LESSON 11: Problem Solving and Creativity

Problem-solving

effort to overcome obstacles obstructing the path to a solution

String problem

Imagine standing in the middle of this room where two strings are hanging down from the ceiling. Your goal is to tie together the two strings, but neither string is long enough to reach out and grab the other string while holding either of the two strings. You have a few clean paintbrushes, a can of paint, and a heavy canvas tarpaulin. How will you tie together the two strings?

Initial state

the situation at the outset in which the problem is not yet solved

Goal state

condition under which the problem has been solved

Obstacle

one or many factors that prevent us from solving our problem

1. Problem identification

2. Problem definition and representation

3. Strategy formulation

4. Organization of information

5. Resource allocation

6. Monitoring

7. Evaluation

Problem-solving cycle

Problem identification

Do we actually have a problem?

Problem definition and representation

What exactly is our problem?

Strategy formulation

How can we solve the problem

Analysis

The strategy may involve - which is the breaking down of the whole complex problem into manageable elements

Synthesis

Instead, or in addition, to/of analysis, strategy may also involve -, which is the putting together of various elements to arrange them into something useful

Divergent thinking

you try to generate a diverse assortment of possible alternative solutions to a problem

Convergent thinking

to narrow down the multiple possibilities to converge on a single best answer.

Organization of information

How do the various pieces of information in the problem fit together?

Resource allocation

How much time, effort, and money should I put into this problem?

Global

Studies show that expert problem solvers (and better students) tend to devote more of their mental resources to (global or local?) planning than do novice problem solvers.

Local

Novices (and poorer students) tend to allocate more time to (global or local?) planning than do experts

Monitoring

Am I on track as I proceed to solve the problem?

Evaluation

Did I solve the problem correctly?

Emotional intelligence

the ability to identify emotions in others and regulate emotions in oneself

Well-structured problems

have clear paths to solutions

Ill-structured problems

lack clear paths to solutions

1. Inadvertently moving backward

2. Making illegal moves

3. Not realizing the nature of the next legal move

three main kinds of errors when trying to solve well-structured problems

Inadvertently moving backward

They revert to a state that is further from the end goal,

Making illegal moves

a move that is not permitted according to the terms of the problem

Not realizing the nature of the next legal move

They become “stuck”—they do not know what to do next, given the current stage of the problem

Computer stimulations

One method researchers use to study how to solve well-defined problems is to develop

Problem space

is the universe of all possible actions that can be applied to solving a problem, given any constraints that apply to the solution of the problem

Algorithms

are sets of procedures (in a problem space) that may be repeated over and over again and that, in theory, guarantee the solution to a problem

Heuristics

informal, intuitive, speculative strategies that sometimes lead to an effective solution and sometimes do not

Availability heuristic

information more readily available

Means-end analysis

In this strategy, the problem solver continually compares the current state and the goal state and takes steps to minimize the differences between the two states.

Working forward

Start at the beginning and attempt to solve the problem from the start to the finish

Working backward

Start at the end and attempt to work backward from there

Generate and test

Generate alternative courses of action, not necessarily in a systematic way, and note whether each course of action will work

Isomorphic problems

two problems’ formal structure is the same, and only their content differs

Tower of Hanoi

In this problem, the problem solver must use a series of moves to transfer a set of rings (usually three) from the first of three pegs to the third of the three pegs, using as few moves as possible

Intermediate states

If you have tried to solve the problem yourself, you will have noticed that there was not just one step from the initial state to the goal state—you had to go through a number of steps, each of which represented an -

Insight problems

ill-structured problems wherein you need to see the problem in a novel way

Insight

distinctive and sometimes seemingly sudden understanding of a problem or of a strategy that aids in solving the problem

Gestalt psychologists

emphasized the importance of the whole as more than a collection of parts

Productive thinking

involves insights that go beyond the bounds of existing association

Reproductive thinking

which is based on existing associations involving what is already known.

Max Wertheimer

Gestalt psychologist that distinguished productive thinking from reproductive thinking

Wolfgang Köhler

studied insight in nonhuman primates, particularly a caged chimpanzee named Sultan

Insight

need not be sudden “a-ha” experiences, they may and often do occur gradually and incrementally over time

Sleep

When an insightful solution is needed but not forthcoming, - may help produce a solution

right anterior superior-temporal gyrus

fMRI studies show that activity in the - increases when a person experiences an insight

Right hemisphere

before insights even become conscious, activity in the - can be observed

Right hippocampus

critical in the formation of an insightful solutions

Right anterior temporal area

Another study demonstrated a spike of activity in the - immediately before an insight is formed.

Mental set

One factor that can hinder problem solving is —, a frame of mind involving an existing model for representing a problem, a problem context, or a procedure for problem solving

Entrenchment

Mental set is also known as

Mental set

When problem solvers have a -, they fixate on a strategy that normally works well in solving many problems but that does not work well in solving this particular problem

Functional fixedness

the inability to realize that something known to have a particular use also may be used to perform other functions

Stereotypes

are beliefs that members of a social group tend more or less uniformly to have particular types of characteristics.

Stereotype threat

Being aware of stereotypes about their group also can limit people’s performance when they expect to be evaluated

Transfer

any carryover of knowledge or skills from one problem situation to another

Negative transfer

occurs when solving an earlier problem makes it harder to solve a later one

Positive transfer

occurs when the solution of an earlier problem makes it easier to solve a new problem.

Analogical problem solving

When people think back to other problems they have encountered and solved, they may ask themselves whether the new problem is somehow similar to other ones they previously solved. If they find a relationship, they may have a starting point to solve the new problem

Transparency

people see analogies where they do not exist because of similarity of content.

Incubation

putting the problem aside for a while without consciously thinking about it—offers one way in which to minimize negative transfer.

Embodied cognition

is the theory that the mind influences the body and the body influences the mind.

Frontal lobes and prefrontal cortex

brain regions essential for planning for complex problem-solving tasks

Expertise

superior skills or achievement reflecting a well-developed and well-organized knowledge base.

Verbal protocols

Statements made by problem solvers are called

Schematization

involves developing rich, highly organized scehmas

Automatization

involves consolidating sequences of steps into unified routines that require little or no conscious control

Creativity

broadly defined as the process of producing something that is both original and worthwhile

Divergent production

Some psychologists measure creativity through -

Divergent production

the generation of a diverse assortment of appropriate responses

Torrance Tests of Creative Thinking

assessment of creativity wherein they measure the diversity, quantity, and appropriateness of responses to open-ended question

Investment theory of creativity

The theme unifying these various factors is that the creative individual takes a buy-low, sell-high approach to idea

Prefrontal regions

especially active during the creative process