Honors Seminar
Critical Thinking
Modified: 2018-11-14 (8:24 am CST)
In this section, we will examine some of the processes involved in critical thinking. One aspect of critical thinking is writing. When you write you force yourself to think critically. Another is problem solving. Solving abstract problems is more difficult than solving concrete ones. Decision making is another important aspect of critical thinking. Much of decision making first involves the gathering of relevant information. Creativity is yet another example of critical thinking, one that is quite different from the others. The section concludes with some additional, classic problems.
Writing
- Prewriting
- Getting ready to write
- know your audience
- break writing into smaller pieces
- Drafting (or Composing)
- Actually writing thoughts down
- pencil and paper
- pen and paper
- typewriter
- word processor
- Revising (or Editing)
- Self editing
- meaning
- style
- grammar
- spelling
- Editing by others
- social aspect of writing
- give-and-take
- "I apologize for the long letter...(see http://www.classy.dk/log/archive/001074.html)
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Problem Solving
Play MasterMind in class as example of abstract problem solving
MasterMind Game
- Wason Selection Problem: Read the problems below. Then decide which minimum number of cards you must turn over and why?
- Wason Selection Problem (Abstract)
- The secretary you replaced may have mistakenly misfiled some documents. The rule was: if a card has a D on one side, it should have a 3 on the other.
- Wason Selection Problem (Concrete)
- You are the new bouncer at a bar. Your job is to be sure the following rule is not violated: If someone is drinking beer, they must be 21 or over. The cards represent drinkers. On one side of the card it says their age and on the other what they are drinking.
- Scientists and Wason Selection task:
- Physicists (21-25% correct), Biologists (8-13% correct),
Psychologists (13-17% correct)
- Problem Solving Definition
- "gap that separates the present state and the goal state"
(Hayes, 1978)
- I need to get to Little Rock.
- I'm in Magnolia = present state
- I need to be in Little Rock = goal state
- Understanding the Problem
- Understanding the problem
- Context
- Why the need to go to Little Rock?
- Emergency?
- Routine?
- Entertainment
- Shopping
- Operators (rules, moves, legality, reality)
- Well defined vs. Fuzzy
- Chess and other games
- Real world rules
- Walking?
- Driving
- Flying?
- Teleporting?
- Goal State
- Games
- Part of game
- Chess = capturing King
- Football = scoring most points
- Golf = taking least strokes
- Real world
- Location in Little Rock
- School
- Work
- Life
- Solving the problem
- Problem Space
- Path from initial state to goal state
- Number of paths
- Types of Solutions
- Algorithms
- Guarantee a solution
- How many desks in Peace Hall?
- How many desks at SAU?
- How many desks in Arkansas?
- How many desks in the World?
- All of the above problems solved by same
algorithm: count them
- Some algorithms do not work in real time
- Heuristics
- Do not guarantee a solution (hunches, guesses, or
experential attempts)
- Traveling Salesman Problem
- Subgoaling
- Divide problem into smaller parts
- get vehicle
- fill with fuel
- establish route
- drive to Prescott
- drive to second Rest Stop
- drive to Little Rock
- Means-Ends Analysis
- Reduce the distance between initial and goal
states
- Working Backwards
- Start at goal and work back to initial state
- Need to be in Little Rock by 5:00
p.m.
- It takes 2.5 hours to drive
- I need to get gas first (add 30
minutes)
- I need to take kids to school (add 30
minutes)
- Leave by 1:30 p.m.
- Analogies
- Similar problems may help solve current
problem
- I have never driven to Little Rock, but I
have driven to Dallas. Much will be the same,
but some things (direction, roads) will be
different.
- Restructuring
- Gestalt idea
- Mental Set
- How are these numbers arranged?
- 8, 5, 4, 9, 1, 7, 6, 3, 2, 0
- Solve the following problem:
- Solution?
- Functional Fixedness
- Scheerer (1963) conducted an experiment where
he manipulated the salience of a piece of string.
The more salient it was, the more likely students
were to solve the problem.
