Introduction & Foundation
Systematic approach to Problem Solving : With as many problems as we are all faced with in our work and life, it seems as if there is never enough time to solve each one without dealing with some adversity along the way.
Problems keep mounting so fast that we find ourselves taking shortcuts to temporarily alleviate the tension points – so we can move onto the next problem.
In the process, we fail to solve the core of each problem we are dealt; thus we continuously get caught in the trap of a never-ending cycle that makes it difficult to find any real resolutions.
So it gets blamed on a scapegoat such as “Failure to communicate.“, or “Pin it on this guy.” and the cycle begins again.
Sound familiar? 🙂
Unfortunately, several workplace environments around the world foster these kinds of management deficiency.
Problem solving is the essence of what leaders exist to do.
As leaders, the goal is to minimize the occurrence of problems – which means we must be courageous enough to tackle them head-on before circumstances force our hand.
We must be resilient in our quest to create and sustain momentum for the organization and people we serve.
But the reality of the workplace finds us dealing with people that complicate matters with their corporate politicking, power-plays, self-promotion, and ploys, and envy.
Silos, lack of budgets and resources, and many other random acts or circumstances also make it harder for people to be productive.
Competitors equally create problems for us when they unexpectedly convert a long-standing client, establish a new industry relationship, or launch a new product, brand or corporate strategy.
Mergers & acquisitions keep us on our toes and further distract us from solving existing problems by creating new ones.
As Karl Popper, one of the most influential 20th-century philosophers of science, once eloquently stated,
“All life is problem solving.”
I’ve often contended that the best leaders are the best problem solvers.
They have the patience to step back and see the problem at-hand through broadened observation; and circular vision.
They see around, beneath and beyond the problem itself.
They see well-beyond the obvious.
The most effective leaders approach problems through a lens of opportunity.
Leaders who lack this wisdom, approach problems with linear vision – thus only seeing the problem that lies directly in front of them and blocking the possibilities that lie within the problem.
As such, they never see the totality of what the problem represents; that it can actually serve as an enabler to improve existing best practices, protocols and standard operating procedures for growing and competing in the marketplace.
They never realize that, in the end, all problems are the same – just packaged differently.
A leader must never view a problem as a distraction, but rather as a strategic enabler for continuous improvement and opportunities previously unseen.
Lets start off with the foundations because one cannot build a castle on sand, right? 🙂
The foundations of problem solving
1. Transparent Communication
Problem solving requires transparent communication where everyone’s concerns and points of view are freely expressed.
I’ve seen one too many times how difficult it is to get to the root of the matter in a timely manner when people do not speak up.
Yes, communication is a fundamental necessity.
That is why when those involved in the problem would rather not express themselves – fearing they may threaten their job and/or expose their own or someone else’s wrong-doing – the problem-solving process becomes a treasure hunt.
Effective communication towards problem-solving happens because of a leader’s ability to facilitate an open dialogue between people who trust their intentions and feel that they are in a safe environment to share why they believe the problem happened as well as specific solutions.
Once all voices have been heard and all points of view accounted for, the leader (with their team) can collectively map-out a path toward a viable and sustainable solution.
As fundamental as communication may sound, don’t ever assume that people are comfortable sharing what they really think.
This is where a leader must trust themselves and their intuition enough to challenge the team until accountability can be fairly enforced and a solution can be reached.
2. Break Down Silos
Transparent communication requires you to break down silos and enable a boundary-less organization whose culture is focused on the betterment of a healthier whole.
Unnecessary silos invite hidden agendas rather than welcome efficient cross-functional collaboration and problem-solving.
Organizational silos are the root cause of most workplace problems and are why many of them never get resolved.
This is why today’s new workplace must embrace an entrepreneurial spirit where employees can freely navigate and cross-collaborate to connect the problem-solving dots; where everyone can be a passionate explorer who knows their own workplace dot and its intersections.
When you know your workplace dot, you have a much greater sense of your sphere of influence.
This is almost impossible to gauge when you operate in silos that potentially keep you from having any influence at all.
In a workplace where silos exist, problem-solving is more difficult because you are more likely dealing with self-promoters – rather than team players fostered by a cross-functional environment.
So how do these self promoters, typically, senior officials / management in a formal and informal chain of command get away with building and maintaining these silos and avoid the responsibilities and actually pass them on to another employee? The answer my friends is simple; plausible deniability.
When you operate in a siloed environment where everyone wants to be a star, it becomes increasingly difficult to help make anything or anyone better. This is when problem-solving becomes a discouraging task.
Breaking down silos allows a leader to more easily engage their employees to get their hands dirty and solve problems together.
It becomes less about corporate politicking and more about finding resolutions and making the organization stronger.
3. Open-minded People
Breaking down silos and communication barriers requires people to be open-minded.
In the end, problem solving is about people working together to make the organization and the people it serves better.
Therefore, if you are stuck working with people that are closed-minded, effective problem solving becomes a long and winding road of misery.
There are many people in the workplace that enjoy creating unnecessary chaos so that their inefficiencies are never exposed.
Sound familiar? 🙂
These are the types of people (loafers and leeches) that make it difficult for problems to get solved because they slow the process down while trying to make themselves look more important.
