Exam 3, Lecture 4 - Problem Solving and Creativity

Problem

When there is an obstacle between a present state and a goal

• need to be identified before they can be solved

• Need to be difficult to solve, can’t be immediately obvious how to get around obstacle

Well-defined problems

Easy to identify and solve

• clear when solution has been reached

• Ex. A crossword puzzle, a maze, etc.

Ill-defined problems

Hard to identify and solve

• ex. Picking a career, addressing homelessness, solving for world peace

• Hard to know when a solution has been reached

Problem representation

The way a problem is translated (or represented) in our mind

• a problem may be presented to us in the same way, but we may represent it differently, resulting in different approaches to solve the problem

  • Ex. Two people solve a crossword puzzle in different ways

Problem restructuring

The process of changing a problems’ representation

• Solving a problem involves first seeing the object, then restructuring/seeing it in a different way

Problem solving: if the length of a circles’ radius is r, what is the length of x?

1. Perceive: x is unknown

2. Represent: same as the image (spatial)

3. Restructure: the triangle is part of a rectangle whose diagonal equal x, which is also r

Insight

Sudden realization of a solution to a problem

• ex. Move 3 dots so the triangle is facing down

• non insight problem: solve for x —> (1/5)x+10=25

• People felt they were closer to the solution for non-insight problems as time continued

Functional fixedness

Tendency to focus on similar functions or uses of objects

Candle problem

Mount the candle to the wall so it will burn without dripping wax on the floor using a matchbox, candle, and tacks

• Example of functional fixedness

• Solution is to think of the matchbox as a container, tack matchbox to wall and put candle on top

• Easier to overcome functional fixedness when the matches are presented outside the box

Two string problem

Tie together the two strings hanging from the ceiling

• participants when told to swing their arms or see the researcher brush the string were able to solve the problem as compared to those without a cue

• Breaks them out of functional fixedness and allows them to think about their tools

Mental set

Preconceived notion about how to approach a problem

• contributes to functional fixedness, based on previous experience with a set of objects

• Prior examples can establish a mental set that inhibits participants from using simpler solution later on

  • Far more likely for participants to use a simpler solution when they didn’t have a mental set

Water jug problem

Measure a specific quantity of water from 3 empty jugs of varying capacities

• can you measure 5 quarts of water given a 18 quart jug (A), 42 quart (B), and 10 quart (C)

  • Fill B, pour into A once, pour into C twice

• Measure 20 quarts given 23 (A), 49 (B), or 3 (C)

  • Fill B, pour into A once, pour into C twice

  • Fill A, pour into C once

  • If you solved the problem by starting with B, the first water jug problem established a mental set

Insight is the process of changing the way a problem is represented in your mind. T or F?

False

Information Processing approach

Problem solving is a search between the posing of a problem and its solution

• initial state

• Goal state

• Intermediate states

• Problem space

• Operators

Initial state

Conditions at the beginning of a problem

Goal state

Solution to the problem

Intermediate states

Conditions after each step is made toward solving a problem

Problem space

All possible states that can occur when solving a problem

Operators

Actions that take the problem from one state to another

• governed by rules

Means-end analysis

There are many ways to get from the initial state to the goal state

• reduce the differences between the initial and goal states by creating sub goals

Means end analysis ex. Traveling

• initial state —> Riverside

• Goal state —> Germany

• Operators → shortest travel time, cost within budget

Problems with information processing

• mutilated checkerboard problem

• Russian marriage problem

• can’t explain how two problems with the same problem space (same initial, intermediate, and goal states) can vary in difficulty

Mutilated checkerboard problem

If we eliminate two corners of a checkerboard, can we cover the remaining squares with dominos

• no!

• However, if given a blank checkerboard (without red and black squares), becomes significantly harder to solve

  • Problem space is the same

Russian marriage problem

Can the matchmaker come up with 31 heterosexual marriages among 62 survivors

• In a small Russian village, 32 bachelors and 32 unmarried women. Two bachelors killed each other. Can the matchmaker comes up with 31 heterosexual marriages among the 62 survivors

• Same problem space as mutilated checkerboard but not same difficulty

  • if information processing approach was correct, there should be no difference in ease of solving Russian marriage problem/blank checkerboard/mutilated checkerboard. Since there are differences in difficulty, it means that

Analogical problem solving

Attempting to solve a problem using the solution to a similar problem

• the Russian marriage solution can be used to solve the mutilated checkerboard problem

Analogical transfer

Experience solving one problem is transferred to another problem

• target problem

• Source problem

Requires that you notice, map, and apply the analogy

Target problem

The problem you are trying to solve

Source problem

Another problem that is similar to and may illustrate a way to solve the target problem

Analogical transfer radiation problem + fortress story

Radiation problem —> 10% solved

Radiation problem —> listen to fortress story —> radiation problem → 30%

Radiation problem —> apply the fortress story —> radiation problem

Analogical paradox

It can be difficult to apply analogies in the laboratory, but we routinely use analogies in real world settings

In the example discussed here, the source problem is ______

• difficult to transfer

• The radiation problem

• What needs to be restructured

• The fortress story

The fortress story

Expert

Someone knowledgeable or skilled in a particular domain

• experts solve problems in their field more quickly and more often than beginners

• Experts possess more knowledge about their field

  • Ex. Chess board with actual game position, masters were more accurate in placing the pieces in the right positions/accurately according to display

  • Ex. Chess board with random placement, grand masters were just as bad at accuracy with non grand masters

• Organize their knowledge differently than novices

  • Experts gave more specific than basic names, non-experts more likely to generate basic bird names

Creativity

The use of imagination or original ideas

• creative problem solving is a process

• To increase creativity: daydreaming, solitude, mindfulness

Divergent thinking

Thinking that is open-ended and involves a larger number of potential solutions

Creative cognition

Technique to train people to think creatively

• ex. Given a task where you’re given three objects and told to make a new object

Daydreaming

Purposeful mind wandering

solitude

avoiding distractions; giving the mind space and time to make new connections and find meaning

mindfulness

pay attention to what is happening in our mind and in the environment