In this article, we examine systematic problem solving: what it is and how it operates. Systematic problem solving is a process. We must learn how to reason through a problem systematically, identifying and evaluating possible alternative solutions until we determine which is best.
In every facet of our lives at work and at home, in our relationships, and as members of a community we face problems for which we hope to find viable solutions. Optimal solutions. What approach to solving our problems is most likely to yield the best outcomes?
The Socratic method and Occam’s razor are analytical techniques with relevant applications to systematic problem solving.
We become better problem solvers when we understand the elements of reasoning and can apply them consciously in keeping with the standards of critical thinking.
We’ve all heard it said of someone: “She just has a knack for solving problems.” While some people are more inclined to analysis and finding solutions, effective problem solving can be learned. We can all become better problem solvers by learning how to approach problems systematically.
Watch the following video to learn more about systematic problem solving.
Exercise: Systematic Problem Solving
Solving problems requires us to follow an ordered sequence of reasoning, one step leading to the next and building on the one that came before. Let’s outline the sequence the critical thinker follows in working systematically through a problem. The problem, we’ll say, is some vital public issue about which people disagree.
1- Identify the viewpoints from all relevant sides of the issue and gather the arguments offered in support of each.
2- Break the arguments down into their component statements (assumptions, premises, conclusions) and determine what further implications may be drawn from them.
3- Look for internal contradictions within these statements and implications.
4- Identify opposing claims between the various arguments.
5- Assign a relative “value” to the competing claims. The values are an index for grading the relative strengths of the opposing claims.
6- Tabulate the values of the various claims to determine which argument (or viewpoint) is strongest, or most justifiable.
When assigning a relative “value” to the competing claims, come up with a values scale. Yours might run from 1 = weak to 4 = strong. You might keep in mind the following:
- Claims supported by strong evidence and reasoning deserve a higher valuation.
- Claims with internal contradictions warrant a lower valuation.
- The values should be adjusted depending on how relevant the claims are to the main issue at hand. (Not all claims are equally relevant or important.)
- Disregard any incredible claim unless it is backed up by sufficient credible evidence.
The problem solving process does not guarantee that we will arrive at the truth or reach the best of all possible solutions. After all, our own biases could affect how we gather and evaluate the information relevant to the issue. Or we simply might not have all the relevant information. But the process gives us a rigorous critical framework for reasoning through problems from start to finish.
The Socratic Method
A couple of other models or techniques for problem solving merit our attention as critical thinkers.
The Socratic method* is a heritage of classical Greek philosophy. It originated more than 2000 years ago with Plato’s Socratic Dialogues.
The Socratic method is a form of reasoned inquiry. It involves asking questions that direct us to examine what we believe about something—an issue, an event, the proposed solution to a problem. These questions prompt us to defend our viewpoints by challenging the grounds (e.g., assumptions, premises, and hypotheses) on which they rest. The Socratic method tests the validity of our reasoning. Why do we believe such-and-such? On what basis? How do we support this belief?
Who poses the questions? We do—to ourselves, in order to critically evaluate our own reasoning; or to others, to challenge them to defend the validity of their positions.
The Socratic method unfolds through a progression of questions and responses. The issue or problem we subject to the method determines what specific questions to ask. If we are good critical thinkers, our inquiry should tell us what questions need to be asked to thoroughly vet our reasoning on any given issue.
In the Socratic method, questions follow a logical sequence, one leading purposefully to the next. What drives our next question is the response to our preceding question. Answer x will direct us to one succeeding question, while answer y will direct us to another.
Consider a simple example:
|Why do you think paper shopping bags are better than plastic ones?
|Because paper is environmentally safer than plastic.
|What evidence do you have that it is safer for the environment?
|Because I can put old newspapers in the paper bags for curbside recycling pick-up.
|How is this criterion relevant to determining the superiority of paper versus plastic?
