psy420leceeeeeeeeeeeeeeeeeeeeeeeeture13.ppt

rrrrr

1. 1
Problem
Solving and
Creativity

2. 2
Problem solving -
definition
•Directed thinking towards a goal
solution –the task is to choose the
best process that will lead to a goal
•1
st
psychological studies by Wolfgang
Kohler (insightful learning)

3. 3
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

4. 4
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?

5. 5
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

6. 6
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?

7. 7
Bowling Pin example
•O O O O
•O O O
• O O
• O
• O
• O O
•O O O
•O O O O

8. 8
Christmas Tree Example
•You have 10 Christmas trees. How
would you arrange them in 5 rows of 4
trees each?

9. 9
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

10. 10
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

11. 11
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 1
st
. What can you do make sure you get the
last one?

12. 12
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

13. 13
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

14. 14
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 isn’t destroyed, it
won’t destroy the tumor. How does she
cure the patient?

15. 15
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 won’t 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?

16. 16
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)

17. 17
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

18. 18
Second example
•A boat can go upstream 24 miles in the
same time it can go downstream 36 miles.
In still water the boat’s 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

19. 19
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

20. 20
3
rd
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”?

21. 21
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

22. 22
2
nd
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

23. 23
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

24. 24
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

25. 25
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

26. 26
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

27. 27
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

28. 28
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

29. 29
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

30. 30
Creativity

31. 31
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

32. 32
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 –doesn’t 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

33. 33
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

34. 34
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

35. 35
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