Each of these exercises will help your students increase their ability to solve problems creatively. While completing the exercises, students shouldn't race through just to see the answers. They should work at each game until they develop the perspective necessary to play it well. Each exercise is designed to demonstrate an important point that should be mastered before going on to the next challenge.
Try to keep students from becoming discouraged. In learning to master creative problem solving, the best way—and sometimes the only way—is to learn through mistakes. Fear of making mistakes is often the most inhibiting attitude to effective problem solving.
Exercise #1: Kindred Relationships
There have been many efforts to define or explain the creative process. Psychologist Sarnoff A. Mednick of the University of Michigan thinks of it as the forming of associative elements into new combinations or arrangements.
That may not be the whole story, but the person who can marshal a great number of associations and ideas and bring them to bear on his problem has the best chance of coming up with an original solution.
In this exercise, think of a fifth word that is related to the preceding four words. (Compound and hyphenated words or commonly used expressions are allowed.)
Examples:
Elephant, bleed, lie, wash
Answer:White (white elephant, bleed white, white lie,
white-wash)
Sleeping, contest, spot, shop
Answer: Beauty (sleeping beauty, beauty contest, beauty spot, beauty shop)
Now train your own associative powers with the following sets:
1. bug rest fellow cover ____________________
2. cross baby blood ribbon ____________________
3. see carpet hot cent ____________________
4. touch palate soap sell ____________________
5. easy hush belt order ____________________
6. tree cup cake forbidden ____________________
7. wagon stand aid dance ____________________
8. dust movie gaze sapphire ____________________
9. tooth talk potato bitter ____________________
10. alley date snow spot ____________________
Answers: 1. Bed 2. Blue 3. Red 4. Soft 5. Money 6. Fruit 7. Band 8. Star 9. Sweet 10. Blind
Exercise #2: More Than Meets the Eye
One of the most useful of all thinking modes in creative problem solving is visual thinking. It is especially effective in solving problems where shapes, forms, or patterns are concerned. To improve your powers of visualization, concentrate on the accompanying illustration.
The question usually asked in connection with this design is whether you see either the vase or the two human profiles. A mentally flexible person will see both. For purposes of this mental exercise, however, try to see as many additional items in the picture as you can. Look at it from many different points of view and from as many angles as you wish. Then check the list below. Some of the items may seem far—fetched. But, remember, the idea is to use your imagination freely.
Answers: 1. An anvil. 2. An overpass pillar on a highway. 3. Champagne glass. 4. Piano stool. 5. Tower with revolving restaurant. 6. Minute-timer. 7. Propeller. 8. Chess-game rook or castle. 9. Fruit holder. 10. Bird bath. 11. Chalice. 12. Rubber grommet. 13. Keyhole slot in door. 14. An extrusion die. 15. Two Pontiac automobiles about to crash head on. 16. A screw jack. 17. An arrowhead going into an object. 18. Two girls sitting back-to-back and holding parcels on their heads.
Exercise #3: Loose Ends
Defining a problem too narrowly can inhibit and delay finding a solution. The creative problem solver tries to state the requirements as broadly as possible at the beginning. If, after a reasonable time, no solution presents itself, he tries to restate it in such a way that a new avenue of approach becomes available.
Less successful problem solvers, on the other hand, persist doggedly in the same direction, even when the difficulty does not yield to their efforts. They are blocked from considering new directions by stubborn commitment to the old.
Look at the first sketch and imagine that you are the person shown standing in the room. You have been given the task of tying together the ends of the two strings suspended from the ceiling. The strings are located so that you cannot reach one string with your outstretched hand while holding the second in your other hand. The room is totally bare, and you have only the resources you would normally have in your pocket or handbag. How do you solve this problem?
Most people will see the difficulty as a shortness of reach. That is, they state the problem to themselves as: "How can I get to the second string?" The consequence of this perspective is that all effort goes into vain efforts to find a means of making one of the strings longer. But the "givens" of this problem make such a solution impossible.