The whole foundation of the Socratic method is to pursue our inquiry where it leads, guided by the answers we derive at each step along the way. We keep asking questions until our reasoning about something has been fully scrutinized and validated (or not).
The Socratic method helps us become better problem solvers. It compels us to analyze our reasoning critically and expose any weaknesses in it. It requires us to defend our viewpoints against thoughtful challenges to their validity. And ultimately, it forces us to abandon in our thinking what we cannot reasonably defend.
Line of Questioning Example
To see how the Socratic method unfolds, let’s pursue our “paper versus plastic” example a bit further. Read each question in the table below and click the answer button to see each reply. Notice how each answer leads to the next question.
|The Socratic Method at the Supermarket
|Paper versus plastic?
Paper bags are better – hands down.
This is your subjective opinion?
It’s my informed judgment.
What makes your judgment “informed”?
I’ve been grocery shopping twice a week forever, so I should know.
Your judgment derives, then, from your subjective experience?
How is your anecdotal experience more valid than anyone else’s in determining which type of bag is better?
I’m not saying it is. I just know that for me, paper is the only way to go.
Would someone else’s experience be as valid a basis for claiming that plastic is better?
I suppose. Although, I really don’t understand how anyone could come to that conclusion.
How did you reach your conclusion?
Through bagging groceries over a long period of time.
What, in your experience, makes paper better than plastic?
For one thing, it’s a stronger bag.
How do you know this?
Whenever I’ve tried plastic – when there weren’t any paper bags available – the handle broke or the bag split.
This has happened every time?
Well, maybe not every time.
What percentage of the time?
Hard to say. But a lot.
Was the number of items you put in a plastic bag comparable to what you would put in a paper bag?
I don’t know – I think so.
Was the weight of the items you put in a plastic bag comparable to what you would put in a paper bag?
I don’t know – I think so.
Do you think your experience with failed plastic bags is a valid basis for making the generalization that paper is stronger?
I think it is strong evidence for that generalization.
Can you offer any other evidence that supports paper’s superior strength?
Can you cite the findings of a study that compared the relative strengths of paper and plastic bags?
I don’t need a scientific study to tell me what the deal is. I trust my experience.
Do you have any other reason for asserting that paper is better than plastic?
I do. Paper is environmentally safer than plastic.
How do you know this?
Please – it’s a no-brainer.
What evidence do you have that paper bags are safer for the environment?
I just saw a segment about it on ABC’s Primetime.
What did the segment report?
That plastic shopping bags are an environmental hazard because they don’t biodegrade and can’t be recycled.
What evidence did the Primetime segment offer to support these claims?
John Stoessel interviewed a couple of environmental activists.
Did you check on the credibility of these activists? Why?
They sure seemed like they knew what they were talking about.
Occam’s razor, also spelled Ockham’s razor (named for the 14th-century English logician William of Ockham), is a philosophical principle with important implications for problem solving. It states that the explanation for something should rely on as few assumptions as possible. (It is, for this reason, known as the “principle of parsimony.”) Occam’s razor tells us that we should side with the less complicated of two equally valid explanations for something. The principle is distilled in a popular adage: The simplest solution is likely the best. Occam’s razor is also often called the “law of succinctness.”
The principle endorses simplicity because fewer assumptions mean fewer possibilities for error. Assumptions that are not needed to support a proposed solution are best left out, or “shaved off.” All they do, Occam’s razor suggests, is make the solution (or explanation) more likely to be in error.
Wielding Occam’s Razor – An Example
SAT scores took a sharp drop nationwide from last year to this year.
Why? What explains this?
Education expert 1 attributes the drop to adoption of a longer, tougher test format.
Education expert 2 attributes it to the new test format, the decline of basic writing skills, unintended consequences of the Leave No Child Behind legislation, and some demographic factors.
Applying Occam’s razor leads us to embrace which explanation? Find below correct answer to see if you are correct.
Explanation 1 is correct
Explanation 1 is correct. This explanation is simpler and assumes less.
