PSY 350 - Chapter 8

Two String Problem

-Maier -Two strings hang from a ceiling but are too far apart to allow a person to hold one and walk to the other. On the floor are some nails, a pair of pliers, a chair, and a few sheets of paper. How could the strings be tied together? -Fixation problem: the general function of pliers gets in the way of seeing them as a weight to use them as a pendulum. -if it was not solved after 10 minutes, the researcher "accidentally" brushed against the string, setting it into motion. -23/37 who had not yet solved the problem solved it within 60 seconds.

_______ solve problems in their field faster and with a higher success rate than beginners, because they possess more knowledge about their fields.

Experts

Disadvantage of being an Expert

Experts are less likely to be open to new ways of looking a problems. -Younger and less experienced scientists are often the ones responsible for revolutionary discoveries.

Creativity

Innovative thinking to generate novel ideas by making new connections between existing ideas.

_________ is organized so it can be accessed when needed to work on a problem.

Knowledge

_______ solve problems using their knowledge of the surface features. _______ solve problems using their knowledge of the underlying structure.

Novices, Experts -Example: when given a set of physics problems to solve: -The novice grouped problems 23 and 24 together because they both involved similar objects (inclined planes). -surface features -The expert grouped problems 21 and 24 together because they both involve similar physics principles (conservation of energy). -structural features

Analogical Transfer

Transferring experience from solving one problem to solving another problem. This includes: 1. target problem 2. source problem: the problem sharing some similarities with the target problem, illustrating the way to solve the target problem. -Example: using the russian marriage problem to solve the mutilated checkerboard problem or using the Red adair problem to solve the radiation problem

Noninsight

Trying to use math to figure something out. These problems are solved gradually.

Using Analogies to Solve a Problem

Using a solution to a similar problem guides solutions to a new problem. -Example of analogical transfer: use russian marriage problem solution (source problem) to solve the mutilated checkerboard problem (target problem).

Working Backward Heuristic

Water lilies are growing on Blue Lake. The water lilies grow rapidly, so that the amount of water surface covered by lilies doubles every 24 hours. On the first day of summer there was just one water lily. On the 90th day, the lake was entirely covered. On what day was the lake half covered? -Value doubling every day is equal to say that the value is halved each preceding day. -the lake was full on day 90 -the lake was half full on day 89

Situationally Produced Mental Set

When a situation influences a participant's approach to the problem.

Design Fixation

When you are fixated on what not to do, based on what is demonstrated by the sample. This inhibits creativity and can inhibit problem solving.

Arrangement

When you present objects and require the problem solver to arrange them to satisfy some criteria. -All of the elements are given, the task is to rearrange them. Examples: Anagrams, seating guests, two strings problem, and the candle problem -RWAET -KEROJ

Think-Aloud Protocol

When you say what you are thinking out loud. This reveals the shift in how one perceives elements of a problem.

A good __________ ________ does not always occur.

analogical transfer

Functional fixedness can make ___________ solutions difficult.

arrangement

Experts are no ______ than novices when given problems outside of their field.

better

Problems can either be solved by being represented in ________ terms (mental image, etc.) or ________ terms.

concrete, abstract

Creativity is often associated with _________ thinking.

divergent

Experts spend ____ time analyzing a problem.

more

More similar surface features between the target and source problems help with ________.

noticing

Problem-solving _________ generate a space of possible states through which the problem solver must search to find a path to the goal. This involves the use of a ______ ____.

operators, search tree

Solving a problem can be described as engaging in a ______, where the problem solver must find an appropriate path through a maze of states.

search

Making __________ features more obvious, aids in analogical problem solving.

structural

Imagery helps in solving ______ problems.

verbal

Kohler's Circle Problem

-An example of restructuring. -Problem: If the length of the circle's radius is r, what is the length of line x? -You look at a circle, where there is a small triangle is in the upper left quadrant. -In order to solve the problem you have to restructure and change the way you are looking at it, by now seeing a rectangle with x as the diagonal line through it. instead of two triangles. -Therefore r = x since the radius is just the middle point of a circle. -First you perceive the objects, then you represent them in another way to find the solution.

Means-End Analysis Example

-Based on Tower of Hanoi -after reading and encoding for the problem into working memory, the means-end analysis is when you search LTM for algorithms and heuristics and then execute the appropriate algorithms and heuristics. -The new problem state from the subgoals are compared with the goal.

Candle Problem

-Duncker -You are in a room with a corkboard on the wall. You are given some candles, matches in a match box, and some tacks. Mount a candle on the corkboard so it will burn without dripping wax on the floor. How? -Fixation problem: seeing boxes as containers inhibited the possibility of using them as supports.

Water Jug Problem

-Each problem specifies the capacities of jugs A, B, and C and a final desired quantity. The task is to figure out how to use the jugs with these capacities to measure out the desired quantity. (b) The first step in solving Problem 1; (c) the second step; (d) the third step. All of the other problems can be solved using the same pattern of pourings, indicated by the equation Desired quantity = B - A - 2 C, but there are more efficient ways to solve Problems 7 and 8. -Mental set problem: a person's given mental set from the situation inhibited participants from using a simpler solution.

Three Steps to Analogical Problem Solving

-Gick and Holyoak 1. noticing the relationship 2. mapping correspondence between the source and target 3. applying the mapping

Tower of Hanoi

-Information processing approach example -The object of the game is to move all the disks over to Tower 3 from Tower 1, but you cannot place a larger disk onto a smaller disk. -Operators: rules that specify which moves are allowed and which are not.

