Every problem may be different, but effective problem solving asks the same 4 questions and follows the same method.
- What’s the problem? Something is wrong. What are we going to do about t his? This is the foundation and the motivation.
- What do you need to know? This is the most important part of the problem. If you don’t know exactly what the problem is, then you can’t come up with possible solutions for it.
- What do you already know? You already know something related to the problem that will help you solve the problem. It’s not always obvious (especially in the real-world) but you know (or can research) something that will help.
- What’s the relationship between the two? This is where your skills and abilities come into play. The previous steps set you up to find many potential solutions to your problem, regardless of its type.
When I used to tutor kids in math and physics, I would drill this problem solving process into their heads. This methodology works for any problem, regardless of its complexity or difficulty. In fact, if you look at the various advances in society, you’ll see they all follow some variation of this problem solving technique.
“The gap between understanding and misunderstanding can best be bridged by thought!”
― Ernest Agyemang Yeboah
Generally speaking, if you can’t solve the problem then your issue is step 3 or step 4; you either don’t know enough or you’re missing the connection.
Good problem solvers always believe step 3 is the issue. In this case, it’s a simple matter of learning more. Less skilled problem solvers believe step 4 is the root cause of their difficulties. In this instance, they simply believe they have limited problem-solving skills.
This is fixed versus growth mindset and it makes a huge difference in the effort you put forth and belief you have in yourself to make use of this step by step process. These two mindsets make a big difference in your learning because, at its core, learning is problem solving.
Let’s dig deeper into the 4 steps. In this way, you can better see how to apply them to your learning journey.
Step 1: What’s the problem?
The ability to recognize the exact nature of a problem is extremely valuable.
Most people only focus on finding solutions. While a “solutions oriented” mindset is a good thing, sometimes it pays to focus on the problem. When you focus on the problem, you often make it easier to find a viable solution to it.
When you know the exact nature of the problem, you reduce the risk of wasting time. This reminds me of a story I was once told.
The lawn mower problem
Homeowners love a well-kept lawn, but hate mowing the grass.
Many companies and inventors raced to figure out a more time-efficient way to mow the lawn. Some even tried to design robots that would do the mowing. They all were chasing the solution, but only one inventor took time to understand the root cause of problem.
Most people figured that the problem was the labor required to maintain a lawn. The actual problem was just the opposite: maintaining a lawn was labor intensive. The rearrangement seems trivial, but it reveals the true desire: a well-maintained lawn.
The best solution? Remove maintenance from the equation. A lawn made of artificial grass solved the problem. Hence, an application of Astroturf was discovered.
This way, the law always looked its best. Taking a few moments to apply critical thinking identified the true nature of the problem yielded a powerful solution.
Word problems: The scourge of high school math students
One thing I’ve learned from tutoring high school students in math: they hate word problems.
This is because they make the student figure out the problem. Finding the solution to a math problem is already stressful. Forcing the student to also figure out what problem needs solving is another level.
Word problems are not always clear about what needs to be solved. They also have the annoying habit of adding extraneous information. An ordinary math problem does not do this. For example, compare the following two problems:
What’s the height of h?
A radio station tower was built in two sections. From a point 87 feet from the base of the tower, the angle of elevation of the top of the first section is 25º, and the angle of elevation of the top of the second section is 40º. To the nearest foot, what is the height of the top section of the tower?
The first is a simple problem. The second is a complex problem.
The questions require the same knowledge (trigonometric functions), but the second is more difficult for students. Why? The second problem does not make it clear what the exact problem is. Before the mathematics can even begin, you must know the problem or else you risk solving the wrong one.
If you understand what the problem is, then finding the solution is much easier. Understanding this, ironically, is the biggest problem for people.
Problem solving is a universal language
Speaking of people, this method also helps settle disagreements.
When we disagree, we rarely take the time to figure out the exact issue. This happens for many reasons, but it always results in misunderstanding. When each party is clear with their intentions, they can generate the best response.
Education systems fail when they don’t consider the problem they’re supposed to solve. Foreign language education in America is one of the best examples.
The problem is that students can’t speak the target language. It seems obvious that the solution is to have students spend most of their time speaking. Unfortunately, language classes spend a ridiculous amount of time learning grammar rules and memorizing vocabulary.
The problem is not that the students don’t know the imperfect past tense verb conjugations in Spanish. The problem is that they can’t use the language to accomplish anything. Every year, kids graduate from American high schools without the ability to speak another language, despite studying one for 4 years.
