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Chapter 10: Thinking and Problem Solving Outline
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Central Idea: There are different kinds of thinking and problem solving.
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Preview the main points: One definition for thinking cannot be determined, thus there are
different types and distinctions of ways of evaluating thinking- focused and unfocused.
Presentation of problems can either be well- defined or ill-defined.
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Main Point:
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Classic Problems and General Methods of Solution
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There are many different types of problems and different ways of solving
those problems.
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There are domain specific problems which can only be answered with very
explicit solutions but we will discuss five categories of problem solving
techniques that will work with general types of problems.
Generate-and-Test Technique
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Generate-and-Test is a problem solving technique in which the solver comes
up with multiple possible solutions to an issue and “tests” them until one of
them works. However, generate and test doesn’t work very well if there are
too many possibilities to test.
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An example is your phone is malfunctioning so you try multiple options like
restarting it, turning off the Wifi, turning off Bluetooth, and calling AT&T
until one of those solutions provides you with an answer.
Means-Ends Analysis
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Means-Ends Analysis is a strategy used in problem solving when an
individual wants to get from their current state to a desired state in the
most effective way possible. Means-Ends sometimes needs sub-goals to
accomplish bigger objectives.
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This strategy utilizes a computer program, the General Problem solver to
measure any differences between the actual object and the desired object.
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An example is the current state of your new bookshelf from IKEA in the box
all disassembled with the instructions to the goal state of the finished
projected cattycornered in your living room. What is the most time effective
way to get this done? You choose to get it done in an hour and use the
instructions. In order to use the instructions you have to open the box. After
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opening the box, you can just pull out the instructions and assume you have
everything or you lay out the materials and categorize them based on what
the instructions say you should have. You choose the latter because you
want to make sure you have all the necessary requirements. This is a
subgoal. You also need to acquire the proper tools that the box did not
come with. You can wait until you get to step eight that requires the
screwdriver to go get it, or you can get it now. You choose to get it now
because you will be too tired later to get it later. Another subgoal. After you
have gone through all the steps and completed the bookshelf, you have
utilized your time in the most efficient way using means-ends analysis.
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Working Backward
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Working backward is a problem solving strategy in which the solver takes
the reverse steps to get a final goal. It is most effective when the path is
original. It is similar in many ways to means-ends analysis in regard to
making sub-goals, requiring a unique course, and step taking.
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An example: Jack walked from Santa Clara to Palo Alto. It took 1 hour 25
minutes to walk from Santa Clara to Los Altos. Then it took 25 minutes to
walk from Los Altos to Palo Alto. He arrived in Palo Alto at 2:45 P.M. At what
time did he leave Santa Clara?
1) UNDERSTAND: You need to find what the time was when Jack left Santa
Clara.
2) PLAN: How can you solve the problem? You can work backwards from the
time Jack reached Palo Alto. Subtract the time it took to walk from Los Altos
to Palo Alto. Then subtract the time it took to walk from Santa Clara to Los
Altos.
3) SOLVE: Start at 2:45. This is the time Jack reached Palo Alto. Subtract 25
minutes. This is the time it took to get from Los Altos to Palo Alto. Time is:
2:20 P.M. Subtract: 1 hour 25 minutes. This is the time it took to get from
Santa Clara to Los Altos. Jack left Santa Clara at 12:55 P.M.
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Backtracking
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Backtracking is another problem solving technique where possible solutions
are listed and kept track of but can be changed if proven to be incorrect.
The solver should keep a list of choices they have made in case they need to
“back up” and re assess their answer.
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Some common examples of backtracking are Sodoku and crosswords. Keep
a list of all possible numbers or words that can fit in a spot to the spot in
case the number or word you filled in is incorrect.
Reasoning by Analogy
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Reasoning by Analogy is a method of problem solving in which the solver
uses a comparison between a problem that has already been answered and
a current problem. The features of one issue must correlate with the other
issue.
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The individual must also look beyond the small details and look at the bigger
picture to understand the analogy. This is called “principle finding” by
Dunker. Multiple examples helps form abstract schemas. Participants who
were given more than one story were better at recognizing the tumor
problem.