Explanation 2 is correct
Explanation 2 is incorrect. This explanation is more complicated than 1 and assumes more.
Elements of Reasoning
The elements of reasoning are its component parts. Gerald Nosich describes them in Learning to Think Things Through as the “nuts and bolts” of critical thinking. There are eight main elements:
All eight are always in the mix whenever we reason through something. They form an inventory of what is happening when we think critically: adopting a point of view, gathering information, making assumptions, drawing conclusions, etc. The elements describe different aspects of critical thinking. Some aspects, as we will see, relate closely to one another and thus overlap.
The critical thinker understands how the elements interact and uses them as tools for reasoning more effectively. The elements, when applied consistently with the standards of critical thinking (for example, clarity, accuracy, relevance, etc.), result in thinking that is sound and well-founded.
We draw on the discussion of the elements in Learning to Think Things Through to describe the elements of reasoning and explain how they are employed.
Point of View
Reasoning always takes place within some point of view. The same matter considered from different points of view may appear not at all the same. For example, a wealthy person is bound to see an inheritance tax differently than would a poor person. These two people would have different perspectives on the tax, stemming from their dissimilar vantage points. Therefore, in reasoning about it, they likely would have different purposes, make different assumptions, and draw different conclusions.
Each of us is at the center of our own point of view (POV). It cannot be otherwise. We see from our vantage point. The egocentric nature of point of view, however, does not automatically mean that we assume ours is more valid than someone else’s.
The critical thinker must be able to identify POVs. From what perspective is an issue being looked at or characterized? It is also important for the critical thinker to be able to apply someone else’s perspective to an issue to understand how he or she would view it.
Purpose is the goal or objective of reasoning. It describes the desired outcome or intent. We can identify purpose in anything that entails reasoning, from an op-ed piece (develop an argument regarding some political issue), to product assembly instructions (explain to consumers how to put the product together), to a “Dear John” letter (offer the rationale for why a relationship must end). The critical thinker always asks, for any product of reasoning, what is its purpose?
All reasoning is directed at some question. In any reasoning endeavor, the critical thinker should ask, “What is the question at issue?” The purpose in reasoning, as we already noted, is the goal. The question at issue is what needs to be answered or addressed in order to realize the purpose. The following example draws the distinction:
- The purpose of product assembly instructions is to enable consumers to assemble a product on their own.
- The question with the assembly instructions is, “What set of instructions would best meet this purpose (that is, would be clearest and most complete)?”
Reasoning has to begin somewhere. It begins with our assumptions. These encompass everything we take as a given when we reason through something.
Consider: You’re the new general manager of a professional baseball team that just finished a losing season. Your task is to improve the team. As you undertake the job, you assume the following:
- The team’s won-lost record faithfully reflects its talent level
- You need better players
- The only way to upgrade your roster is to spend more money
These suppositions mark your starting point. You take their validity for granted. Assumptions may be acknowledged upfront. But the core ones people make when they reason—the ones on which their reasoning very much relies usually go unstated. Assumptions are always present in any form of reasoning. They are at the heart of arguments. Being able to identify them (others’ assumptions and our own) is crucial to critical thinking.
Implications and Consequences
Reasoning delivers us to a position or viewpoint about something. The implications and consequences of our reasoning are what extend beyond the position we reach. They form the answer to the question, “What follows from our reasoning?”
Let’s see how this operates: After much thought, we conclude that the sale of tobacco should be banned because tobacco is a public health scourge. A consequence of our reasoning would be the loss of massive public revenues from taxes on cigarette sales—money that governments would have to recover through some other means. Another consequence might be the rise of a black market in contraband cigarettes. An implication of our reasoning would perhaps be that a ban should also be considered in the sale of high-fat foods, which are directly implicated in epidemic levels of cardiovascular disease and diabetes.
As critical thinkers, we must always consider the likely consequences of reasoning and what implications it points toward. Being able to identify and evaluate these consequences and implications is indispensable to critical thinking.