Exercise #4: Breaking Out
Most of us impose too many imaginary boundaries, restrictions, and constraints upon our problems, and hence fail to solve them.The problem: Draw four straight lines through the nine dots without retracing and without lifting your pen from the paper.
The key to the solution is, of course, that the imaginary boundaries formed by the dots need not be observed. Once freed from this restriction, you will find the solution easy, as shown here. Researchers at Stanford University have come up with an even more interesting solution to this puzzle. One subject realized that it wasn't necessary to draw four lines through the centers of the dots; the problem can be solved with only three lines.
Exercise #5: Nature's InventionsBiology and zoology are considered by many to be rich sources of analogies from which significant inventions can be derived. One of the most celebrated cases is the invention of the telephone. As Alexander Graham Bell wrote: "It struck me that the bones of the human ear were very massive as compared with the delicate thin membrane that operated them; and the thought occurred to me that if a membrane so delicate could move bones so relatively massive, why should not a thicker and stouter piece of membrane move a piece of steel." Thus was the telephone conceived.
Here is a list of animals and the inventions they exemplify. Try matching the animal with the invention.
1. bat ( ) parachute
2. armadillo ( ) snowshoes
3. chameleon ( ) anesthetic
4. fish ( ) helicopter
5. flying squirrel ( ) suction cup
6. squid ( ) hypodermic
7. hummingbird ( ) radar
8. scorpion ( ) camouflage
9. snake ( ) electricity
10. abalone ( ) tank
11. caribou ( ) jet propulsion
Answers:
1. bat (5) parachute
2. armadillo (11) snowshoes
3. chameleon (9) anesthetic
4. fish (7) helicopter
5. flying squirrel (10) suction cup
6. squid (8) hypodermic
7. hummingbird (1) radar
8. scorpion (3) camouflage
9. snake (4) electricity
10. abalone (2) tank
11. caribou (6) jet propulsion
Exercise #6: More or Less
We frequently fail to solve problems because we approach them with prejudgments or unwarranted assumptions. These assumptions restrict our thinking processes and hamper our imaginations.
When doing this problem, try to defer any prejudgments that pop into your mind and try to deliberately change your point of view: Add one line to the roman numeral XI, and end up with the number ten. Try for at least three different solutions.
The most obvious solution is to add a fraction bar, X/l. Other solutions:
The solutions shown above are just some of those that involve the use of a straight line. However, the problem statement was: "Add one line.. . " With no qualifications as to the shape of the line, it would be an unwarranted assumption to try to solve this problem with only straight lines.
As long as we produce a mark with just one sweep of the pen, without lifting the pen from the paper, that is "one line." With this in mind, the following solutions are permissible:
Exercise #7: The Collected Works
We are frequently hampered in creative problem solving by our habitual ways of looking at things. The more familiar a situation or an object is, the harder it is to see it differently. Creativity, however, requires a "fresh" pair of eyes.
While this problem looks deceptively simple, it is actually quite diffficult. There are four volumes of Shakespeare's collected works on the shelf.
The pages of each volume are exactly 2 in. thick. The covers are each 1/6 in. thick. A bookworm started eating at page 1 of Volume I and ate through to the last page of Volume IV. What is the distance the bookworm covered?
Exercise #8: Joined Together
Most people rush in to tackle a problem without considering the alternatives and without attempting to understand what is involved. As the result, they waste a lot of time and effort.To illustrate the importance of analysis, copy this design and keep track of how long it takes you. (Tracing is not allowed.)
If it took anywhere from one to three minutes, try a different approach and copy it again to see if that new point of view helps you copy the design more quickly.The design can be copied easily and accurately in less than 15 seconds. One step-by-step approach is as follows:
Another imaginative solution occurs when you recognize the pattern as being made up of four identical parts. Drawing them one after another and rotating each successive part 90 degrees makes a speedy reproduction:
You can tape two pencils together and zip through to a speedy solution.