- Nearly all students knew they needed string
to solve the problem. The solution was to tie
the two sticks together to make them effectively
longer. Picture
- Insight
- Learning characterized by sudden realization
about solution
- Incubation
- Delaying the problem solving process
- Works by:
- loss of detail and subsequent focusing on
important details
- better integration of recent and
pre-existing memories
- weakening of mental sets
- relaxation
- take a day to plan trip to Little
Rock
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Decision Making
- Finding Relevant Information
- Library Skills
- Online Skills
- Real Time and Decision Making
- Many factors contribute:
- Specific Experience
- Noisy toilet was bothering my wife. I could not fix it.
- Experience with plumbing helps
- My student Diane instantly solved the problem
- Turn down the water pressure
- Logic
- Economic solutions
- Lowest bidder
- Lowest price
- Satisficing (Herbert Simon)
- Restricting choices to those easily available
- Find your soulmate nearby, don't search the whole world
- Realize there may be a better soulmate out there, but it's not worth the search
- Emotion
- Advertising uses emotion successfully
- Buy a particular car and people will like you more
- Drink an expensive whiskey and others will think you sophisticated
- Heuristics (Kahneman & Tversky)
- Availability
- basing judgment of the frequency of events on the
ease by which then can be brought to mind. For example:
doctors and nurses, police officers, shark attacks
- Illusory correlation: people overestimate the
likelihood of simultaneous events
- Representativeness
- basing judgment of likelihood on the degree to which
the particular instance resembles a general class. For
example: librarian, college professor, painter,
minister
- Anchoring-Adjustment
- The "anchor" is like a first impression. Later, the
anchor is adjusted up or down as necessary. However,
anchor often exerts undue influence
- Hindsight
- After the fact, people overestimate the
predictability of an event. For example: the 9/11
attacks
- Critiques
- Heuristics are descriptive and atheoretical
approach
- Heuristics tend to be task specific
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Creativity
- Divergent Thinking
- Finding many uses for object
- low frequency answers judged as
creative
- Convergent Thinking
- Linking several weakly associated elements into
one correct concept (similar to crossword puzzle
thinking)
- Ellis Paul Torrance (Wikipedia)
- Artistic and Scientific
- Christidou, Dimopoulos, and Kouladis (2004)
reported that science was reported as a construct
that "...involves inspiration, originality,
imagination and creativity, as well as, skillful or
even artistic handlings;" (p. 352)
- Artistic creativity is difficult to study
- Investment Theory (Sternberg and Lubart)
- Buy low, sell high approach to ideas
- creativity is taking undervalued idea and
promoting it, then "selling" it to a
now-understanding world
- think of Xerox, first invented in 1938
and not made into a commercial product until
1959
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More Problems
- Cheap necklace problem:
- Meier's two string problem: How can you tie two strings together if you cannot reach both at the same time. You also have: a chair, a pliers, some copier paper, and a jar of tacks.
- Missionaries and cannibals problem:
- Three missionaries and three cannibals all wish to cross a river. But there are some constraints. Their boat can only hold two people at a time. If ever the cannibals outnumber the missionaries then the missionary will end up as lunch. Get everyone across the river without anyone being eaten.
- Mutilated chessboard:
- Can the chessboard shown be covered by 32 dominoes? Why or why not?
- King and his daughter:
- Once upon a time there was a beautiful princess named Anna. Anna's father, the King, wanted to be sure his daughter married an intelligent man. To test his daughter's suitors the King hid Anna's picture in one of three boxes. The suitor had to be able to select the box with Anna's picture on one try and within twenty seconds. On the gold box was the message "Anna's picture is in this box". The silver box had the message "Anna's picture is not in this box." "Anna's picture is not in the gold box" was written on the bronze box. The King would tell each suitor "Only one of the three messages is correct." Which box contained Anna's picture?
- Anagrams (easy):
- kmli
- graus
- teews
- recma
- foefce
- ikrdn
- Why did they get easier?
- Anagrams (hard):
- Find an anagram for: DRY OXTAIL IN REAR
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