In What Ways Might We Formulate a Problem Statement?

questionmark.The initial statement of a problem often reflects a preconceived solution. Once we have settled on a perspective, we close off but one line of thought. Certain kinds of ideas occur to us, but only those kinds and no others. What if the crippled man who invented the motorized cart had defined his problem as: “How to occupy my time while lying in bed?” rather than “How to get out of bed and move around the house?”

Have you ever looked closely at the wheels on a railroad train? They are flanged. That is, they have a lip on the inside to prevent them from sliding off the track. Originally train wheels were not flanged–instead, the railroad tracks were. Because the problem of railroad safety had been expressed as: “How can the tracks be made safer for trains to ride on?” hundreds of thousands of miles of track were manufactured with an unnecessary steel lip. Only when the problem was redefined as: “In what ways might we make railroad traffic safer? was the flanged wheel invented.

INVITATIONAL STEM: The formulation of a problem determines the range of choices: the questions you ask determine the answers you receive. To start with, it’s helpful to coin problems in a particular way. Write the problems you want to solve as a definite question. Use the phrase “In what ways might I…?” to start a problem statement. This is sometimes known as the invitational stem and helps keep you from settling on a problem statement that may reflect only one perception of the problem.

For example, in the series of letters below, cross out six letters to make a common word.


If you state the problem as: “How to cross out six letters to form a common word?” you’ll find it difficult to solve. If, instead, you framed it: “In what ways might I cross out six letters to form a common word?” you will likely find yourself inspired to think of many alternative possible solutions, including the solution which is to literally cross out the letters “S,” “I,” “X,” “L,” “E,” “T,” “T,” “ and so on, leaving the word CREATE.

Before you brainstorm any problem, restate the problem at least five to ten times to generate multiple perspectives. The emphasis is not so much on the right problem definition but on alternative problem definitions. Sooner or later, you’ll find one that you are comfortable with. Following are some different ways to look at your problem.

GLOBAL AND SPECIFIC: One can always look at a system from different levels of abstraction. A very fine-grained description of a beach would include every position of every grain of sand. Viewed from a higher vantage point, the details become smeared together, the grains become a smooth expanse of brown. At this level of description, different qualities emerge: the shape of the coastline, the height of the dunes, and so on.

The idea is to look for the appropriate level of abstraction, the best viewpoint from which to gather ideas. In the 1950s, experts believed that the ocean-going freighter was dying. Costs were rising, and it took longer and longer to get merchandise delivered.

The shipping industry experts built faster ships that required less fuel and downsized the crew. Costs still kept going up, but the industry kept focusing its efforts on reducing specific costs related to ships while at sea and doing work.

A ship is capital equipment and the biggest cost for the capital equipment is the cost of not working, because interest has to be paid without income being generated to pay for it. Finally, an outside consultant globalized the challenge to: “In what ways might the shipping industry reduce costs?”

This allowed them to consider all aspects of shipping, including loading and stowing. The innovation that saved the industry was to separate loading from stowing, by doing the loading on land, before the ship is in port. It is much quicker to put on and take off preloaded freight. The answer was the roll-on, roll-off ship and the container ship. Port time has been reduced by three quarters, and with it, congestion and theft. Freighter traffic has increased fivefold in the last thirty years, and costs are down by 60%.

One of the keys to Freud’s genius was his ability to find the appropriate level of abstraction of his problem so that he could operate beyond the usual assumptions and interpretations. To find the appropriate level of abstraction, ask “Why?” four or five times, until you find the level where you’re comfortable.

Suppose your challenge is: “In what ways might I sell more Chevrolet Luminas?”
Step One: Why do you want to sell more Luminas? “Because my car sales are down”
Step Two: Why do you want to sell more cars? “To improve my overall sales.”
Step Three: Why do you want to improve overall sales? “To improve my business.
Step Four: Why do you want to improve your business? “To increase my personal wealth.”
Step Five: Why do you want to improve your personal wealth? “To lead the good life.”

Now you shape your challenge in a variety of ways including:
In what ways might I sell more Luminas?
In what ways might I sell more cars?
In what ways might I improve overall sales?
In what ways might I improve my business?
In what ways might I improve my personal wealth?
In what ways might I lead the good life?

You may choose to stick with the original challenge of selling more Luminas or you may choose a more global challenge of improving your personal wealth. Improving your personal wealth allows your thinking to embrace more opportunities. You could negotiate a higher commission return for each vehicle sold, go into another business, make investments, sell other products and so on.