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An example: Studies show that beyond a modest level of income and
wealth, additional money does not make us happier. Therefore by analogy,
beyond a modest level of public recognition, more fame does not make us
happier.
Blocks to Solving Problems
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Constraints on solving problems include barriers that restrain one’s ability to
think logically and rationally.
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Sometimes blocks are so strong that they interfere with one’s capacity to
reach a conclusion and actively solve tasks.
Mental Set
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Mental set is the tendency to see a problem in only one way as opposed to
seeing it from multiple standpoints. Mental set often causes people to make
certain unwarranted assumptions without being aware of making them.
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There were a few activities we did in class that served as examples for
mental sets: The first one was when we did the nine-dot problem in class
and how each of us were constrained by the boundaries and did not stray
outside the borders of the dots. Another example of a mental set was the
man at home and man in a mask example where we failed to view the
situation from multiple standpoints. The last example we did in class was
the two string problem in which the solution was to tie the screwdriver to
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one of the strings. People who failed to realize the solution were caught in a
mental set because they did not stray from the idea that the screwdriver
could serve a different function than what it was intended for. This
phenomenon is called functional fixedness. It appears to be an instance of
mental set, in that a person subject to functional fixedness has apparently
adopted a rigid mental set toward an object.
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Using Incomplete or Incorrect Representations
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A separate difficulty in solving problems has to do with the original
interpretation of the problem. The situation can result in failure if the solver
focuses on the wrong information or if the problem is misunderstood. In
class, the checkerboard problem served as an example of this. This was the
situation in which the checkerboard only had 62 squares and the problem
was to see if there is a way to arrange 31 dominoes such that every
checkerboard square is covered by a domino? The key to the solution was
to realize that what- ever the arrangement, each domino will cover exactly
one black square and one red square, given the way checkerboards are
arranged. Since the two squares that were removed were the same color
and because a domino must cover two differently colored squares, there is
no way to arrange 31 dominoes to cover the mutilated checkerboard. The
difficulty most people have with this problem is that they fail to include
these two pieces of crucial information in their initial representation of the
problem. Thus the representation is incomplete.
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Another in-class example of using incomplete or incorrect representations
was the numbers game problem. The objective of the game was for each
player is to choose three digits from a set of digits such that the digits
chosen total exactly 15. Two players are given a sheet of numbers, 1 2 3 4 5
6 7 8 9. They take turns crossing one of the digits off the list and adding it to
their own list. A way of solving the problem was to view is as a game of tictac-toe. Seen from this perspective, the game is stress-free, but without this
representation, the problem is much more difficult to solve.
Lack of Problem-Specific Knowledge or Expertise
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Expertise knowledge about tasks is an integral part of accomplishing them in
a more concise and informative manner. A study of expert and novice
studies was conducted by Groot (1965). He examined the thinking processes
of both chess masters and weaker players, finding that the master players
considered about the same number of possibilities but somehow chose the
best move more easily.
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In problem solving, experts see and represent a problem in their domain at
a deeper and more principled level than do novices, who tend to represent
information superficially. In class we talked about the differences between
experts a novices in the realm of physics. Studies have shown that when
solving complex problems, experts tend to organize the problems in terms
of physics principles, such as Newton’s first law of motion; novices instead
tend to focus on the objects mentioned in the problem, such as an inclined
plane or a frictionless surface. Experts have also been shown to spend more
time analyzing problems whereas novices look at the problem and
immediately try and solve it. The point is that in order to accurately solve a
problem, sometimes it takes more time.
The Problem Space Hypothesis
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The central idea behind the problem space hypothesis is that every possible
state of affairs within a problem corresponds to a node in a mental graph.
The entire set of nodes occupies some mental area, and this area, together
with the graph, is the problem space.
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Each circle, or node, corresponds to a certain state of affairs at some point
during the problem-solving process. If the problem is to win a chess game,
for example, each node corresponds to a possible chess- board
configuration at each point in the game. The initial state node corresponds
to the conditions at the beginning of a problem, for example, a chessboard
before the first move. The goal states correspond to conditions when the
problem is solved, for example, configurations in which a game is won.
