Problem Solving and Creativity

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Problem Solving and Creativity
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Problem solving - definition

• Directed thinking towards a goal solution the
  task is to choose the best process that will lead
  to a goal
• 1st psychological studies by Wolfgang Kohler
  (insightful learning)

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Four Characteristics

• 1. problem solving is goal directed
• 2. it involves a series of operations
• 3. it involves cognitive processes
• 4. it involves sub-goal decomposition - reaching
  overall goal requires reaching sub-goals

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3 Steps in Problem Solving

• Representing or defining exactly what the problem
  is to solve
• Generating possible ways of solving the problem
  and choosing the best solution
• Evaluating the solution is it the best solution?

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Representing the Problem

• This is not referring to the surface problem, but
  the actual problem that has to be solved
• Examples
• Mathematical word problems
• Bowling pin Problem
• Christmas tree problem

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Word Problems

• John and Mary want to buy new plants for their
  garden. They agree on how many to buy, but not
  on how many of each to buy. John wants to buy a
  lot of a few kinds and suggests 10 of each. Mary
  wants more variety so she wants 4 of each kind.
  They agree on 5 of each kind. They realize that
  they have room for 2 more, so they bought 6 of
  each. How many did they buy?

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Bowling Pin example

• O O O O
• O O O
• O O
• O
• O
• O O
• O O O
• O O O O

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Christmas Tree Example

• You have 10 Christmas trees. How would you
  arrange them in 5 rows of 4 trees each?

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Generating Solutions

• Use of algorithms - a mathematical formula or
  other procedure that guarantees a correct
  solution if followed correctly. Can be too time
  consuming if there is a large number of actions
  that have to be tried.
• Heuristics choosing a strategy that looks like
  it will work and trying it a short cut
  sometimes called a problem solving protocol

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Types of Heuristics

• 1. Hill climbing heuristic follow the route
  that seems to get you closer to the goal always
  move toward the goal
• 2. Means-ends analysis compare the current
  situation to the end goal. Ask what means do I
  have to get from here to there? Involves the
  development of sub-goals

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Types of Heuristics

• Working backwards start at the goal and
  determine what is the last step to the goal, then
  the second to the last, etc.
• Example 1 Water lilies grow on a lake every
  summer. It begins with one lily, and each day
  the amount of lake covered by the lilies doubles.
  On day number 80 the lake is completely covered.
  On what day was the lake half covered?
• Example 2 You and a friend have each put 50
  quarters on a table and take turns removing at
  least 1, but no more than 5. The person who
  removes the last quarter keeps all of them. You
  go 1st. What can you do make sure you get the
  last one?

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Use of Analogies

• Analogies identifying the relationship between
  two concepts or two problems to solve
• Recognizing that a new problem has similar
  beginning situation and end goal as an early
  problem so you try the same solution

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Standard Analogies

• Tar is to ____ as coal is to ____.
• a. roofing shovel c. black heat
• b. construction heating d. black heating
• Fur is to bear as ___ is to _____.
• a. coat man c. rug floor
• b. warmth animal d. wool
  sheep
• ________ is to torso as branch is to __________.
• a. arm leaf c. fingernails acorns
• b. Leg twigs d. arm trunk
• Centaur is to horse as ____ is to ____.
• a. woman mermaid c. Mermaid fish
• b. mermaid woman d. Fish mermaid
• ____ is to ocean as lake is to ______.
• a. ship boat c. Atlantic Erie
• b. island land d. rough calm

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Examples of the use of an analogy to solve
problems

• Physician has a patient with inoperable tumor in
  the abdomen. She has radiation equipment that
  can direct radiation to the tumor and destroy it,
  but if she makes the radiation strong enough it
  will kill the surrounding tissue and the patient.
  If she makes it weak so tissue isnt destroyed,
  it wont destroy the tumor. How does she cure
  the patient?

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Examples of the use of an analogy to solve
problems

• An evil dictator has a fort in the middle of his
  round country with 10 roads that radiate out from
  the center to the border. The good general is
  outside the country and wants to overthrow the
  dictator. His army has to attack the fort at the
  same time to win. The dictator has put land
  mines on the roads. Since he needs to use the
  roads, the mines are placed so they wont blow up
  if a small group uses them, but will if a large
  army comes down a road they will blow up. How
  can the general attack the fort and win?

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Examples of the use of an analogy to solve
problems

• A high school marching is practicing. They try
  marching in rows of 12, but they have an extra
  person. Then they try 8, but still have an extra
  person. So they try 3, but still have an extra
  person. They finally try 5 and it works. How
  many band members are there? (there are more
  than 45 and less than 200)

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Types of Heuristics

• Drawing a picture
• A man is standing on a bridge 300ft from the near
  side and 500ft from the far side. A train is
  coming from the near side. If he runs to the near
  side, he and the train will reach the end of the
  bridge at the same time. If runs to the far
  side, he and the train will also reach the end of
  the bridge at the same time. He can run 10mph.
  How fast is the train moving?
• 500ft 300ft
• ?--------------------------------I----------------
  ----?
• I____________________ I______________I

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Second example

• A boat can go upstream 24 miles in the same time
  it can go downstream 36 miles. In still water
  the boats engines drive the boat 12 miles an
  hour more than the rate of the current. What is
  the rate of the current?
• ?------------------------B---------------?
• 36 miles 24 miles
• ?---------------
• speed of current

