Ch. 8 Problem Solving

difference reduction is also called...

"hill climbing": if we imagine the goal at the highest point of land, one approach to reaching it is always to take steps that go up.

Problems solving in other species (Kohler)

- Chimpanzees able to use tools to solve problems - Skinner showed similar behaviour in pigeons

Qualitative differences between experts and novices

- Expert's knowledge is domain specific, - Experts see and represent a problem in their domain at a deeper and more principled level than novices who represent knowledge superficially, - Experts are more likely to check for errors in their own thinking.

What is thinking?

- Focused thinking (goal-based problem solving) or unfocused thinking (daydreaming/creative thinking) - Process of searching through a problem state

Raven's Progressive matrices test

- measure of intelligence for analogical reasoning.

problems with generate & test approach

- not useful if there are too many possibilities - no guidance over generation - hard to keep track of all the possibilities we have tested thus far

Insight problem

One that people are not aware that they are close to a solution. Multistep problems, like the Tower of Hanoi, are not insight problems. The mutilated checkboard problem is.

Comparative problem solving

PFC has a high contribution.

local maxima

Point that is very similar to goal state but not the goal state. May have to go back and rearrange to achieve goal state

Hobbits and Orcs problem

Problem: 3 orcs and 3 hobbits on 1 side of the river.Have to get them from one side to the other, but orcs can never outnumber hobbits on one side, they must be equivalent. Implications: people get stuck at local maxima, problem requires working backward momentarily when close to goal, and then goal can be achieved.

Problem solving by analogy

Process by which a problem solver maps the solution for one problem onto a solution for another problem.

Search trees

Representation of the set of states that can be reached by applying operator to a start state. Any path through such tree represents a possible sequence of moves that a problem solver can make (you can also find the shortest way by doing this).

Difference reduction

Tend to select the non-repeating operator that most reduces the difference between the current state and the goal. - seek similarity to the goal

Backup avoidance

Tendency to avoid going back to a state already visited. - biases the problem solver against any operator that undoes the effect of the previous operators - people take great reluctance to take back steps even if it helps solve the problem.

Search

Finding some sequence of operators in the problem space that lead from start to goal state.

What is GPS?

General Problem Solving: a problem-solving simulation created that models human problem solving.

Generate & Test approach

Generate a number of solutions then test them. Only useful when there is a limited number of possibilities.

PFC plays a critical role in maintaining...

Goal structure. - Damage shows difficulty when problems solving involves going backwards, and difficulty inhibiting a predominant response.

blocks in problem solving

Mental set is the tendency to adopt a certain framework, strategy, or generally, see things in a certain way. - can occur from just a little amount of practice - causes people to make unwarranted assumptions without being aware of making them - we have the tendency to try solving problems without going outside the box

The essential feature of means-ends analysis is that it focuses on ...

enabling blocked operators. Temporarily becomes the end.

THe difference-reduction technique relies on...

evaluation of the similarity between the current state and the goal state, it works more often than not

When people spontaneously use past examples to solve problems, they are often guided by ...

superficial similarities

Analogical problem solving is ....

the hallmark of human cognition. Capability is uniquely human (evidence from chimpanzees) - right anterior PFC - children cannot do this from lack of PFC development

The problem with difference reduction

It is myopic in that it considers only whether the next step is an improvement and not whether the larger plan will work.

how is means-end analysis similar to difference reduction?

Means-ends will also identify the biggest difference first and try to eliminate it.

Einstellung Effect

Mechanism of thought - refers to the set effect in which people repeat a solution that has worked for previous problems even when a simpler solution is possible (operators get reinforced) - set effects result when the knowledgeable relevant to a particular type of problem solution is strengthened

What are 3 ways problem-solving operators can be acquired?

1. Discovery: Eg. Thorndike's puzzle box 2. Being told/instruction (only in humans) 3. Example

Problem Solving Techniques (2)

1. Generate & test (Brute force) 2. Operator Selection: backup avoidance, difference reduction, means-ends analysis.

3 features of problem solving

1. Goal-directed, 2. Subgoal decomposition, 3. Operator application (transform one problem state into another)

Analogy involves (2 things)

1. Noticing that a past problem is relevant 2. Mapping the elements from that solution to produce an operator for the current problem.

insight in the brain

A comparison of brain activity for successful and unsuccessful attempts to solve a remote association problem. The activity plotted is from a prefrontal region that is sensitive to retrieval (Mednick, 1962).

Incubation effects

After trying to solve a problem and getting nowhere, the problem is put aside and then upon returning to it see the solution quickly. During initial attempts to solve a problem, people set themselves to think about the problem in certain ways. If this is not the appropriate approach, they will be stuck so going away will deactivate the innapropriate procedures.

operator discovery neural basis

Basal ganglia: associations are gradually reinforced PFC: mental models are built of how these operators work.

Difference between novel and expert chess players

Both considered the same number of moves, but masters chose the best move more easily. Experts are able to extract more info from brief exposure, whereas novel players have many more routes/moves to consider.

Problem space

Consists of various states of the problem

Tower of Hanoi

Initial problem solving period during which participants adopted difference reduction then switched to means-ends strategy( breaking into subgoals) where the solution was quickly realized.

Problem-solving operators generate...

a space of possible state through which the problem solver must search to find a path to the goal.

T or F: to be successful, participants had to be explicitly told to use the general dictator analogy for solving the tumor problem.

True.

Well defined vs. ill-defined problems

Well defined: having a start and a goal state (many different ways of achieving the goal). Consists of rules and guidelines. Ill-defined: We don't know about them. More difficult to solve these.

functional fixedness

When people are fixed on representing an object according to its conventional function and fail to represent it as having a novel function. Eg. Two strings experiment

set effect

When people's experiences can bias them to prefer certain operators when solving a problem. - results when the knowledge relevant to a particular type of problem solution is strengthened. - can be reversed - occur when some knowledge structures become more available than others. Eg. Water Jug experiment

problem state, what are the 3 states>

a representation of the problem in some degree of solution, 1. Start state 2. Intermediate state 3. Goal state

Means-ends analysis

creation of a new goal/end to enable an operator/means. - more resourceful approach - more sophisticated than difference reduction - use subgoals to eliminate differences

Instruction for pyramid problems

given directed specifications or example. Learning by example can fail, even though most people will choose to learn by example, this method does not help in every case.

A major prerequisite to developping complex goal structures is the ability to...

maintain these goals in working memory.

We can think of problem space as a ____ and of the operators as ____.

maze of states, paths for moving among them.

What type of analysis is the basis for GPS tracking systems?

means-ends analysis.

Analogy invloves noticing that _____ and then ___ to produce an operator for the current problem.

noticing that a past problem solution is relevant, mapping the elements from that solution.

the term _____ is used to refer to a subgoal whose purpose is to eliminate a difference that is blocking application of an operator.

operator sub-goal.

Participants have a strong tendency to move to states that were _____ to the goal state.

similar.