creative problem solving

Creative in relation to a produced is generally defined as novel to the producer of the product and valuable in some way. Alternatively that the product is novel and meets a goal.

If a solution is new to the solver, it is creative.

Personal accounts

Wallas’s four-stage analysis

1. Preparation
   Person familiarizes themselves with the problem.
   Involves conscious work
   Rarely leads to solution
   Without initial work no further progress would come about
2. Incubation
   Problem ‘set aside’
   No conscious work
3. Illumination (or inspiration or insight)
   Doesn’t always lead to solution of problem
   Great idea might come to mind. But must be developed and verified
4. Verification
   Conscious work must be done on ideas generated through illumination
   Solutions can be tested an developed.

The four stages constantly overlap each other as we explore different problems.
Even when exploring the same problem the mind may be unconsciously incubating on one aspect of it, while it is consciously employed in preparing for or verifying another aspect.

Incubation research

How might incubation work?

Main hypotheses:

• Conscious work
  Although incubation is intended to be a period without conscious work on the target tasks participants may nevertheless carry out intermittent conscious work.
  Any conscious work during the supposed incubation period would reduce the time required when the target problem was re-addressed, but would impair performance on the interpolated task.
• Unconscious work
  Incubation effects occur through active but unconscious processing of the problem materials.
  The ‘subliminal self’ unconsciously combined and recombined ideas until an interesting relevant combination was formed whereupon the valuable idea would become conscious.
  Unconscious thought has a large capacity, proceeds relatively slowly, tends to be bottom up, is good at integrating many sources of information, is relatively poor at following rules and tends to be divergent rather tan convergent thinking.
• Fatigue dissipation
  A break is simply an opportunity to rest and return with more energy to the problem.
• Selective forgetting
  Misleading strategies, mistaken assumptions and related ‘mental sets’ weaken through forgetting and thus a fresh start or ‘set shifting’ is facilitated when the problem is resumed.

Information processing theory of creative processes

Simson model

Creative advances are rare events.
Incubation is analyses as familiarization with repeated attempts and selective forgetting between attempts, allowing fresh approaches to be taken.

Geneplore model

Geneplore is a model for creative thinking which stresses the role of a generative and exploratory phase.
Creative work involves an initial stage in which pre-invertive structures are generated and are then interpreted during an exploratory phase.

Creative synthesis task is a task in which participants have to combine presented shapes to make novel interesting combinations.

Increasing idea production

Cues for creativity

Small cues can have large unconscious effects.
Cues or primes unconventional thinking.

Brainstorming

Stimulating the production of unusual ideas, by stressing quantity as against quality and deferment of evaluation of ideas.

Two main principles:

• Deferment of judgment
• Quantity breeds quality

Four rules:

• Criticism is ruled out
• Free-wheeling is welcomed
• Quantity is wanted
• Combination and improvement sought

Evaluation of ideas was to be proposed until after a fixed period of idea production.