Chapter 11 Problem Solving & Creativity Flashcards
Components of a problem
Initial state
Goal state
Obstacles
Problem solving is used
When you want to reach a certain goal, but the solution is not immediately obvious
Missing information or obstacles block the path
Understanding the problem
Construct a well-organized mental representation of the problem based on the information provided in the problem and previous experience
Paying attention to important information
Identify and attend to the most relevant information
Bransford and Stein 1984
Algebra story problems
Distracting negative thoughts
Effective problem solvers read the description of a problem very carefully, paying particular attention
to inconsistencies
Symbols
Algebra
Translating words into symbols can cause issues
-oversimplification and misremembering the problem
Matrix
A grid showing all possible combination of items
Matrices
Matrix
Most useful for complex, stable, categorical information
Problem representation
The way you translate the elements of the problem into a different format
Visual images
Escape boundaries of traditional concrete representations
Good visual-imagery skills provide advantage
Diagrams
Instructions for assembling objects
Represent abstract information in a concrete fashion
Reduce large about of complicated information into a concrete form
Hierarchical tree diagram
Graphs
Novick and Morse 2000
Origami
Participants were more accurate with both a verbal description and a step-by-step diagram rather than only a verbal description
Hierarchical Tree Diagram
A figure that uses a tree like structure to show various possible options in a problem. This kind of diagram is especially helpful in showing the relationship between categorized items
Situated-cognition approach
We use helpful information in our immediate environment to create spatial representations; importance of external situation/context
Embodied cognition approach
We often use our own body and our own motor actions, in order to express our abstract thoughts and knowledge; importance of own body as context
Situated Cognition
Problem solving does not only take place inside a persons head
Real life provides information needed to solve complicated problems
Other people provide information
Embodied Cognition
People solve certain kinds of problems more quickly or more accurately if allowed to move parts of their bodies
Mental rotation tasks
Swinging rope problem
Movement of gears problem
Exhaustive search
Try all possible answers
Heuristic
General rule/strategy in in which you ignore some alternatives and explore only those alternatives that seem especially likely to produce a solution
Analogy approach
Using a salutation to a similar, earlier problem to help in solving a new problem
Algorithm
A well-defined procedure or set of rules that is used to solve a problem or accomplish a task or they is used for conducting a series of computations
Always produces a solution; sometimes inefficient
The structure of the analogy approach
Determining the real problem
Problem isomorphs
Surface features
Structural features
Factors that encourage appropriate use of analogies
overcoming the influence of context
trying several structurally similar problems before the target problem
training to sort problems into categories based on structural similarities
Problem isomorphs
A set of problems that have the same underlying structures and solutions, but different specific details
Surface features
Such as specific objects and terms used in the questions
Structural features
The underlying core that they must understand in order to solve the problem correctly
The means-ends heuristic important components
Divide the problem into sub problems
Try to reduce the difference between the initial state and the goal state for each of the sub problems
The means ends heuristic
identify the “ends” you want and then figure out the “means” to reach them
one of the most effective and flexible problem- solving strategies
Elves and Goblins (Greeno, 1974)
People pause at points in the problem when they begin to tackle a subproblem and need to organize a sequence of moves.
Working memory is active during planning.
Sometimes the correct solution requires moving backward, temporarily increasing the distance to the goal.
People are reluctant to move away from goal state.