Discover the lifters and high-potential leaders within the organization and you will see examples of the benefits of being open-minded and how this eventually leads to more innovation and initiative.
Open-minded people see beyond the obvious details before them and view risk as their best friend. They tackle problems head-on and get on with the business of driving growth and innovation.
Close-minded employees turn things around to make it more about themselves and less about what is required to convert a problem into a new opportunity.
With this explanation in mind, carefully observe the actions of others the next time you are dealt a real problem.
4. A Solid Foundational Strategy
Without a strategy, change is merely substitution, not evolution.
A solid strategy must be implemented in order to solve any problem.
Many leaders attempt to dissect a problem rather than identify the strategy for change that lies within the problem itself.
Effective leaders that are comfortable with problem-solving always know how to gather the right people, resources, budget and knowledge from past experiences (hindsight.)
They inspire people to lift their game by making the problem-solving process highly collaborative; for them, it’s an opportunity to bring people closer together.
You don’t know the true potential and character of a person until you see the way they solve problems.
Effective leaders connect the dots and map-out a realistic plan of action in advance.
They have a strategy that serves as the foundation for how the problem will be approached and managed.
They anticipate the unexpected and utilize the strengths of their people to assure the strategy leads to a sustainable solution.
Never shoot from the hip when problem-solving. Avoid guessing.
Take enough time to step back and assess the situation and the opportunities that each problem represents.
Make the problem-solving process more efficient by recognizing that each problem has its own nuances that may require a distinct strategy towards a viable resolution.
You know that you have great leadership in your organization when problem-solving becomes a seamless process that enables the people and the organization to grow and get better.
If problem-solving creates chaos, you may have a serious leadership deficiency.
Problem solving is the greatest enabler for growth and opportunity.
This is why they say failure serves as the greatest lesson in business and in life.
Be the leader that shows maturity, acts courageously and requires accountability.
Applying each of these lessons can help you become a master problem solver.
Each experience teaches us all new things.
Embrace problem-solving and the many unseen treasures it represents.
Strategies to help you understand the problem
Clarify the problem.
It is easier to solve a specific problem than a vague one. Therefore, clarify the problem before you start looking for a solution.
If your problem is that your spouse tells you that you are not supportive enough, find out what he or she means by supportive.
If your problem is that your mother can’t get the new VCR to work, determine what doesn’t happen that she wants to happen.
If your problem is a math homework question, read carefully the question (usually at the end): Is the answer supposed to be in metres or centimetres, rounded or not, square or not, etc.
Clarifying Questions are simple questions of fact. They clarify the dilemma and provide the nuts and bolts so that the participants can ask good probing questions and provide useful feedback.
Examples of Clarifying Questions:
- Is this what you said…?
- What resources were used for the project?
- Did I hear you say…?
- Did I understand you when you said…?
- What criteria did you use to…?
- What’s another way you might…?
- Did I hear you correctly when you said…?
- Did I paraphrase what you said correctly?
- If we did XYZ, what would happen?
- What benefit does XYZ have?
- What would change once XYZ is in place?
- How does XYZ change things?
- Why should I care about XYZ?
- What’s your goal? (or, the goal)
- How would XYZ impact you? (a good technique to shift the conversation to a non-participant)
- What else do we need to think about if we do XYZ?
- Let’s talk about what problem we might be trying to solve here. (it’s often necessary to re-iterate, just re-phrase if you can!)
- How would your day-to-day work change if we did this?
Probing Questions are intended to help think more deeply about the issue at hand.
Examples of Probing Questions:
- Why do you think this is the case?
- What do you think would happen if…?
- What sort of impact do you think…?
- How did you decide…?
- How did you determine…?
- How did you conclude…?
- What is the connection between… and…?
- What if the opposite were true? Then what?
Identify key elements of the problem.
Problems come to us with varying amounts of important and useless information.
Focusing on useless information distracts us and wastes time.
Identify the key elements of the problem before you start looking for a solution.
If the problem is that of a couple who come to you for counselling because they argue continually, ask them what they argue about, when, and where.
If the problem is that your bike squeaks when you ride it, determine what part squeaks.
Perhaps when? IE: in the rain only.
Visualize the problem or relevant process or situation.
Sometimes we can see the problem and all its important details right in front of us.
This helps us understand the problem.
Other times we can’t see important elements because they have already occurred or are not visible.
In these cases, it is valuable to visualize important elements of the problem.
So, if you want to predict the future of the universe, visualize the big bang and the ensuing events.
If you want to open a lock without a key, visualize the lock mechanism.
If you want to determine how a murder was committed, visualize events that would explain the physical evidence.
Draw a picture or diagram of the problem or a relevant process or situation.
Visualizing a problem can aid understanding.
However, we can keep only some much visual information in our minds at once.
Hence, it is often useful to draw a picture or diagram.
So, if you want to calculate when two airplanes will collide, draw their paths and speeds.
If you plan to assault a house where a terrorist holds hostages, draw a picture of the room, doors, windows, hostages, etc.
If you want to speed up delivery of goods to retailers, draw a diagram showing the steps in the process. (making notes of any bottlenecks/inefficiencies)
Create a model of the problem or a relevant process.
Creating a model of a problem or relevant process helps us focus on essential elements and gives us the potential to alter the model and see what happens.