Problem

An obstacle between a present state and a goal, where how to get around the obstacle is not immediately obvious.

Functional Fixedness

An obstacle to problem solving where you restrict the use of an object to its familiar functions.

Problem-Space Theory

Approaching problem solving as a search process through a problem space using means-end analysis. -algorithms vs. heuristics

Intermediate States

All the steps and situations on the way to the goal state.

Gestalt Approach

An approach of problem solving by representing a problem in the mind. -Success is influenced by how well a problem is represented in the mind. -Restructuring Example: crossword puzzles

Insight Example

-Metcalfe and Wiefe -measuring insight with a triangle problem and a chain problem -Triangle problem: Move only three of the dots to make the triangle point downward. Solved by moving the top dot to the bottom and the two side bottom dots to the top. -Chain. Form a closed loop, every time you up a link its two cents, every time you close a link it's three cents. You only have 15 cents. -Noninsight: algebra problems -Warmth judgments every 15 seconds of how hot or cold they were to the solution. -Insight problems were solved suddenly -Noninsight problems were solved gradually.

Importance of how a problem is stated

-Mutilated checkerboard problem: conditions differed in how much information was provided about the squares. -Problem was easier to solve when information was provided that pointed towards the correct representation of the problem.

Information Processing Approach to Problem Solving

-Newell and Simon -The approach that you must search a problem space to find a solution. -Problem space: A representation of the problem, often in the form of a tree diagram, with possible states and associated operations. -Initial state -Intermediate state(s) -Goal state

Representation Example

1. Picture a large sheet of paper. 2. In your imagination fold it once. (now 2 layers) 3. Fold it again (4 layers), and keep folding it a total of 50 times. 4. How thick is this now 50 times folded sheet of paper? -Solved with an algorithm, to be 71 million miles thick.

Two Factors Influencing Noticing and Mapping

1. Surface features 2. Structural features

Mutilated Checker Board Problem

64 squares on a checker board. You can completely cover the board with 32 dominos. If you take off two squares from opposite sites of the checker board, you now have 62 squares. Can you now cover the checker board with 31 dominos? The answer is no because cutting the corners made it impossible to line up all 31 dominos.

Hill-Climbing Strategy

A heuristic where for any particular state, you carry out the operation that moves you closest to the final goal state. -This is often not a good strategy Example: dog is on one side of the fence, and his food bowl is on the other. He takes the step to get closest to the bowl by just moving forward until he is barred by the fence, instead of going around and through the opening of the fence, to then be able to reach the food bowl.

Generate and Test

A heuristic where the problem solver generates a list of alternative ways of action, not necessarily in a systematic way, and then notices in turn whether each course of action will work.

Restructuring

A method of the Gestalt approach that changes the problem's representation in the mind. Example: Kohler's circle problem

Inducing Structure

A problem where the relationship between objects is fixed, and the problem is to discover the relationship. -Example: analogy -Merchant: sell :: customer: _____ -Lawyer: client :: doctor: _______ -Example: series completion: -12834656__(4) from looking at the line ABMCDME -the relationship is the numerical order of each letter

State

A representation of the problem in some degree of solution. It is either in the start state, intermediate states, or goal state.

Search Trees

A representation of the set of states that can be reached by applying an operator to a start state.

Problem Space

A representation of the various sequences of problem solving operators that lead among various states of the problem.

Algorithms

A set of rules that will solve a problem if correctly followed. -Example: directions to put a desk together.

Heuristics

A strategy that is often, but not always helpful in solving problems. Includes: 1. Means-end analysis/difference reduction: forming subgoals 2. Working forward: difference reduction -start at the beginning and try to solve the problem from start to finish 3. Working backward: Start at the end and work backwards

Insight

A sudden realization of a problem's solution.

Well-Defined Problems

A type of problem that contains a correct answer, with certain procedures that lead to the solution. Examples: 392 - 45 or driving to the airport with good directions.

Transformation

A type of problem where the initial state, goal state, and a sequence of operations for changing the initial state into the goal state are presented. -These problems primarily require skills in planning, using the means-end analysis. -Examples: Tower of Hanoi, water jug problem, missionaries and cannibals

Ill-Defined Problems

A type of problem where the path to the solution is unclear, with no one correct answer. Examples: solve world hunger or how to have an interesting career

Restructuring And Insight

Restructuring is the sudden discovery (moment of insight) of a crucial element that changes the path, leading to the solution. -This is an "Aha!" moment.

Operators

Rules that govern the actions of a situation, taking the problem from one state to another.

Surface Features

Specific elements making up the problem. Example: rays and tumor in the radiation problem

________ create intermediate states closer to the goal state.

Subgoals

Analogical Paradox

The contradicting phenomena that participants in experiments tend to focus on surface features for problem solving, where people in the real world focus on structural features.

Means-End Analysis

The goal in the information processing approach to reduce the difference between the initial and the goal state, using subgoals.

Start State

The initial conditions of the problem.

Mental Set

The set of preconceptions about the uses of objects.

Goal State

The solution to the problem.

Structural Features

The underlying principle that governs the solution. Example: -target: light bulb problem -source: radiation problem -fragile-glass condition (similar structural features to source): 69% mapped and solved the problem -insufficient-intensity condition (different structural features from the source): only 33% mapped and solved the problem

Divergent Thinking

Thinking that is open-ended, with a large number of potential solutions that does not have a "correct" answer.

Convergent Thinking

Thinking that works toward a solution to a specific problem with one correct answer.