Expert Systems
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Problem space hypothesis created expert systems, model the judgments of
human experts. An expert cannot state all of his or her knowledge. Creating
expert system is complex. Developers follow experts around; developers
elaborate on their thinking as it happens, allowing developers to formulate
rules. Expert systems created because humans are limited, not an expert for
everything, only in certain domains. Humans are biased, can be
overwhelming, preventing the finding of the best solution.
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Expert systems contain inference rules. Format includes several antecedents
or conditions. Each antecedent specifies a condition that must be met for
the rule to be activated. Rules have consequent parts, then/ because.
Finding Creative Solutions
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Insight, the frame of reference or in the way elements of the problem are
interpreted and organized, plays a role in creativity; originality that suits
some purpose. If lacking novelty, ideas are mundane. Creativity also seen as
a combination, recombination, knowledge, information, or mental
representation the owner already has, knows of, or has depictedunderlying.
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Artists or inventors share the "Eureka!" moment, the "lightbulb" goes on,
suggests their thought processes work in different ways.
Unconscious Processing and Incubation
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Unconscious processing/ incubation is the unconscious processing that
works on a specific problem without giving rise to conscious awareness.
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Testing with misleading cues- rebuses. 15 rebuses, presented with 16th,
resulting in induced fixation on an incorrect interpretation. Most studies
cannot find a positive effect of incubation, mental breaks did not show an
increased ability of problem solving, still thought about problem on break.
Difficult to test because experimenters cannot be sure that participants fully
stop thinking about the problem.
Everyday Mechanisms
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Perkins: cognitive processes leading to creativity are not extraordinary
versus special ideas such as incubation. Creativity values originality,
willingness to search harder and longer for solutions that meet multiple
constraints. Difficult to test because undecided if creativity is based on
special- purpose of regular cognitive processes.
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Relevant cognitive processes ideas, not theories: 1. Creative invention, or
direct remembering, is the ability to channel your memory in order to make
conscious some past experience or knowledge that meets various
constraints, example: remembering food/ drinking beginning with c. 2.
noticing where the problems are, the "aha!" of creators noticing a similarity
between one problem and another. 3. Contrary recognition the ability to
recognize object not for what they are but for something else, moving
beyond the bounds or reality to imagine reality in other ways- castle as
cloud. Supports creative and noncreative individuals use the same cognitive
processes "flashes of insight"
Critical Thinking
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Critical thinking: questioning "off the wall" novel ideas. Gestalt: finding the
area of a parallelogram, problem having a "rote" is if you forget the formula,
you have no other way of solving the problem. Wertheimer: identify and
understand the fundamental issues.
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Perkins tested controversial issues, measuring critical thinking by looking at
number of times a participant raised objections or challenges to his own
thinking, presenting an objection to the previous one. Good thinking
requires using knowledge efficiently, including objections, construct and
counterexamples. Overcoming the tendency to give up on an issue requires
searching harder and looking longer for other possibilities and
interpretations.
Conclusion:
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Thinking is a very general term and can be applied to many different activities.
However, it is not clear yet whether the cognitive process used for are themselves
really different in kind. Some psychologists studying problem solving have found
general, domain-independent techniques like generate and test and means-ends
analysis, that they believe people use in a many types of situations. They also have
looked at different blocks to problem solving such as mental set and incorrect or
incomplete problem representations. Some psychologists say that domain specific
problem solving strategies are important for coming to a successful solution. This
kind of problem solving relies on a person’s expertise or background knowledge.
Psychologists states that similarities among kinds of thinking can be identified and
explained by a common framework which accepts the problem space hypothesis.
Expert systems is a class of problem space hypothesis which imitate a human expert
in a certain field. There is a lot of debate on what creativity is as far as domain
specific, independent of domain, and everyday normal cognitive processes. Some
psychologists have also discussed what makes a thinker a good one including being
open-minded and thinking critically. This chapter suggests that good thinking skills
help you get the most out of knowledge that you have.