For instance, if you want to minimize harm to individuals in auto accidents, create a computer model of the structures and forces involved.
If you want to build a Mars rover, build a model.
If you want to reduce international strife, create a model of causes.
If you are designing an app or coding make a prototype (beta) and test it.
Imagine being the problem, a key process, or the solution.
Imagination can help us understand a problem by visualizing it.
More understanding can occur in some cases if we go farther and imagine being the problem, a key process, or the solution.
So, if you want to understand space and time, you can imagine, as Einstein did, riding a light beam.
If you want to help a person who is very paranoid, you can imagine being that person and seeing the world as he does.
If you want to get a hit in a big baseball game, you can imagine going up to bat, seeing the ball clearly, and swinging crisply while you step into the pitch, etc.
Simulate or act out a key element of the problem.
Understanding complex or vague problems can be difficult.
Simulating or acting out some key elements of the problem can be productive.
For instance, if you are calculating probabilities of some event happening, you can simulate the situation and observe outcomes yourself.
If you want to help someone become more socially successful, you can act as that person does and observe the consequences.
If you want to determine why a spacecraft exploded, simulate its flight, and try ways of recreating the explosion. (perhaps using a computer model.)
Consider a specific example.
Problems often come to us in the abstract.
Creating a concrete example helps us explore the problem just as we might explore a specific example of dinosaur bones to understand dinosaurs.
So, if you want to determine what makes a person psychotic, consider real people who have become psychotic.
If you want to learn how to calculate the volume of a sphere, use a specific radius, such as one metre, and apply the formula.
If you want to determine why frogs are dying right and left in your community, examine the dead frogs.
We got a frog in the ER 🙂
Consider extreme cases.
Considering extreme cases is a type of considering a specific example.
Here the example is chosen to test the limits of a relevant parameter.
Sometimes this gives insight into important processes.
So, if you want to determine whether the level of intelligence affects retention on a police force, consider officers with the highest and lowest intelligence on the force.
If you want to determine what happens to black holes, in the long run, consider black holes that continue for infinitely long or black holes that suck up everything in the universe.
If you want to determine how temperature affects the flow of electricity, consider a temperature of absolute zero.
Acquire knowledge about relevant domains.
If you want to understand and solve an electrical problem, it may be necessary to learn about electrical systems.
If you want to solve the problem of how to keep humans free from solar-wind harm on the way to and from Mars, you may need knowledge of various domains of science, engineering, and medicine.
Great knowledge of relevant domains sometimes helps experts solve problems that others cannot.
If you want to reduce crime in a community, look at crime from the perspective of criminals and victims.
If you want to convince a hostage taker to surrender, take that person’s perspective.
If you want to avoid being bitten by a vicious dog, take the dog’s perspective.
Consider levels and systems.
If you want to prevent skin cancer, consider events that trigger cancer at the level of the external environment, the inter-cellular level, and the intra-cellular level.
If you want to reduce school violence, consider systems such as communities, families, and individuals.
If you want to predict the weather, consider local conditions and approaching fronts.
Strategies to help you simplify the task
Solve one part at a time.
It is sometimes possible to make a problem easier to solve by attacking one part at a time.
For instance, if you want to reduce international conflict in the Middle East, choose two countries with continuing conflict and focus on those.
If you want to send a human to Mars, send and retrieve information-gathering robots first.
If you want to improve your personality, choose one characteristic to improve at a time, starting, for instance, with your outgoingness.
Redefine the problem.
If a problem seems presently unsolvable, consider what value underlies the desire to solve that problem, and redefine the problem into something solvable.
For example, if a farmer cannot solve the problem of how to grow a specific crop on his land, he might analyze why he finds growing this crop is desirable.
If he decides that the reason is that the crop generally has a high-profit margin, he might review what other crops have a high-profit margin or even consider profitable uses of his land that do not involve farming.
He thereby has redefined the problem from raising a certain crop on his land to making a high profit with his land.
Strategies to help you determine the cause of the problem
Collect information about what happens before, during, and after the problem.
Problems are often triggered by something observable and reinforced by something that happens afterward.
So if Carrie often has temper tantrums, observe her and the situation carefully to collect information about what happens before, during, and after the tantrum.
You may find that pressing her to do difficult schoolwork usually happens before and allowing her to avoid the schoolwork happens after.
If Jake often has digestive problems, you might find that nothing special happens before, during, or after.
No specific foods seem to trigger the problem, so diet restriction is unlikely to help.
If you want to help heart surgery patients avoid depression after their surgery, observe them before, during, and after surgery.
Organize information into a table, chart, or list and look for patterns.
Information collected about a problem often becomes easier to search for patterns when put into a table, chart, or list.
The patterns may reveal the causes of the problem.
So, if you want to predict the next time a man will beat his wife, organize information about his prior instances of wife beating and look for a pattern, such as beating being delivered after he suffered an affront and drank heavily.
If you want to determine how to prevent auto accidents, put information about causes of past accidents into a table and look for patterns in the aggregated data, such as a high proportion of the accidents being caused by young males who have been drinking and were driving faster than the speed limit.
If you want to predict when a stock will rise, chart its price fluctuations over time and events in the past.
Try to make the problem worse.
One way to determine whether you know what causes a problem is to try to make the problem worse.