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Second example (cont)

• Look at the boat going upstream
• 1. it can travel 12mph speed of the current
• 2. going upstream it is going 12mph the speed
  of the current the speed of the current
• It has to be going 12 mph for 2 hours and
  downstream it goes 18mph for 2 hours
• Downstream 12mph speed of the current the
  speed of the current 18 mph
• Or 12 mph 2 X the speed of the current 18mph
• So the seed of the current is 3 mph

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3rd example

• Solomon has a 26-volume encyclopedia sitting in
  alphabetical order on his shelf. Each volume is
  3 inches thick (including covers), so the set
  takes up 78 inches of space. A bookworm is
  sitting on the front cover of volume A and
  begins to chew his way through the pages directly
  toward volume Z. If he chews at a rate of 6
  inches a month how, long will it take him to
  reach the back cover of Z?

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Problems people have with generating solutions

• Water Jar problem
• Problem A B C Amount
• 1 29 3 20
• 2. 21 127 3 100
• 3. 14 163 25 99
• 4. 18 43 10 5
• 5. 9 42 6 21
• 6. 20 59 4 31
• 7. 23 49 3 20
• 8. 15 39 3 18
• 9. 18 48 4 22
• 10. 14 36 8 6

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2nd Example

• Two trains are approaching each other. One is
  traveling at 20 miles an hour while the other
  travels at 30 miles and hour. A bird flies back
  and forth between the two trains at 60 mph. The
  trains meet in 4 hours. How far did the bird
  fly?
• Called the development of a mental set

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Problems people have with generating solutions

• You are given a box of thumbtacks, a box of
  matches, and a small candle. Using what you
  have, how would you mount the candle vertically
  on a wall so it can be lit?
• Two ropes are hanging from the ceiling of a room
  that contains a short stool and a hammer. If you
  grab one rope, the other rope is beyond your
  reach. How can you tie the 2 ropes together?
• Functional fixedness

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Common Errors in Problem Solving

• 1. Inaccuracies in reading
• Reading material without fully understanding the
  material
• Reading the material too fast
• Missing words or misreading words because you are
  not reading completely
• Failing to reread difficult passages

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Common Errors in Problem Solving

• Inaccuracy in thinking
• Placing more importance on speed or ease of
  obtaining an answer rather than accuracy
• Not being careful to perform needed operations
  accurately
• Being inconsistent in the way problems are
  interpreted and solved
• Not checking the accuracy of a solution
• Drawing a conclusion in the middle of the problem
  without sufficient thought
• Working too quickly results in the above errors

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Common Errors in Problem Solving

• Weakness in problem analysis
• Trying to solve the whole problem without
  breaking it down into sub-goals
• Failing to use prior knowledge and experiences
• Skipping difficult material or unfamiliar words,
  etc.
• Not properly constructing a representation of the
  ideas presented in the problem

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Common Errors in Problem Solving

• Lack of perseverance
• Making a weak attempt to solve the problem lack
  of confidence?
• Choosing an answer quickly because it looked or
  felt right instead of fully analyzing the problem
• Jumping to a conclusion halfway through the
  process

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Proficient Problem Solvers

• Have a positive attitude confident
• Great concern for accuracy
• Break problems into parts that can be
  accomplished
• Avoid guessing and jumping to conclusions
• More active do more things and put in more
  effort

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Improving Problem Solving Ability

• 1. Increase knowledge base experts have more
  efficient methods for problem solving
• 2. Automate some components through expertise
• 3. Follow a systematic plan of attack
• 4. Draw inferences from information given and
  memory
• 5. If solution not obvious look at possible
  heuristics
• 6. Reformulate problem have you defined the
  problem correctly
• 7. Draw a picture

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Creativity
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Creativity

• Definition a cognitive activity that results in
  a new or novel way of viewing a problem or
  situation
• Involves the ability to avoid the traps of
  problem solving
• Mental sets
• Functional fixedness
• Misrepresentation of the problem

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The Process of Creativity

• Stage 1 Preparation knowledge acquisition and
  developing and testing possible solutions
• Stage 2 Incubation getting away from the
  problem can lead to creative solutions doesnt
  always occur
• Insightful learning
• Non-insightful learning
• Stage 3 Illumination sudden discovery of a
  solution
• Stage 4 Verification evaluation of the
  insight does it really solve the problem or is
  it he best solution

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Characteristics of a Creative Person

• 1. Knowledgeable and intelligent
• 2. Personality self-confident and not afraid to
  be wrong or look foolish
• 3. Motivation willing to make the cognitive
  investment and effort to develop a solution

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Environmental Influences on Creativity

• If creativity is valued in the cultural setting,
  motivation to be creative increases
• When practical constraints are put on creative
  thinking, low creativity
• Practical evaluation of creative ideas occurs
  early restricts the ideas that can be produced
• Thinking about completely impractical ideas can
  lead to less impractical ideas which can lead to
  practical innovative ideas
• Individual production of ideas produce more
  creative ideas than group production

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Measuring Creativity

• Most people know who a creative person is, but
  creativity is difficult to measure
• Frequent procedure involves divergent thinking
  How many uses for a brick can you think of?
• Problem is that evaluating possible solutions
  just as important as generating