The answer is five inches. If you had trouble with this one, you were probably trapped by a conventional way of visualizing. We are accustomed to seeing a book in a certain position—facing us, with the first page near the left hand cover and the last page nearest the right hand cover. But it was specified in this problem that the volumes were on the shelf. With the backs facing you, the order of pages is reversed.
In creative problem solving it serves well to heed this warning: The more familiar the object, the harder it is to see it in another context.
Exercise #9: Concealed Colors
This game is designed to increase your flexibility and your ability to overcome the restrictions of habit. The name of what color is concealed in each sentence?
1- Newspaper editors decided to go on strike. (Red)
2- The cab lacked proper brakes to stop at the intersection. (Black)
Now try these:
1- A big, old, hungry dog appeared at our door every morning.
2- The cop persuaded him not to create a disturbance.
3- The Brazilian student Paulo lives around the corner from us.
4- You shouldn't let an upstart like him bother you.
5- He let out a big yell, owing to the injuries he received when he fell.
6- La Jolla venders decided to cut their prices in half.
7- Long rayon fabrics were loaded on the truck.
8- The Austrian physicist Wolfgang Pauli lacked the requisite documents to enter the U.S.
9- You shouldn't sell this fossil very cheaply because it is a rare specimen.
10- The new law hit everybody's pocketbook pretty hard.
Answers: 1. Gold 2. Copper 3. Olive 4. Tan 5. Yellow 6. Lavender 7. Gray 8. Lilac 9. Silver 10. White
In order to identify the hidden colors, you have to disregard the signs that say "stop"—such as word spacings, periods, and commas. People who are habit-ridden will find this exercise very difficult.
Exercise #10: Scams
The purpose of this exercise is to build your fluency of thought and expression. At first, you might find that you can think of only a few sentences but, if you persist, many more will occur to you.
Write five-word sentences from the five given letters, one letter for each word.
S C A M S
Here are a couple of examples:
1- Senior citizens arrange maximum security.
2- Sarcastic comments are meant seriously.
Now see how many sentences you can produce in exactly five minutes, then check some of the possibilities given below.
1- Sleepy cats always move slow.
2- Singing cellos alter mood substantially.
3- Sabotage caused army's move southward.
4- Spoiled children angered mother steadily.
5- Straightened circumstances affect man's stability.
6- Strike caused austerity moves subsequently.
7- School classes appear moderately satisfying.
8- Studious children always merit success.
9- Sly crocodiles attacked migrating settlers.
10- Siamese cats age much slower.
Exercise #11: A Woman's Ingenuity
With some problems, a creative solution can only occur after the elements or parts of the problem have been reorganized into a different pattern. This requires that you juggle the parts in your mind's eye. With this in mind, see if you can solve this problem: A businessman brought back from Europe four pieces of chain in solid gold, each consisting of three links.
He wanted to keep them as an investment, but his wife felt that—joined together—the pieces would make a lovely necklace. She went to a jeweler and said, "I want you to connect these pieces to make a necklace. How much will it cost?" The jeweler laid the individual pieces of chain out in this pattern: He told the lady, "I charge $2.50 to break a link and $2.50 to melt it together again. Since you have four corners, it will cost you $20." The lady said, "That's too much. Actually you can do it for $15." The problem, then, is to construct a necklace, breaking and joining only three links. How would you do it?
As long as you think of the segments of chain as four sides of a square or as segments of a circle, you can't solve this problem. The moment you shift your focus and regard one of those segments—not as an immutable structure—but as a stockpile of individual links, you've made the necessary breakthrough. At the woman's suggestion, the jeweler placed three segments in a triangular pattern, took apart the remaining segment, and used those three links to close the three comers of the necklace.
Most people will have to juggle the elements visually, drawing them in different arrangements before arriving at the triangular pattern that leads to solution. This juggling of the parts of a problem results in a reorganization. But before that can happen, you have to feel free to destroy the original pattern in which the problem was presented.
No comments:
Post a Comment