This may be worth doing when the supposed solution is so difficult, inconvenient, expensive, or dangerous as to justify caution in trying it.
So, if you suspect that eating strawberries is causing your nose to turn red, wait until your nose is its usual colour and eat a few strawberries.
If you think that a mentally exceptional child has tantrums because of changes in his routine, change the routine substantially on a few occasions and observe his behaviour.
Compare situations with and without the problem.
Comparing situations with and without the problem can sometimes shine a light on a difference that causes the problem.
So, if you want to eliminate bacterial infections that kill women giving birth, compare the care given to women who become infected with those who don’t.
You might see, as a 19th Century researcher did, that the women who are “helped” by physicians who don’t wash their hands between patients, women become ill, and the women who are helped by midwives, who do wash their hands, do not become ill.
If you want to know what causes AIDS, compare people who do and don’t have HIV and observe the people for several years.
If you want to know what causes violent crime, compare the intelligence of individuals who have and have not been convicted of violent crimes.
Consider multiple causes and interactions.
Sometimes two or more variables or influences cause a problem to occur.
For instance, the level of drunkenness depends on many factors, including the amount of alcohol consumed and the body weight of the person.
A harmful level of carbon monoxide gas may flow into a house only if the wind is blowing hard in a certain direction, the heat exhaust pipe is less than a meter above the roof, and the heat is on high.
If we do not look at all the causes of a problem, we may never find them.
So if you want to determine what causes autism, wood rot in a house, or the cause of someone’s death, consider multiple causes and interactions.
Consider non-linear effects.
Variables sometimes cause problems in a linear way, e.g., the more lead a child eats, the greater the harm.
However, some variables have curvilinear effects.
For instance, some arousal aids human performance, while a great deal of arousal impairs performance.
So, if you want to determine what causes a problem, consider non-linear effects.
Strategies involving the use of external aids to help you identify possible solutions
Ask someone, especially an expert.
If we look hard enough we can usually find someone who knows more about how to solve a particular problem than we do.
The fastest way to solve the problem may be to ask that person.
So if you don’t know how to fix a leaking faucet, or help your child act more outgoing, or improve your job interviewing success, ask an expert.
- Supervisor, Manager
- Ask an expert. (quality, medical, etc…)
Seek the answer in written material.
Written materials exist that show how to solve many problems.
New devices often come with instruction manuals.
Libraries and bookstores are loaded with “How To” books.
The Internet offers answers to many problems – if we ask the right question and use judgment about which websites are credible.
So if you want to learn how to improve the appearance of your nose, you could look up “cosmetic” or “nose” surgery in an Internet search engine and in a medical encyclopedia in the library.
Use a tool or technology.
Some problems require the right tool, which could be a hammer, a computer, or a metal detector.
So whenever you have a problem to solve, consider whether some type of technology might help you.
Apply a theory.
Good theories can point us in the right direction to find a solution to a problem.
For instance, Albert Bandura’s social learning theory suggests that if we want to teach a child to act altruistically, we would set an altruistic model in our behaviour, talk about our altruistic goals, and reward the child (perhaps with praise) when she acts altruistically.
Other theories in fields as different as economics and physics provide possible solutions to various types of problems.
Apply the scientific method.
The scientific method has helped to produce many of the great accomplishments of recent human history, such as doubling the average human lifespan, putting a human on the moon, and discovering planets orbiting other stars.
The method involves systematically collecting data to test a hypothesis, applying certain types of research design and analysis methods to the data, and being skeptical about the results.
Below is an overview of the Scientific Method.
APPENDIX: Introduction to the Scientific Method
- Introduction to the Scientific Method
The scientific method is the process by which scientists, collectively and over time, endeavour to construct an accurate (that is, reliable, consistent and non-arbitrary) representation of the world.
Recognizing that personal and cultural beliefs influence both our perceptions and our interpretations of natural phenomena, we aim through the use of standard procedures and criteria to minimize those influences when developing a theory.
As a famous scientist once said, “Smart people (like smart lawyers) can come up with very good explanations for mistaken points of view.”
In summary, the scientific method attempts to minimize the influence of bias or prejudice in the experimenter when testing a hypothesis or a theory.
1. Observation and description of a phenomenon or group of phenomena.
2. Formulation of a hypothesis to explain the phenomena. In physics, the hypothesis often takes the form of a causal mechanism or a mathematical relation.
3. Use of the hypothesis to predict the existence of other phenomena, or to predict quantitatively the results of new observations.
4. Performance of experimental tests of the predictions by several independent experimenters and properly performed experiments.
If the experiments bear out the hypothesis it may come to be regarded as a theory or law of nature (more on the concepts of hypothesis, model, theory and law below).
If the experiments do not bear out the hypothesis, it must be rejected or modified.
What is key in the description of the scientific method just given is the predictive power (the ability to get more out of the theory than you put in; see Barrow, 1991) of the hypothesis or theory, as tested by experiment.
It is often said in science that theories can never be proved, only disproved. There is always the possibility that a new observation or a new experiment will conflict with a long-standing theory.
As just stated, experimental tests may lead either to the confirmation of the hypothesis or to the ruling out of the hypothesis.
The scientific method requires that a hypothesis is ruled out or modified if its predictions are clearly and repeatedly incompatible with experimental tests.