The Means–Ends Heuristic
Computer Simulation
involves a computer program that will perform a task the same way that a human would
includes false starts
should be no better (or worse) at solving the problem than a human would be
test by comparing program with the steps humans would take in solving the problem
generality not as great as researchers had wished
real-life problems not so clear cut
Computer Simulation
Newell and Simon’s General Problem Solver (GPS)
had participants talk out loud while working on a relevant problem
narrative then used to create computer simulations
uses means–ends analysis strategy; difference reduction strategy
Computer Simulation
Newell and Simon’s General Problem Solver (GPS)
had participants talk out loud while working on a relevant problem
narrative then used to create computer simulations
uses means–ends analysis strategy; difference reduction strategy
Anderson’s ACT-R theory
computer simulations for problem solving (like Elves and Goblins), algebra, geometry, computer science
developed to learn more about how people acquire skills in problem solving
developed “cognitive tutors” for use in mathematics classes
The Hill-Climbing Heuristic
When you reach a choice point, choose the alternative that seems to lead most directly toward your goal
Expertise
consistent exceptional skill and performance on representative tasks for a particular area
Expertise
Problem-Solving Strategies
are more likely to use the means–ends heuristic effectively on a novel problem
approach problems systematically
are more likely to emphasize structural features when using the analogy approach
Expertise
Speed and Accuracy
problem-solving operations become more automatic
parallel processing serial processing
Expertise
Knowledge Base
knowledge
schemas
training in variety of relevant settings training with immediate feedback
Expertise
Memory
Memory skills of experts tend to be very specific.
Chess experts’ memory is better only if the information fits a particular schema.
Experts are only slightly better than novices at remembering random arrangements of chess pieces.
Expertise
Metacognitive Skills
Experts are better than novices at monitoring their own problem solving.
Experts are also better at judging the difficulty of the problem, allocating time, monitoring the usefulness of ideas, recovering from errors.
Experts underestimate the amount of time novices will require to solve a problem in the experts’ area of specialization.
Mental Set
using the same solution from previous problems, even though the problem could be solved by a different, easier method
close mind prematurely; stop thinking
breaking mental set associated with greater change in event-related brain potentials (ERPs)
overactive top-down processing
Fixed mindset
You believe that you possess a certain amount of intelligence and other skills, and that no amount of effort can help you perform better
Growth mindset
You believe that you can cultivate your intelligence and other skills
Functional fixedness
We assign stable/fixed uses to an object results in a failure to think about the features of the object that might be useful in helping solve a problem
Gender stereotypes and math problems
generally not supported by research when it comes to problem solving skills
consistent gender similarities on standardized math tests for students of all ages
Stereotype threat
If you belong to a group that is hampered by a negative stereotype, and you think about your membership in that group, then your performance may suffer
Insight problem
A problem that seams impossible untill sudden solution appears light bulb aha
Non-insight problem
A problem that you solve gradually
The nature of insight
gestalt psychologists vs. behaviorists
begin with inappropriate assumptions that need to be discarded
inappropriate use of top-down processing
Advice About Problem Solving
If a problem seems to be an insight problem:
try to represent the problem in a different way
think about a different meaning for an ambiguous word
draw sketches, work with physical objects, use gestures
be willing to think “outside the box”
Creativity
finding solutions that are novel and
useful
Psychologists disagree as to whether creativity involves ordinary thinking or exceptional people
Divergent production
A measure of creativity in terms of the number of different responses made to a test items
Divergent production tests
Moderate correlations between divergent production test scores and other judgments of creativity
Number of salutations doesn’t indicate novelty and/or usefulness
The nature of creativity
Creativity includes convergent thinking as well as divergent thinking. (In contrast, convergent production asks test-takers to supply a single, best response.)
Creativity is associated with many regions within the left hemisphere as well as many regions within the right brain.
Creativity can occur when we use focused attention (conscious attention) as well as defocused attention (altered states of consciousness).
Extrinsic motivation
Desire to work on a task to earn a promised reward
People often produce less creative projects if they are working on these projects for external reasons.
Creativity can actually be enhanced if the extrinsic factors provide useful feedback
Intrinsic motivation
Motivation to work on a task for its own sake, because you find it interesting, exciting or personally challenging
People are more likely to to be creative when they are working on a task that they truly enjoy
Intrinsic Motivation and Creativity
Ruscio and colleagues (1998)
students rate level of interest in writing, art, and problem solving
later perform tasks in the three areas
had judges rate projects
high intrinsic motivation was related to higher judged creativity of projects
Intrinsic Motivation and Creativity
Prabhu, Sutton, and Sauser (2008)
Slides 811-815