Well begun is half done
Before you begin to learn something, be sure that you understand the exact nature of the problem. This will make clear what you need to know and what you can discard. When you know the exact problem you’re tasked with solving, you save precious time and energy. Doing this increases the likelihood that you’ll succeed.
Step 2: What do you need to know?
All problems are the result of insufficient knowledge. To solve the problem, you must identify what you need to know. If you get this wrong, you can only be disappointed.
Either you’ll solve what you thought was problem, only to find out this wasn’t the real issue and now you’ve still got trouble or you won’t and you still have trouble. Either way, the problem persists.
The only thing that wastes more time than an unsolved problem is solving the wrong one.
Imagine that your car won’t start. You replace the alternator, the starter, and the ignition switch. The car still doesn’t start. Now you replace the engine, but you still can’t get it to start. Your replacements and repairs solved other problems, but not the main one: the car won’t start.
Then it turns out that all you needed was gas.
This example is a little extreme, but I hope it makes the point. For something more relatable, let’s return to the problem with language learning.
You need basic communication to navigate a foreign country you’re visiting, let’s say Mexico. When you enroll in a Spanish course, they teach you a bunch of unimportant words and phrases. You stick with it, believing it will eventually click.
When you land, you can tell everyone your name and ask for the location of the bathroom. This does not help when you need to ask for directions or tell the driver which airport terminal to drop you off at.
Finding the solution to chess problems works the same way
The book “The Amateur Mind” by IM Jeremy Silman improved my chess by teaching how to analyze the board.
It’s only with a proper analysis of imbalances that you can make the best move. Though you may not always choose the correct line of play, the book teaches you how to recognize what you need to know. It teaches you how to identify the problem.
The problem solving method always starts with identifying the problem or asking “What do you need to know?”. Only then can you move on to the next step.
Step 3: What do you already know?
The only way to know if you lack knowledge is by gaining some in the first place. All advances and solutions arise from the accumulation and implementation of prior information. You must first consider what it is that you already know in the context of the problem of at hand.
Isaac Newton once said, “If I have seen further, it is by standing on the shoulders of giants.” This is Newton’s way of explaining that his advancements in physics and mathematics would be impossible if it were not for previous discoveries.
Mathematics is a great place to see this idea at work. Consider the following problem:
What is the domain and range of y=(x^2)+6?
This simple algebra problem relies on you knowing a few things already. You must know:
- The definition of “domain” and “range”
- That you can never square any real number and get a negative
Once you know those things, this becomes easy to solve. This is also how we learn languages.
Speaking languages on the shoulders of computers
Anyone interested in serious foreign language study (as opposed to a “crash course” or “survival course”) should learn the infinitive form of verbs in their target language. You can’t make progress without them because they’re the root of all conjugations. It’s only once you have a grasp of the infinitives that you can completely express yourself. Consider the problem solving steps applied in the following example.
I know that I want to say “I don’t eat eggs” to my Mexican waiter. That’s the problem.
I don’t know how to say that, but last night I told my date “No bebo alcohol” (“I don’t drink alcohol”). I also know the the infinitive for “eat” in Spanish (comer). This is what I already know.
Now I can execute the final step of problem solving.
Step 4: What’s the relationship between the two?
I see the connection.
I know the infinitive for the spanish word “drink” is “beber”. Last night, I changed it to “bebo” to express a similar idea. I should be able to do the same thing to the word for “eat”.
“No como huevos” is a pretty accurate guess.
In the math example, the same process occurs. You don’t know the answer to “What is the domain and range of y=(x^2)+6?” You only know what “domain” and “range” mean and that negatives aren’t possible when you square a real number.
A domain of all real numbers and a range of all numbers equal to and greater than six is the answer.
This is relating what you don’t know to what you already do know. The solutions appear simple, but walking through them is an excellent demonstration of the process of problem solving.
In most cases, the solution won’t be this simple, but the process of finding it is the same. This may seem trivial, but this is a model for thinking that has served the greatest minds in history.
A recap of the 4 steps of the simple problem solving process
- What’s the problem? There’s something wrong. There’s something amiss.
- What do you need to know? This is how to fix what’s wrong.
- What do you already know? You already know something useful that will help you find an effective solution.
- What’s the relationship between the previous two? When you use what you know to help figure out what you don’t know, there is no problem that won’t yield.
Learning is simply problem solving. You’ll learn faster if you view it this way.
What was once complicated will become simple.
What was once convoluted will become clear.