Further, no matter how elegant a theory is, its predictions must agree with experimental results if we are to believe that it is a valid description of nature.
In physics, as in every experimental science, “experiment is supreme” and experimental verification of hypothetical predictions is absolutely necessary.
Experiments may test the theory directly (for example, the observation of a new particle) or may test for consequences derived from the theory using mathematics and logic (the rate of a radioactive decay process requiring the existence of the new particle).
Note that the necessity of experiment also implies that a theory must be testable. Theories which cannot be tested, because, for instance, they have no observable ramifications (such as, a particle whose characteristics make it unobservable), do not qualify as scientific theories.
If the predictions of a long-standing theory are found to be in disagreement with new experimental results, the theory may be discarded as a description of reality, but it may continue to be applicable within a limited range of measurable parameters.
For example, the laws of classical mechanics (Newton’s Laws) are valid only when the velocities of interest are much smaller than the speed of light (that is, in algebraic form, when v/c << 1).
Since this is the domain of a large portion of human experience, the laws of classical mechanics are widely, usefully and correctly applied in a large range of technological and scientific problems. Yet in nature, we observe a domain in which v/c is not small.
The motions of objects in this domain, as well as motion in the “classical” domain, are accurately described through the equations of Einstein’s theory of relativity. We believe, due to experimental tests, that relativistic theory provides a more general, and therefore more accurate, description of the principles governing our universe, than the earlier “classical” theory.
Further, we find that the relativistic equations reduce to the classical equations in the limit v/c << 1.
Similarly, classical physics is valid only at distances much larger than atomic scales (x >> 10-8 m).
A description which is valid at all length scales is given by the equations of quantum mechanics.
We are all familiar with theories which had to be discarded in the face of experimental evidence. In the field of astronomy, the earth-centred description of the planetary orbits was overthrown by the Copernican system, in which the sun was placed at the center of a series of concentric, circular planetary orbits.
Later, this theory was modified, as measurements of the planets motions were found to be compatible with elliptical, not circular, orbits, and still, later planetary motion was found to be derivable from Newton’s laws.
Error in experiments has several sources. First, there is error intrinsic to instruments of measurement. Because this type of error has an equal probability of producing a measurement higher or lower numerically than the “true” value, it is called random error.
Second, there is non-random or systematic error, due to factors which bias the result in one direction. No measurement, and therefore no experiment, can be perfectly precise. At the same time, in science, we have standard ways of estimating and in some cases reducing errors.
Thus it is important to determine the accuracy of a particular measurement and, when stating quantitative results, to quote the measurement error. A measurement without a quoted error is meaningless. The comparison between experiment and theory is made within the context of experimental errors.
Scientists ask, how many standard deviations are the results from the theoretical prediction? Have all sources of systematic and random errors been properly estimated?
As stated earlier, the scientific method attempts to minimize the influence of the scientist’s bias on the outcome of an experiment. That is, when testing a hypothesis or a theory, the scientist may have a preference for one outcome or another, and it is important that this preference, not bias the results or their interpretation.
The most fundamental error is to mistake the hypothesis for an explanation of a phenomenon, without performing experimental tests.
Sometimes “common sense” and “logic” tempt us into believing that no test is needed. There are numerous examples of this, dating from the Greek philosophers to the present day.
Another common mistake is to ignore or rule out data which do not support the hypothesis. Ideally, the experimenter is open to the possibility that the hypothesis is correct or incorrect. Sometimes, however, a scientist may have a strong belief that the hypothesis is true (or false), or feels internal or external pressure to get a specific result.
In that case, there may be a psychological tendency to find “something wrong”, such as systematic effects, with data which do not support the scientist’s expectations, while data which do agree with those expectations may not be checked as carefully. The lesson is that all data must be handled in the same way.
Another common mistake arises from the failure to estimate quantitatively systematic errors (and all errors). There are many examples of discoveries which were missed by experimenters whose data contained a new phenomenon, but who explained it away as a systematic background.
Conversely, there are many examples of alleged “new discoveries” which later proved to be due to systematic errors not accounted for by the “discoverers.”
In a field where there are active experimentation and open communication among members of the scientific community, the biases of individuals or groups may cancel out, because experimental tests are repeated by different scientists who may have different biases.
In addition, different types of experimental setups have different sources of systematic errors. Over a period spanning a variety of experimental tests (usually at least several years), a consensus develops in the community as to which experimental results have stood the test of time.
In physics and other science disciplines, the words “hypothesis,” “model,” “theory” and “law” have different connotations in relation to the stage of acceptance or knowledge about a group of phenomena.
A hypothesis is a limited statement regarding cause and effect in specific situations; it also refers to our state of knowledge before experimental work has been performed and perhaps even before new phenomena have been predicted. To take an example from daily life, suppose you discover that your car will not start. You may say, “My car does not start because the battery is low.”
This is your first hypothesis. You may then check whether the lights were left on, or if the engine makes a particular sound when you turn the ignition key. You might actually check the voltage across the terminals of the battery. If you discover that the battery is not low, you might attempt another hypothesis (“The starter is broken”; “This is really not my car.”)
The word model is reserved for situations when it is known that the hypothesis has at least limited validity. An often-cited example of this is the Bohr model of the atom, in which, in an analogy to the solar system, the electrons are described as moving in circular orbits around the nucleus.