We use information whenever we reason. Information takes many forms: statistical data, evidence, our observations, the testimony of others, etc. In thinking critically about an issue, we need to determine what information is relevant to it. We also must be adept at identifying what information we need to assess the issue but are lacking.
Say we’re trying to decide whether to go with DSL or cable modem for our home Internet connection. We gather as much information as we can to help us decide. We find a good explanation of the technological difference between DSL and cable (and what this difference means for the home user). We research the computer hardware requirements for being able to operate on each. We get information on the comparative costs. A friend, whose opinion we invite, e-mails us an article about Wi-Fi technology. The article, though interesting, is not relevant to our consideration so we set it aside. As we proceed, we realize that in order to make the soundest decision, we really need some information on consumers’ comparative experiences with DSL and cable. So we go in search of such information.
Reasoning often follows from bad or incomplete information. Therefore, as critical thinkers, we must be able to skillfully evaluate information Is it accurate? Is it all here? We need to recognize when we don’t have sufficient information to draw a reasonable conclusion.
Our reasoning takes form in concepts. When we think about anything, our thinking turns on some concept of that thing. Say, for example, we are reasoning about the fairness of a new law. Our thinking must have an operative concept of fairness. The concept, not the thing itself, is what we hold in our mind as our understanding of it.
Spotting the concepts in reasoning can be a challenge for the critical thinker. Most of us tend to take our concepts for granted. To think critically requires us to be aware of the concepts we hold and consider how they bear on our reasoning.
Conclusions and Interpretations
All of our reasoning entails conclusions about and interpretations of things ideas, situations, issues, events, etc. These are the outcomes of our thinking. Let’s return to our previous “cable modem versus DSL” example to see how they fit in. After due consideration of all the information, we concluded that cable is the better service for us. En route to that conclusion, we interpreted all the information in terms of its application to us.
When we think critically, we ask what conclusions are being drawn and how something is being interpreted.
Gerald Nosich directs us to consider two additional elements in order to gain a fuller understanding of reasoning: context and alternatives. These extra ones, plus the 8 elements of reasoning, comprise what Nosich calls the 8+ elements.
There are always alternatives when we reason. There are assumptions we could make other than the ones we do make. There are interpretations possible other than those we arrive at. We could reach an alternative conclusion to the one we come to. Thinking about the elements in terms of alternatives, Nosich suggests, is empowering because it allows us to see many paths down which our reasoning could go.
Our reasoning doesn’t happen in a vacuum. It always takes place in a context. The context is the setting or background for our reasoning. It might be cultural, psychological, emotional, scientific—or countless others. We could reason our way through an issue in distinctly different contexts. Take criminal sentencing guidelines, for example. We could think about them in the context of victims’ rights, or the context of the public costs of incarceration, or the context of fairness (i.e., does the punishment fit the crime?), etc.
When we think through an issue in a particular context, we subject the issue to the values, norms, and presumptions of that context. It is always of interest to the critical thinker to understand how context shapes reasoning.
Exercise: Employing the Elements of Reasoning
You have a job offer in your field from a company located in another state. Should you accept it? Employ the elements of reasoning to think your way through this important personal decision. Consider the following questions, which will guide you through the circle of elements.
What points of view should I consider?
- My own
- My spouse’s
- My children’s
- That of a good friend and colleague, whose judgment I value
What is the purpose of my career?
- To do fulfilling work
- To earn enough to support my family and our lifestyle aspirations
- To reach the pinnacle of my profession
What is/are the main question(s) at issue?
- Is this a wise career move?
- Is this move the best thing for my family?
What are the main assumptions I make about my career?
- That it is an important part of my self-identity
- That I need to balance it with my family life
- That I could jeopardize my long-term aspirations if I make the wrong decision
- That I will never want to switch careers
What are the main consequences of accepting the job offer?
