Psych 207 - Chapter 10 (Thinking and Problem Solving)

What is thinking?

- Going beyond the information given (Bruner)

- High-level skill that fills gaps in evidence (Bartlett)

- Process of searching through a problem space

Focused thinking

- Goal-directed flow of ideas focussed on arriving at a conclusion

- Clear starting point with a specific end goal

- Solving problems

Unfocused thinking

- Unintentionally calling to mind a number of different loosely related ideas

- Daydreaming, mind-wandering

Problem-solving

- Begins with deciding on a goal and seeking steps that will lead to that goal

Well-defined problem

- Have a clear goal

- Know immediately if we've reached a solution

- Small set of information to start from

- Often rules/guidelines to follow when looking for a solution

Ill-defined problem

- No clear goals

- No guidelines

- No starting info

Problem space

- Set of all states that can be reached in solving a problem

Generate and Test

- Generate and test a number of solutions

- Good if number of things to test is limited

- Problematic if we can't keep track of what has been tested, or if there are an indefinite number of things to test

Means-End Analysis

- Compares goal to the starting point (like a search in a maze)

- Initial state

- Goal state

- Intermediate states: various conditions that exist along pathways between initial and goal state

- Operators: available tools or actions

- Path constraints: limits that rule out some operations

- By reducing the difference between the initial state and goal state, we end up creating subgoals

- May be multiple solution paths

- Tower of Hanoi

Working backwards

- Involves creating subgoals and working from the goal state

- Tower of Hanoi (textbook)

- Most effective when the backwards path is unique

Backtracking

- Remember working assumptions

- Assess which assumptions failed

- Correct assumptions and try again

Reasoning By Analogy

- Using knowledge from one relatively well-known domain and applying it to another domain

- The tumor problem (Gick and Holyoak)

- People had to have the analogy pointed out to them to be able to solve the tumor problem, unless they were given two similar stories and told to compare them. This forces subjects to create a convergence schema

Scientists used 3 to 15 analogies in a single one-hour lab meeting.

Similarly, lots of political articles use analogies that aren't specific to the political domain

Functional fixedness

- A tendency to be rigid in thinking about an object's function

- Inhibits engagement of abstract or critical thinking when solving problems

- An instance of mental set

Chase and Simon

- Master chess players are able to extract more information from a board after brief exposure

- Can also recall more items

- This only happens when the board looks like it represents a real game (ie. has some sort of tactical structure)

Insight

- Change frame of reference when approaching problems

- Manipulate the way the elements of the problem are understood

- Plays role in creativity

Incubation (subconscious processing)

- Setting the problem aside can lead to novel solutions later

- A part of our brain may still be working on the problem

- Leads to eureka moments

- Hard to study empirically

Directed remembering

- Ability to channel memory to bring about relevant past experiences to solve similar problems

Noticing

- Realizing where problems are (eg. revising drafts)

Contrary Recognition

- Recognize objects beyond what they are

Problem solving and creativity

Shared characteristics:

- Prolonged mental search for novel possibilities

- Solutions based on prior knowledge/skills

- Willingness to search harder/longer for multiple solutions

- One's willingness to think hard analytically about the problem predicts success in a creative thinking task (Bar,, Pennycook, et. al) which challenges the notion that creativity is from an unconscious process

Reasoning

- Focused thinking that may have one or more specific goals

- Involves inferences or conclusions drawn from other information

- Involves making syllogisms (arguments) that involve premises (assumptions) which lead to conclusions

Deductive reasoning

- Top-down logic

- Taking a general fact and applying it to a specific case

- No new information is added

Problems:

- Rely on the general premise being true (deductive validity)

Inductive Reasoning

- Bottom-up logic

- Goes from specific case to general

- Hypothesis testing

Problems:

- Inductive strength - improbable for premises to be true and conclusion false

- Difficult to make broad claims based on limited information

Abductive reasoning

- Find simplest and most likely observation for results

- Sherlock Holmes

Problems:

- limited by number of observations possible

- Contain uncertainty/doubt

Dual Process modelling of reasoning

Type 1: Going with your gut

- autonomous, no working memory required

- source of reasoning biases

Type 2: Using your head

- slow, deliberative, analytical

- requires working memory

- metacognitive processes (like confidence) are required

Schraw, Dunkle and Bendixen

Demonstrated that performance on well-defined problems is not correlated with performance on ill-defined problems.

Crypt arithmetic problems

Problems where letters stand for digits

Newell and Simon used these to study means-end analysis problem solving.

General Problem Solver

Computer program that solves crypt arithmetic problems using means-end analysis

Mental set

Tendency to adopt a certain framework. Analogous to perceptual set

Kasparov

Did just as well with a time constraint: indicates that he was not thinking ahead but rather had an increased ability to recognize patterns

Glaser and Chi

Experts:

- excel in their own domains

- perceive larger meaningful patterns in their own domains

- more likely to check for errors in their thinking

- spend more time analyzing a problem before trying to think of a solution

Patient P.F.

- Experienced architect with lesion to prefrontal cortex

- Could structure a problem, but could not solve it (create a design)

- Conclusion: preliminary designs represent ill-structured problem solving

Smith and Blakenship

- Used rebuses (picture-word puzzles) to test incubation

- They report more success on identifying the rebus when given a break from the problem

Most studies don't support incubation: people who take breaks don't have higher chance of success than people who work steadily at the problem.

Perkins

- Creativity uses the same cognitive processes as everyday problem solving

Everyday cognitive processes

- Directed remembering

- Noticing

- Contrary recognition

Flashes of insight occur in a step-by-step fashion

Kinds of deductive reasoning

- Propositional reasoning

- Syllogistic reasoning

Propositional reasoning

Drawing conclusions from premises in the form of propositions (assertions that are either true or false)

- Card/rule problem

Syllogistic reasoning

Presents two or more premises and asks reasoner to draw a conclusion to see if the conclusion is true when the premises are true

Categorical syllogisms

- Present premises that deal with classes of entities

- Premises have quantifiers (all, some, none...)

Content effect

Two people reasoning with the same kind of premises will perform differently depending on what the premises are "about"

Griggs and Coz - drinking card vs letter card rule problem

Explanation: memory cueing - contents of the problem recall personal experiences relevant to the rule

Believability effects

People are likely to judge as valid any conclusion that reinforces their initial assumptions, regardless of whether the conclusion follows from the premises.

Disconfirmation hypothesis

People are more critical of conclusions they do not believe.

Reasoners took longer to justify believable conclusions.