#### Chapter 11

problem-solving

what you do when you want to reach a specified goal, but the solution is not obvious because you are missing important info/ it is not clear how to reach the goal

1) the initial state
2) the goal state
3) the obstacles

what are the three components of problems?

initial state

-component of a problem
-describes the situation at the beginning of the problem
-"I need to reach my prof before the exam

goal state

-component of a problem
-when you have solved the problem

obstacles

-component of a problem
-the restrictions that make it difficult to proceed from the initial to the goal state

thinking

task that requires you to go beyond the info you were given so you can reach a goal

understanding

when you have constructed a well-organized mental representation of the problem, based on info provided in the problem and previous experience

because competing thoughts can produce divided attention

Why is attention important in problem-solving?

effective problem solvers read the description of the problem very carefully, they pay a lot of attention to inconsistencies, and they are best at deciding what is most important

How do effective problems solvers use attention differently than ineffective problem solvers?

problem representation

the way you translate elements of the problem into a different format
-choosing an appropriate one will make you more likely to reach an effective solution to a problem

they emphasize finding a good method of problem solving

What is the gestalt perspective of problem solving?

working memory capacity

What is correlated with one's ability to solve an algebra problem, and to categorize geometric patterns?

-symbols
-matrices
-diagrams
-visual images

What are some ways of representing a problem?

-people often make mistakes when translating words into symbols, like reversing roles of two different variables
-they also tend to oversimplify the problem during translation, misrepresenting the info

what are problems associated with using symbols to solve problems?

if the problem is complex and if the relevant info is categorical

When are matrices most ideal?

they let you represent abstract info in a concrete fashion,, and discard unnecessary details, so you have more mental space in working memory
-also when there is a lot of info

Why are diagrams helpful with representing problems?

the person's eye movements are drawn to the most relevant parts of the diagram that accompanied verbal instruction

Why are diagrams successful at helping people solve problems?

they allow us to escape from the boundaries of traditional, concrete representations

How are visual images helpful with solving problems?

situated cognition approach

-problem solving approach that says we often use helpful info in our immediate environment to create spatial representations
-argues that our ability to solve a problem is tied into the specific physical and social context in which we learned to solve the

up-down dimension

according to the situated cognition approach, do we make decisions about the up-down dimension or the left-right dimension faster?

embodied cognition approach

-problem solving approach that says we often use our own body and our own motor actions in order to express our abstract thoughts and knowledge
-emphasizes the benefit of using hand gestures

-situated cognition emphasizes the external situation
-embodied cognition emphasizes your own body

How do situated and embodied cognition differ?

-kids should study complex and authentic math problems that they will encounter in real life
-college kids should learn from internships

What educational implications come from the situated cognition approach?

algorithm

problem-solving technique that will always produce a solution, but can sometimes be inefficient and unsophisticated

exhaustive search

an algorithm where you try out all possible answers using a specified system

heuristic

a general rule that is usually correct

analogy approach

a problem solving technique where you employ a solution that you used with a similar problem you have had before to a new problem

determining the real problem underneath all of the details

What is the main challenge for people using the analogy approach?

problem isomorphs

a set of problems that have the same underlying structures and solutions, but different
-people tend to focus more on the superficial content of the problem than on its abstract, underlying meaning

1) divide the problem into subproblems
2) reduce the difference between the initial state and the goal state for each of the subproblems

The 2 components of the means-end heuristic

means-ends heuristic

heuristic that requires you to identify the final result that you want and then figure out the methods to get you there

working memory

what cognitive ability is especially active when tackling subproblems?

computer simulation

a computer program that will perform a task in the same way a human would

General Problem solver (GPS)

-a computer simulation that mimics the processes that normal humans use when tackling problems

means-ends analysis

What problem solving technique does the GPS use?

hill-climbing heursitic

the heuristic that says you are most likely to choose a path that seems to lead directly to your goal
-emphasizes short term goals, not long term

when you do not have enough info on your alternatives

when is the hill-climbing heuristic most useful?

expertise

demonstrated by consistent exceptional skill and performance on representative tasks for a particular area

number of years of expertise is not strongly correlated with excellent performance in a variety of fields

Why does expertise no longer require at least 10 years of experience?

-superior long term memory of their discipline as well as detailed structure of topics
-they have better schemas for topics
-better memory of their knowledge, when it fits into a schema
-use means-ends heuristic effectively to solve problems more
-more li

How are experts better than novices?

because they divide their problems into subproblems, and solve them in a specific order

How come experts use the means-ends heuristic more effectively?

parallel processing

processing that handles 2 or more ideas at a time

mental set

this is shown when you keep trying the same solution you used in previous problems, even though there is a much more effective and easier method

you close your mind prematurely, and you stop thinking about how to solve a problem effectively

What are you doing when you have mental set?

they have greater change in ERP with mental set

How is ERP affected in people who have mental set?

overactive top-down processing (too strongly guided by previous experience)

What do both mental set and functional fixedness represent?

fixed mindset

occurs when you believe that you possess a certain amount of intelligence and other skills, and no effort can make you any better

growth mindset

occurs when you believe that you can cultivate your intelligence and other skills

-mental set refers to our problem solving strategies
-functional fixedness refers to the way we think about physical objects

what is the difference between mental set and functional fixedness?

functional fixedness

when we tend to assign stable functions to an object

stereotype threat

when a person performs worse because of expectations from stereotypes

-reminded of ethnicity: best
-control: middle
-reminded of gender: worst

How were Asian American females' performance on math tests affected by certain stereotypes?

-those who were told there was a gender difference did worse

How were White females affected by gender stereotypes in math testing?

-it can produce high arousal, which interferes with working memory
-women have to work hard during the test to suppress pressure from stereotypes

Why does the stereotype threat affect women in math?

insight problem

when a problem initially seems impossible, but an alternative approach suddenly comes to you

noninsight problem

when you solve a problem gradually by using memory, reasoning skills, and a routine set of strategies

insight

what concept is very important to gestalt psychologists?

they believe those solving an insight problem, at first, hold incorrect assumptions