- That I will have to relocate my family
- That we will have to sell our house and find a home where we’re moving
- That I will leave valued colleagues
- That I will earn more and have greater responsibilities
What are the main implications of accepting the job offer?
- That professional demands on me will increase because of increased responsibilities
- That my young children will see less of their grandparents
- That I will need to stay at the new job for 3 to 5 years in the interest of my career development
What information do I have about making this decision?
- I have done my homework about the company that has made the offer (e.g., recent performance, reputation in the industry, how it compares with other companies)
- I have all the details of the offer (salary, benefits, relocation stipend, title and responsibilities, who I would report to)
- I know my spouse’s concerns/issues
What information do I need to have about making this decision?
- Information on area school systems where we would be moving
- Information on the housing market
- Information on cost of living in the destination state
What main concepts do I use when I think about whether to accept the job?
- Career fulfillment
- Proper balance of job and family
- Wisdom of my decision as a career move
What conclusions should I be reaching?
- This is (or is not) the right offer for me and my family
- The timing of the offer is (or is not) right for me and my family
- The pros of the offer sufficiently outweigh the cons (or not)
What alternatives do I have in reasoning through this decision?
- Stay in my present job
- Rethink my assumptions
What’s the context in which I’m deciding this question?
- Personal and family
Standards of Critical Thinking
Critical thinking is thinking that satisfies high standards of quality. These standards are the criteria against which reasoning is measured to determine if it “makes the grade.” There are seven main standards of critical thinking.
In Learning to Think Things Through, Gerald Nosich describes them as being like a set of filters that screen out flawed thinking-i.e., thinking which is unclear, inaccurate, irrelevant, or insufficient; and which lacks depth, breadth, or precision.
Let’s look at each of the standards and how it applies in judging the quality of our thinking.
We draw on the discussion of the elements in Learning to Think Things Through to describe the elements of reasoning and explain how they are employed.
Our thinking is clear when it is easily understood. This comes in two parts: We must be clear in our own minds about what we mean, and we must express what we mean clearly so that others readily understand us.
Clear thinking is unlikely to be misunderstood. When we think clearly, we are able to see what follows from it-i.e., where our thinking is leading us. When we express ourselves clearly, our words convey our intended meaning. Thinking is unclear when it is ambiguous, murky, easily misunderstood, or when it is not apparent what follows from it.
It isn’t easy being clear. Most of us are not always adept at expressing what we mean. This might be because we’re not really clear in our own minds what we’re thinking. Furthermore, our emotions can get in the way of clarity. When we are angry or elated, for example, our reasoning is less likely to be clear.
We think accurately when our reasoning expresses the way things actually are. Accurate thinking reflects what is true. As applied in critical thinking, the word true does not mean absolute truth in the philosophical sense. It just means that our thoughts and the words used to express them convey the way things truly are, as best they can be understood.
Nosich points out some common barriers to accurate thinking and expression:
- We won’t open ourselves to the truth of something if we find it threatening (The weapons of mass destruction must be there. Keep searching.)
- Wishful thinking blinds us to the reality of things (I’m sure Social Security will be solvent when I reach retirement age.)
- We generalize too quickly from our anecdotal experience. (I recently started taking the bus to work and it has been late twice in the last 2 weeks. Public transportation is so unreliable.) This tendency inclines us to ignore whatever contradicts our experience.
- Our reliance on news reports to draw conclusions about what the world is like leaves us with a distorted (i.e., inaccurate) picture. (Student-on-student violence is an epidemic problem in urban schools.) This stems from the news media’s tendency to report on what is unusual or sensational—what is newsworthy—rather than on what usually happens.
Thinking is relevant when it focuses on what is important—on what matters in understanding or deciding the issue at hand. The critical thinker asks how relevant or central the reasoning is to the issue. As Nosich observes, everything is relevant to something. That does not mean, however, that everything is relevant to the issue in front of us. As critical thinkers, we are concerned with reasoning that matters to the issue we happen to be evaluating.