This is not an accurate depiction of what an atom “looks like,” but the model succeeds in mathematically representing the energies (but not the correct angular momenta) of the quantum states of the electron in the simplest case, the hydrogen atom.
Another example is Hook’s Law (which should be called Hook’s principle, or Hook’s model), which states that the force exerted by a mass attached to a spring is proportional to the amount the spring is stretched. We know that this principle is only valid for small amounts of stretching.
The “law” fails when the spring is stretched beyond its elastic limit (it can break).
This principle, however, leads to the prediction of simple harmonic motion, and, as a model of the behaviour of a spring, has been versatile in an extremely broad range of applications.
A scientific theory or law represents a hypothesis, or a group of related hypotheses, which has been confirmed through repeated experimental tests. Theories in physics are often formulated in terms of a few concepts and equations, which are identified with “laws of nature,” suggesting their universal applicability.
Accepted scientific theories and laws become part of our understanding of the universe and the basis for exploring less well-understood areas of knowledge. Theories are not easily discarded; new discoveries are first assumed to fit into the existing theoretical framework.
It is only when, after repeated experimental tests, the new phenomenon cannot be accommodated that scientists seriously question the theory and attempt to modify it.
The validity that we attach to scientific theories as representing realities of the physical world is to be contrasted with the facile invalidation implied by the expression, “It’s only a theory.”
For example, it is unlikely that a person will step off a tall building on the assumption that they will not fall, because “Gravity is only a theory.”
Changes in scientific thought and theories occur, of course, sometimes revolutionizing our view of the world (Kuhn, 1962). Again, the key force for change is the scientific method and its emphasis on experiment.
While the scientific method is necessary for developing scientific knowledge, it is also useful in everyday problem-solving. What do you do when your telephone doesn’t work?
Is the problem with the handset, the cabling inside your house, the hookup outside, or in the workings of the phone company?
The process you might go through to solve this problem could involve scientific thinking, and the results might contradict your initial expectations.
Like any good scientist, you may question the range of situations (outside of science) in which the scientific method may be applied.
From what has been stated above, we determine that the scientific method works best in situations where one can isolate the phenomenon of interest, by eliminating or accounting for extraneous factors, and where one can repeatedly test the system under study after making limited, controlled changes in it.
There are, of course, circumstances when one cannot isolate the phenomena or when one cannot repeat the measurement over and over again. In such cases, the results may depend in part on the history of a situation. This often occurs in social interactions between people.
For example, when a lawyer makes arguments in front of a jury in court, she or he cannot try other approaches by repeating the trial over and over again in front of the same jury. In a new trial, the jury composition will be different. Even the same jury hearing a new set of arguments cannot be expected to forget what they heard before.
The scientific method is intricately associated with science, the process of human inquiry that pervades the modern era on many levels. While the method appears simple and logical in the description, there is perhaps no more complex question than that of knowing how we come to know things.
In this introduction, we have emphasized that the scientific method distinguishes science from other forms of explanation because of its requirement of systematic experimentation.
We have also tried to point out some of the criteria and practices developed by scientists to reduce the influence of individual or social bias on scientific findings. Further investigations of the scientific method and other aspects of scientific practice may be found in the references listed below.
1. Wilson, E. Bright. An Introduction to Scientific Research (McGraw-Hill, 1952).
2. Kuhn, Thomas. The Structure of Scientific Revolutions (Univ. of Chicago Press, 1962).
3. Barrow, John. Theories of Everything (Oxford Univ. Press, 1991).
Mathematics is essential to solving some problems, such as how to put an exploring robot on Mars, how to determine whether one treatment is generally more effective than another for pancreatic cancer, and how to defend an area from enemy missiles.
There are many types of mathematics, but even the simplest can be helpful in problem-solving.
For example, if you want to make yourself happier, you might start by counting the number of days in the next 14 that you feel happy.
Then you have a baseline to use as a comparison after you make some behavioural or situational changes in pursuit of more happiness.
If you wanted to determine whether a new treatment for diabetes is better than the usual treatment, you might use a t-test to compare what the blood sugar levels are of the group of people using the new treatment with a group of people using the usual treatment.
Use a formula.
Sometimes, a formula can help solve a problem.
The formula could be a recipe, a set of chemicals, pressures, and heat levels, or an established method of doing something else.
So, if you want to develop a permanent way of marking the right lens for contact lens wearers, start with the formulas for permanent pens and markers.
If you want to create a better toothpaste, start with a typical formula and try altering its components.
Strategies involving the use of logic to help you identify possible solutions
Reason by analogy, using what you have learned about similar problems.
Going through life we solve many problems. Often the problem-solving methods we used and the actual solutions we found effective in the past can work to solve a current problem.
So, if you have solved before a problem with a neighbour’s dog barking all night, the same solution may work with another neighbour who plays loud music all night.
In fact, the same solution might be something to try with anyone who is chronically annoying.
Use deductive reasoning.
Deductive reasoning involves going from a general rule to an application in a specific instance.
So, if we assume that people commit murder only if they have a motive, then we look for murder suspects among people who had a motive.
If we start with the premise that people do what they think is in their best interest, we try to provide employees incentives to work productively.