SEPARATE THE PARTS FROM THE WHOLE. Seeing is one of the most comprehensive operations possible: your vison embraces an infinity of forms and objects, yet it fixes on but one object at a time. Similarly, when Leonardo Da Vinci embraced a subject, he would see the whole but would move from one detail to another seeking the origin or cause of each detail. He believed you gained knowledge by separating the parts from the whole and examining all the relationships and key factors that may influence a given situation.

Professor Kaoru Ishikawa of the University of Tokyo incorporated this strategy in his Ishikawa diagram, which is commonly known as the “fishbone” diagram because of its unique shape. The “fishbone” diagaram is a way to visually organize and examine all the factors that may influence a given situation by identifying all the possible causes that produce an effect. An effect is a desirable or undesirable result produced by a series of causes. In teaching this tool, the Japanese often use as an effect a “perfect plate of rice.” In a typical diagram, minor causes are clustered around four major cause categories. For example, common major cause categories in the manufacturing process might be materials, people, methods, and machinery, and major cause categories in public education might be teachers, methods, environment, students, and policies.

Suppose we want to improve creativity in our organization. Following are guidelines for fishboning the situation:

1. Our effect would be “perfect organizational creativity.”We would write this in the box on the right (the fish’s head). A straight line is drawn to the left to resemble the backbone of the fish.
2. The next step is to brainstorm the major cause categories. What are the major causes that would produce perfect organizational creativity? You can have as many major causes as are warranted. There are typically three to six. We decide that the four major categories for organizational creativity are: people, environment, materials and policies. The major cause categories become the ribs of the fish.
3. Minor causes are then grouped around the major causes as fish bones. E.g., “train to be creative” would be a bone attached to the “People” rib, and “stimulating” would be a bone attached to the “Environment” rib.
4. For each minor cause, ask “How can we make this happen?” and post the response as branches off the bones. E.g., “hire an outside expert to conduct the training” would be a branch off the “train” bone.

[NOTE: Click on diagram]

Fishboning allows you to see the relationships between causes and effects, allows you to consider all the different parts of a situation, and allows you to identify those areas where you need more data or information. It also triggers your subconscious. Ishikawa described the process as one in which you fishbone your problem and let it cook overnight. When you come back to it, you’ll be amazed at the new thoughts and ideas that your subconscious has cooked up.

REPHRASE THE PROBLEM IN YOUR OWN WORDS. Richard Feynman once reviewed his children’s school books. One book began with pictures of a mechanical wind-up dog, a real dog, and a motorcycle, and for each the same question: “What makes it move?” The proposed answer–”Energy makes it move”– enraged him.

That was tautology, he argued–empty definition. Feynman, having made a career of understanding the deep abstractions of energy, said it would be better to begin a science course by taking apart a toy dog, revealing the cleverness of the gears and ratchets. To tell a first-grader that “energy makes it move” would be no more helpful, he said, than saying “God makes it move” or “moveability” makes it move. He proposed teaching students how to rephrase what they learn in their own language without using definitions. For instance, without using the word energy, tell me what you know now about the dog’s motion.

Other standard explanations were just as hollow to Feynman. When someone told him that friction makes shoe leather wear out, his response was “Shoe leather wears out because it rubs against the sidewalk and the little notches and bumps on the sidewalk grab pieces and pull them off.” That is knowledge. To simply say, “It is because of friction,” is sad, because it is empty definition.

Always try to rephrase the problem in your words without using definitions. In another famous Feynman example, he was working with NASA engineers on a serious problem and they kept defining the problem as a “pressure-induced vorticity oscillatory wa-wa or something.” After considerable time and discussion had passed, a confused Feynman finally asked them if they were trying to describe a whistle? To his amazement they were. The problem they were trying to communicate to him exhibited the characteristics of a simple whistle. Once he understood what they were trying to do, he solved it instantly.

CHANGE THE WORDS. For every word a person uses, psychologists say there is a mediating response which provides the meaning of that concept for that individual. Just what the mediating responses are for all words is not known. Many times they may not be responses in the usual sense but all provide meaning of that concept for that individual. When you change the words in your problem statement, you initiate an unobservable process in your mind that may lead to a new thought or idea.

A few years back, Toyota asked employees for ideas on how they could become more productive. They received few suggestions. They reworded the question to: “How can you make your job easier?” They were inundated with ideas.