Be mindful that what is relevant to us personally might not be relevant to the issue we’re reasoning through. For example, suppose the town in which we live plans to build a security fence around a municipal pond to keep children out. How the fence looks – the aesthetics of it – might be relevant to us. But it does not bear on whether the proposed fence will be an effective barrier. The fence’s appearance is not relevant to a consideration of its effectiveness.
Failure to recognize that not all aspects of an issue or problem are equally relevant can distract our focus from what matters most. And if we get too bogged down in the details of an issue, we can lose sight of its larger relevance – we “miss the forest for the trees,” as the saying goes.
Reasoning must be sufficient to the question at hand. This means thinking it through thoroughly enough to arrive at a reasonable position about it. Our thinking is insufficient when we leave out important considerations or when we don’t pursue it far enough.
As critical thinkers, we must ask whether we have reasoned an issue out enough. This invites the question, “Enough for what?” Nosich suggests that reasoning is enough when it achieves our purpose. We could always think about an issue at greater length. After all, maybe there’s some other unidentified factor we have yet to weigh that would inform our position. But sufficiency does not equal proof. Nosich says that it is unreasonable to require too much thinking before drawing a conclusion. Most of the practical issues we face cannot be proved conclusively. In the real world, to require that reasoning be enough to prove something conclusively is an unrealistic and unreasonably strict standard.
Depth and Breadth
We think deeply and broadly when we think critically.
Our reasoning about a problem is deep enough when it plumbs beneath the surface to identify the underlying complexities. Deep thinking takes account of these complexities in working through the problem.
Our reasoning about an issue is broad enough when we look at other related issues and consider other perspectives on the issue at hand, and take full stock of them in working through the issue.
Depth and breadth are different, though complementary, facets of sufficiency. They differ in where they point our reasoning. Depth directs us to delve deeper into an issue. Breadth directs us to look more broadly around us, at alternative perspectives and other related issues.
Reasoning is precise when it is specific, exact, and sufficiently detailed. Precision is related to clarity, but is distinct from it. Something may be clear but not precise. Consider the following:
I am going to the party soon and will return before long.
This is a clear statement, but it lacks precision. Modification makes it precise:
I am going to the party at 8 o’clock and will return by midnight.
Exercise: Applying the Standards of Critical Thinking
Progress through the exercise below to see if you have a full understanding of the standards of critical thinking.
Each of the following statements corresponds to one of the standards of critical thinking. Explain why the statement fails to satisfy the corresponding standard.
“The movie was interesting.”
The statement could mean almost anything and therefore conveys nothing. What made the movie interesting? Is “interesting” good, bad, or neutral? A clearer statement would be:
“The movie was interesting because it explored a set of complex characters in a riveting story with multiple plot twists.”
“There are 10 main standards of critical thinking.”
The statement is clear and precise. But it is not accurate. There are 7 main standards.
“The crime rate increased significantly.”
The statement indicates nothing specific about the magnitude of the increase. A precise statement would be:
“The crime rate increased by 300% from the preceding year.”
“The company doesn’t permit telecommuting because not all of its employees are able to telecommute.”
The reasoning is not relevant to the conclusion it informs. Whether or not to permit telecommuting should hinge on its relative advantages/disadvantages, for the employer and its workers. By extension of its reasoning, should the company not permit driving to work because its employees don’t all have cars?
“I am going to sign up for Acme cell phone service because it’s the least expensive one I have found.”
The reasoning here is insufficient. Price, in and of itself, isn’t the only consideration. One must also determine what level of service one gets for that price. A more expensive plan might provide so much more in service features that it actually is a more economical choice.
“Kicking a serious drug habit is just a matter of will power.”
The statement lacks depth because it does not acknowledge, and takes no account of, the complex nature of drug dependency, including physical, psychological, and social factors.
The statement lacks breadth because it doesn’t consider any other perspective on the issue of vouchers. It just anoints the NEA position.