If we believe causes must occur prior to effects, we can conclude that a huge grass fire did not cause a high level of asthma attacks that started two days before the fire.
Use inductive reasoning.
Inductive reasoning involves drawing on specific instances to form a general rule.
So, if you want to know whether your child will leave your yard if left outside alone, one thing you could do would be to set up that situation and covertly observe the child on several occasions.
If you want to find out whether eating chocolate causes your acne, eat chocolate every day for two weeks, then not at all for two weeks, then every day again for two weeks, then not at all for two weeks, and record the state of your skin every day.
If you want to know whether a genetically altered microbe will reproduce in field settings, put a specific number of the microbes in field settings and later count the number.
Our thinking contains many assumptions or beliefs that have never been well tested, such as that our religion or ethnic group is the best one.
If you want to reduce inter-group conflict, questioning these assumptions might help.
If you want to stop children from starting to use illegal drugs, question the assumption that educating them about the effects of the drugs will discourage use.
If you want to develop close relations with your supervisor, you may benefit from questioning your assumption that all supervisors are power hungry and self-centered.
Strategies using a possible solution as a starting point to help you solve a problem
Guess, check, and adjust.
It may work to guess at a solution, especially if the range of possible solutions is limited as in a multiple-choice test.
You can check to see whether your guess is right, and then eliminate the option if it is not.
As Sherlock Holmes said, once you have eliminated all the possibilities except one, that one must be the solution.
Sometimes guessing can help us even when the range of possible answers is unlimited.
For instance, in solving for x in x + y = 12 and 2x – y = 3, if there are no answers from which to choose, and you don’t know how to solve simultaneous equations, you can guess at what x is, and if you miss, you can use how much you miss by to make a better second guess, and so on, adjusting your guessing as you go.
That, in essence, is how software for structural equation modelling proceeds to a solution.
In solving a printed maze, looking at the goal area and working backward sometimes offers the fastest solution.
That may occur because the maze maker did not expect you to use this strategy.
Also, if you want to recreate the events involved in a crime, you could start with a possible perpetrator and the available evidence, work backward in time, and see what makes sense.
Strategies to help you determine which possible solution is best
Estimate the likely costs and benefits of possible solutions.
Use deductive and inductive reasoning and the scientific method to estimate the costs and benefits of each possible solution.
For instance, if you have a wart on your hand, one option is to buy a commercial product that slowly disintegrates the wart.
The costs include the financial cost of buying the product, the time spent in applying it daily, the cost of bandages to cover the area, the inconvenience of wearing bandages, the possible embarrassment of being asked why you are wearing a bandage, and the possibility of a life-long scar.
On the benefit side, the wart is very likely to be eliminated.
Choose one or more options to implement.
Solving a problem usually involves doing something.
So, use deductive and inductive reasoning and the scientific method to choose one or more options to implement.
This usually involves weighing the costs and benefits of each option according to your values.
For instance, if you want to eliminate a wart, you might choose to do nothing and bet on the significant chance the wart will go away on its own and leave no scar.
You might choose this approach because you have strong feelings against creating a life-long scar, such as those caused by more active approaches.
Implement the best possible solution and collect information about the effects of it.
Use deductive and inductive reasoning and the scientific method to determine the effects of the chosen option.
So, if you want to eliminate a wart, you might wait a year and see whether it goes away on its own.
If it doesn’t, you could choose a more active option.
Strategies using geometry for problem solving
Do the opposite of what you have been doing.
This 180-degree shift in approach is often essential for helping individuals reduce anxiety about specific situations, such as public speaking or seeing someone bleeding.
Phobics tend to avoid the situation, thereby making their anxiety increase.
The best way to reduce anxiety is to expose oneself, gradually or not, to the feared situation.
This principle also comes into play when a physician notices a patient is getting worse and worse.
That may be the time to decrease the medication rather than increase them — if the medications are causing the worsening.
Try a totally different approach.
If many individuals have tried to solve a certain problem and failed, it might be helpful to try an approach that is not just somewhat different but very different.
One might describe this method geometrically as moving the attack to a different plane.
Einstein did that with his theory of general relativity.
Most such efforts will eventually be considered crackpot; some will be called a work of genius.
Strategies to help you function optimally while problem solving
Record and fully consider options.
It is often wise to consider a range of solution options when engaged in problem-solving.
Several options may solve a problem, but one may solve the problem more completely or cheaply.
Individuals may squelch their own good ideas or the good ideas of others by immediately rejecting ideas.
Hence, it may help to record possible solutions and consider them fully.
Even a very bad idea might point in a useful direction if it is not pushed aside too quickly.
Set a goal with a purpose you value.
Setting a goal with an outcome we value tends to help us achieve more.
So, if you have an assignment of math problems to complete, you might set a personal goal of completing all of them correctly for the purpose of earning an “A” on the assignment and in the course so that you can improve your chances of gaining admission to medical school, so you can spend your life helping ill children.
If you have a problem of getting your research approved by an ethics board, set a goal of gaining approval so that you can do the research and help others with your findings.
Distractions slow the problem-solving process.
Distractions can include environmental events such as phone calls and machinery noise.
Distractions can also include repeated intrusive thoughts (“This is a terrible situation!”).
