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?
-component of a problem
-describes the situation at the beginning of the problem
-"I need to reach my prof before the exam
-component of a problem
-when you have solved the problem
-component of a problem
-the restrictions that make it difficult to proceed from the initial to the goal state
task that requires you to go beyond the info you were given so you can reach a goal
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?
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?
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
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?
problem-solving technique that will always produce a solution, but can sometimes be inefficient and unsophisticated
an algorithm where you try out all possible answers using a specified system
a general rule that is usually correct
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?
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
heuristic that requires you to identify the final result that you want and then figure out the methods to get you there
what cognitive ability is especially active when tackling subproblems?
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
What problem solving technique does the GPS use?
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?
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
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?
processing that handles 2 or more ideas at a time
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?
occurs when you believe that you possess a certain amount of intelligence and other skills, and no effort can make you any better
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?
when we tend to assign stable functions to an object
when a person performs worse because of expectations from stereotypes
-reminded of ethnicity: best
-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?
when a problem initially seems impossible, but an alternative approach suddenly comes to you
when you solve a problem gradually by using memory, reasoning skills, and a routine set of strategies
what concept is very important to gestalt psychologists?
they believe those solving an insight problem, at first, hold incorrect assumptions
What do those who follow gestalt psychology believe about insight problems?
-people's confidence for noninsight problems builds gradually
-people's confidence for insight problems leaps suddenly
How does one's confidence vary in insight vs noninsight problems?