A simple change of words or the order of words in a problem statement will stimulate your
imagination by adding new dimensions of meaning. Consider the statement “Two hundred were killed out of six hundred,” as compared to “Four hundred were spared out of six hundred.”

Examine your problem statement, identify the key words, and change them five to ten times to see what results. One of the easiest words to change is the verb. Suppose you want to increase sales. Look at the changing perspectives as the verb is changed in the following:
In what ways might I increase sales?
In what ways might I attract sales?
In what ways might I develop sales?
In what ways might I extend sales?
In what ways might I repeat sales?
In what ways might I keep sales? Magnify sales? Restore sales? Target sales? Inspire sales? Cycle sales? Encourage sales? Grow sales? Copy sales? Complement sales? Acquire sales? Vary sales? Spotlight sales? Motivate sales? Prepare sales? Renew sales? Force sales? Organize sales? And so on.

PLAYING WITH VERBS AND NOUNS. Playing with verbs and nouns encourages you to think of perspectives that you would probably not think of spontaneously. Try changing the nouns into verbs and verbs into nouns in your problem statement. For example, a problem might be “How to sell more bottles ?” Changing the verbs into nouns and nouns into verbs makes this into “How to bottle more sales?” Bottling sales now suggests looking for ways to close sales, instead of ways to sell more bottles.

The problem “How to improve customer relations?” becomes “How to customize related improvements?” This new perspective leads one to consider customizing products and services for customers, customizing all relevant aspects of the customer relations department, and so on.

The problem “How to motivate employees?” becomes “How to employ motivated people?”

TRANSPOSE THE WORDS. One of Aristotle’s favorite ways to test a premise was what he called “convertibility.” He felt that if a premise were true than the negative premise should be convertible. For example, if every pleasure is good, some good must be pleasure. Sometimes changing the order of words in a problem statement will create a verbal-conceptual chain that may trigger a different perspective.

In the following illustration, words were arranged in two different series, “A” and “B,” and subjects were asked to solve certain situations. When “skyscraper” was listed first, subjects
tended to come up architectural concepts, and when “prayer” was transposed with “skyscraper” and listed first, it increased the likelihood of a religious direction.


To change the order, transpose the words in your problem. Following are some examples:
In what ways might I get a promotion?
To: In what ways might I promote myself?
In what ways might I advertise my T-shirts?
In what ways might I use my T-shirts to advertise?
In what ways might I learn how to use the Internet?
In what ways might I use the Internet to learn more?

A very simple change in the way something is looked at can have a profound effect. One of the most effective medical discoveries of all time came about when Edward Jenner transposed his problem from why people got small pox to why dairymaids apparently did not. From the discovery that harmless cowpox gave protection against deadly smallpox came vaccination and the end of smallpox as a scourge in the western world.

POSITIVE ACTION STATEMENTS. In the Universe Within, Morton Hunt details experiments conducted by Herbert Clark at Stanford University that demonstrate how thinking positively facilitates and speeds up thinking. In the Figure below, are the statements true or false?

The square is above the plus =

The square is above the plus =

Notice how much longer it takes to reply to the false statement than to the true one. We instinctively assume statements are true. If they are, we do no further thinking and move on. If they are not true, we have to step back and revise our assumption, thus answering more slowly. It takes approximately a half-second or longer to verify denials than affirmations. We are programmed to think more easily about what is than what is not.

Read the following sentences, pausing briefly between them.
Should we allow gays to serve in the military?
Should we not allow gays to serve in the military?

Did you feel your mind slowing down to interpret the second statement? Negatives give us pause and slow down our thinking process. Suppose you misplaced your watch somewhere in your house. If you search for it and keep searching, you will eventually find it. This is a different perspective from “Did I misplace my watch in the house or did I misplace it somewhere else?” The belief that the watch is in the house speeds up your thinking and keeps you focused on your goal. Positive, active statements speed up our thinking and keep us focused on our goal. Try framing your problem statement as a positive action statement. A positive action statement has four parts:

1. THE ACTION. The thing you want to do.
2. THE OBJECT. A thing or person you want to change.
3. THE QUALIFIER. The kind of action change you want.
4. THE END RESULT. The result you expect to follow.

EXAMPLE: In what ways might I package (ACTION) my book (OBJECT) more appealingly (QUALIFIER) so that people will buy more (END RESULT).

This is a convenient way to transform your thoughts into words that will shape the kinds of action you need to take to solve the problem.

Michael Michalko

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