One way to avoid external distractions is to go somewhere peaceful where no one can find you.
Another way is to disconnect the phone and put up a “Do not disturb, please” sign.
One way to reduce intrusive thoughts is to tell yourself that you will think about these emotion-laden matters at a specific later time, but for now, you are going to yell “STOP!” every time the thought intrudes.
Another way of reducing intrusive thoughts is to write them down or to tell someone close to you about them.
Work in a new setting.
New settings sometimes prompt new types of thinking that can be useful in solving hard problems.
For instance, go sit and think in the quiet park across from your headquarters, in a forest cabin, or in a different library.
Adjust the time limit to optimum.
Some problems are easy to solve but tedious.
It may facilitate efficiency to set an artificially brief time frame for completion, e.g., “I’m going to finish these math problems in 30 minutes.”
For difficult problems, increasing the time frame for the solution may help by reducing distraction-provoking anxiety.
So if you are asked to solve a difficult problem, ask for an amount of time that will be sufficient to eliminate time pressure but still not so long as to induce inefficiency.
Work with someone.
All else being equal, several people working on a difficult problem tend to produce a better solution than one person.
Some efficiency may be lost, so working with someone may best be reserved for very difficult problems.
So, if you want to clone a bonobo, work with someone.
If you want to end your dependency on tobacco, work with someone.
Create a positive mood with an optimal arousal level.
People work better when they have a positive mood and a moderate arousal level.
To create a positive mood, you could engage in some activity you greatly enjoy, such as listening to music or reading a book, or you could think back about huge triumphs and outstanding moments in your life.
To avoid excessive arousal, you could use a relaxation method such as deep breathing, tensing and relaxing muscle groups, and telling yourself to stay calm.
Think of the problem as a challenge or an opportunity.
No one wants to have “problems.”
So we often think of problem-solving as an unfortunate, unpleasant task.
Such a negative view of the problem solving may impair our performance on the task.
In order to keep a positive mood and keep working on a problem, it is helpful to think of the problem as a challenge or an opportunity.
So, if the barking of your neighbour’s dog is driving you batty, look at the situation as an opportunity to practice your assertion skills.
If your PC won’t come on, look at the situation as an opportunity to challenge yourself, as you might with an anagram.
If your investments go sour, think of the situation as a challenge: Do you still have what it takes to make yourself rich through earnings or investment?
Confidence helps us persist in problem-solving, and confidence comes most powerfully from problem-solving success.
So, think about past problem-solving successes or solve another problem to boost your confidence in solving a specific problem.
Useful thoughts include “I have solved more difficult (or similar) problems,” “I know how to approach this problem,” and “I can solve this problem if I try hard enough.”
Take a break.
People can get fixed on a certain way of thinking about a problem or a specific class of possible solutions.
It sometimes helps to take a break and think about matters unrelated to the problem in order to open the mind to new ideas.
Some people benefit from sleeping on a problem.
Persistence in problem-solving often pays off.
It took many years to build the Great Wall of China.
It may take you some time to solve a problem.
Your odds of success often go to 0 when you give up.
With continued effort, you have a chance. So, whether you want to want to become a millionaire or you want to eliminate the use of landmines, persist.
If one possible solution fails, try another one or try another problem-solving strategy.
Note though that persistence can become maladaptive if the goal is unrealistic.
In some cases, the best course is to accept a problem as presently unsolvable and focus (with persistence) on other, solvable problems.
Strategies to help you solve multiple problems
Adopt a problem solving orientation.
People who look for problems to solve have a decided advantage over others.
These individuals can often identify problems when the problems are small enough to be easily solved and when enough time is available to allow the use of good problem-solving strategies.
For instance, it is far easier to lose a few kilograms of weight than to lose 50 kilos.
Individuals who wait for problems to become unbearable or unavoidable before dealing with them may experience unnecessary stress when circumstances force them to tackle a problem.
Naturally, looking for problems to solve will tend to lead to more problems solved.
A math student who does all the problems in a textbook rather than just the half assigned is an example of that principle.
So is an executive who looks for problems that keep her workers from being productive.
Often there are multiple problems a person could try to solve at any one time.
Emergency room physicians have developed the custom of triage, which is assessing the urgency of the health problem of each of the current patients.
In problem-solving, it is wise to consider during triage which problem has
(1) the most important outcome, (2) the greatest chance for the solution, and (3) the nearest deadline.
So, if you lose your 3-year-old child in an outdoor crowd and your 8-year-old child has a headache, you focus on the lost child because the risk of harm is greater with that child.
If you have two problems to solve, and one, such as developing a method of time travel, seems currently unsolvable, work on the other problem first.
If you have two important problem-solving assignments, with one due tomorrow and one due in a week, focus first on completing the one due tomorrow.
Sometimes the problem with the most important outcome is different from the problem with the best chance of solution or the nearest deadline.
Then you have to apply your own judgment in weighing the triage considerations.
Solve one problem at a time.
When faced with multiple problems, individuals may panic or lose hope and then quit trying.
When facing more than one problem, to the extent possible, focus on solving one at a time.
So if you are overweight and smoke, choose one of these problems to work on at a time.
If you dislike your job and your roommate, choose one to work on.
If you want to improve your writing and speaking skills, choose one with which to start.