Chapter 12 - Problem Solving

Problem

Occurs when there is an obstacle and there is not an immediate way of resolving it

Gestalt Approach

How we solve problems is based on how we represent them in our minds

-Restructuring - Process of changing a problem’s representation, key mechanism of problem solving

-Insight - Sudden comprehension, realization, or problem solution that makes the reorganization of a person’s mental representation to yield an interpretation

Experimental Prediction - Insight is surprising (you don’t see it coming); it’s unpredictable

Weibe and Metcalfe

Created insight and non-insight problems (analytical problems)

-Asked participants to make ‘warm judgements’, ratings on how close they are to the solution, every 15 seconds as they were working on problems

-Insight problems resulted in a much more sudden jump in warmth ratings, indicating that the solutions occur suddenly

Functional Fixedness

An effect that occurs when the ideas a person has about an object’s function inhibits the person’s abiility to use the object for a different functions, serving as a barrier to problem solving

-Demonstrated in the Candle and Two-String problems

Candle Problem

Person is given a number of objects (candles, nails, match box), has to mount a candle onto a wall so it can burn without dripping wax on the floor

-Solution is to use the matchbox as support

-The group that was presented with the match box as containers found the problem more difficult than the group presented with empty boxes 

Two-String Problem

Problem is given the task of attaching two-strings together that are too far apart to be reached at the same time

-Solution is to tie the pliers to one of the strings to create a pendulum which could thenb e swung to within the person’s reach

-People thinking of the plier as a tool, not as a weight, thus 37/60 participants didn’t solve the problem

Mental Set

A preconceived notion about how to approach a problem based on a person’s experience, demonstrated in the Water-Jug problem

Water-Jug Problem

Shows how a mental set can rise out of the situation created as a person solves a problem

-Participants told that their task was to figure out (on paper) how to obtain a required volume of water given 3 empty jars as measures

-Demonstration of Problem 1 was provided

-All problems can be solved using the procedure shown in the demonstration, but problem 7 and 8 have a simpler solution

Mental Set Group - Given the demonstration, they solved problems 2-8 using the exact procedure

No-Mental Set Group - DId not receive the demonstration, solved problem 7 and 8 using a simpler mechanism 

-Only 23% of participants in the mental-set group used the simpler solution

Information Processing Approach

Newell and Simon saw problem solving as a search that occurs between the posing of the problem and it’s solution

-Demonstrated in the Tower of Hanor Problem - problem involving moving discs from one set of pegs to another 

Newell and Simon’s Approach

Saw problems in terms of a various states

Initial State - In problem solving, the condiitions at the beginning of a problem

Goal State - Actions that are undertaken to work towards a problem’s solution

Intermediate States - Various conditions that exist along the pathways between the initial and goal states

Problem Space - Initial state, goal state, and all the possible intermediate states for a particular problem

Means-End Analysis

Strategy to reduce the difference between initial and goal states using subgoals (intermediate states that are closer to the goal)

-Tower of Hanoi context; subogal 1 - free up large disc, subgoal 2 - free up third peg, subgoal 3 - move target disc onto third peg

-Real Life Subgoal - flying from home to copenhagen; edmonton → toronto → paris → copenhagen

-Multiple subgoals, each reducing difference between initial and goal states

How a problem is Stated Affects its Difficulty

Demonstrated in the mutilated chessboard problem

Using Analogies to Solve Problems

Analogical Problem Solving - Use of analogies as an aid to solving problems

Analogical Transfer - Transferring experience in solving one problem to the solution of another, similar problem

Target Problem - Problem to be solved, made easier when the problem-solver is exposed to an analogous source problem/story

Source Problem — A problem or ostory that is analogous to the target problem and provides information that can lead to a solution to the target problem

Radiation Problem

Problem that involves finding a way to destroy a tumor by radiation without damaging other organs in the body, used to study the role of analogy in problem solving

-After participants read the fortress problem, 30% could now do the radiation problem (as opposed to 10%). It jumps to 75% if you are reminded about the story

Steps to Analogical Transfer

1. Noticing the rlationship between the target and source problem

2. Mapping the correspondence between the source problem and the target problem

3. Applying the mapping to generate a parallel solution to the target problem

Noticing/Mapping are the most difficult steps in the analogical problem solving, one way to help people notice similarities is through a training procedure called ‘analogical encoding’

Analogical Encoding

Technique in which people compare two problems that illustrate a principle

-Designed to help people discover similar structure features of cases or problems

Trade-Off and Contingency Strategies

Trade-Off Strategy - A negotiating strategy in which one person says to another, “ill give you A if you’ll give me B”

Contingency Strategy - A negotiating strategy in which a person gets what he or she wants if something else happens

-Participants are familiarized with both strategies, then given some sample cases of a single type. Whichever strategy you practiced is the one you are more likely to use later on 

Analogical Paradox

People tend to rely on analogy in real life, but routinely use them in the real-world settings

-In-Vivo problem solving - observing people to determine how they solve problems in real world situations

Role of Expertise in Problem Solving

Experts possess more knowledge; had expert/nonexpert players reproduce arrangement of pieces of chess

-When the pieces were arranged in real game positions, experts did better, but when it was random experts and non-experts performed around the same 

Experts organize knowledge differently than novices

-Had physics professors and novicies organize physics problems into groups based on their similarity

-Professors organized the problems based on principles of physics, novices sorted the problems based on characteristics

Experts spend more time analyzing problems

-Spend more time analyzing since they are attempting to understand the problem, rather than immediately finding the solution

-Experts may be less flexible than nonexperts 

Creativity in Problem Solving

Involves divergent thinking - thinking that is open ended and involves a large number of potential solutions

-Can be based on observation

-Can be based on analogical thinking

-Is a process; problem generation → problem formulation → problem solving → solution implementation