How to Solve Any Problem, Step 2: Identify and Clarify

And, now, we’re back to problem solving…

The NASA spaceship Odyssey was 205,000 miles away from earth when astronauts Jim Lovell, Fred Haise and Jack Swigert heard what they described as a “pretty large bang”.  This was accompanied by electrical fluctuations onboard and the momentary loss of communication with Earth.  Their second oxygen tank reading was zero.  When they looked out the window, they saw that the Odyssey was venting gas.  Clearly, they had a problem—but what?  They didn’t even know if what they heard was an explosion or the impact of a meteorite.  And if it were an explosion, what caused it and which parts of the Odyssey did it affect?  The specific answers to all these questions marked the difference between the success and failure of the mission, with “success” meaning that Lovell and Haise would land on the moon in the Aquarius and then plant the flag.

In the latter parts of the math section of the SAT the questions get harder. The questions have fifty words or so and the student has less than fifty seconds to read it and solve it.  If they get past their intimidation—which they often do—as they read the question they will recognize many elements, realize that they know all the necessary math, start executing the steps they know and then get an answer.   

Only later on do they find out they got wrong answer because they solved the wrong problem.  They hadn’t read all the way to the end of the question so they didn’t actually know what the real problem was.  Or they simply misunderstood the question because the excitement of recognition drew them away from complete understanding and, therefore, the correct solution.

After the accident on the Odyssey, it wasn’t immediately obvious that the astronauts’ survival was at stake. After all, they were still breathing and they were still moving towards their original target—the moon.  Only after an examination of the all the monitors on the Odyssey and a long series of physics calculations run by the NASA engineers on earth did the gravity of the situation become clear.  Only then did they understand the true nature of the problem.   Not only were Lovell and Haise not going to be able to take the Lunar Module and land on the moon, it wasn’t even clear that they were necessarily going to survive.  The problem to be solved wasn’t a lunar landing.  It was whether they were going to live and land back on earth. Their supply of breathable oxygen was now severely limited and they were hurtling away at thousands of miles per hour from the nearest known source of oxygen in the universe—talk about time pressure!

You know how this movie ends, of course.  Lovell, Haise and Swigert returned home, their mission hailed as a “successful failure.”  The movie Apollo 13 was largely accurate, down to the lines in the script taken directly from actual NASA communication transcripts (a bit of trivia: unlike Tom Hanks in the movie, what Jim Lovell actually said was, “Houston, we’ve had a problem”, not, “Houston, we have a problem”.  Impress someone with that at your next party).  But for all the excitement in the movie of solving the problem, most of the movie was really spent trying to understand the problem in the first place.  Most of the movie was spent problem identifying instead of problem solving: identifying the real problem (survival) and clarifying the problem (the constraints imposed by a limited supply of oxygen and Newton’s Laws of Motion).

So this is step two of solving any problem, what my students have to do in less than fifty seconds.

How to Solve Any Problem

Step 1: Get your mind right

Step 2: Identify and clarify the problem

How to Handle Fear

Imagine having the ability to dispatch forty armed assailants with your bare hands.  Or the agility to dodge heavy machine gun fire unscathed.  Or the strength and speed to take on  interstellar opponents.  Of course, our friendly neighborhood Spider-Man can do these things because he has the proportionate strength and speed of a spider.  

But the foundation of all of his amazing ability is his “spidey sense”, his extra sensory perception that warns him of all forms of danger.  When his spidey sense “tingles”, he knows he’s about to be punched, or that an energy burst from a blaster is coming, or someone is about to drop a bucket of paint on his head.  And since he knows what’s about to happen, he can handle it appropriately: punch back, get out of the way or simply do nothing.

Wouldn’t you love it if you had a spidey sense?  I would!  If you could just peer a little bit into the future to see what harm may befall you, imagine how prepared and ready you would be to handle what life has to throw at you.

Actually, you already have this superpower.  Mother Nature is no fool.  We call this superpower “fear” and it does for us what Spidey’s sense does for him.  Fear warns us of danger.  Fear tells us when to fight, when to flee and when to stand our ground and do nothing at all.

It is possible to be truly fearless, i.e., feel no fear at all, but this is a very bad state to be in.  To be truly fearless, you would have to be cut off from your amygdala—essentially the reptilian part of your brain.  There are such people running around, who by genetic circumstance or brain injury cannot feel fear at all.  They tend to walk right into the middle traffic. When a punch is thrown, they don’t know why they should get out of the way.  In the face of a predator, they feel no need to run.  Without outside protection, they are not likely to make it into the next round of life.
You need the gift of fear.  Evolution gave it to you for a reason.  Evolution wants you alive and ready to procreate.

The problem is not fear but an excessive attachment to it.  This is what happens to my students when they see a problem they don’t understand. Their anxiety goes through the roof and understandably so.  They’ve been told over and over that their future is on the line.  And it is. 

So what to do with the gift of fear at that exact moment?  When the amygdala starts blaring, all mental processing is taken away from the neocortex—the part that’s brilliant at math—and drawn to their reptilian brain—the part that knows about—among other things—digestion.  How to get the focus back on their brilliant neocortex?

You can try to ignore the fear, but that won’t work since any ignored emotion will simply return more intensified.  You can challenge the fear but—like ignoring it—it will simply make it stronger.  Why not do what Spidey does when his spider sense tingles?  He pays attention to it.  Then he decides what to do, whether it be fight or flee.  Note that he does not do what his spider sense tells him to do.  He listens to it, evaluates its warning then he decides and acts.

Fear is not designed to tell you what to do.  It tells you that there’s a threat and you might need to do something, but the decision is left entirely up to you.  But how can you make a good decision when your fear is at its most intense and you amygdala is demanding all of your attention?

You can breathe.  Deeply, evenly and consciously.

This sounds simple but the decision to breathe deeply and consciously actually sets off a complex series of neurological events.  This decision to focus wrests control of your brain from your primitive amygdala to your far more intelligent and advanced neocortex.  

You don’t need to take my word for it.  Take it from the experts in fear management: the United States Military.  This is the breathing technique the US Navy teaches to prepare for extreme situations (“extreme” meaning the probability of a life terminating event is high, aka death): Combat Tactical Breathing

Relax yourself by taking 3 to 5 breaths as described below. Visualize each number as you count.
Breathe in counting 1, 2, 3, 4
Stop and hold your breath counting 1, 2, 3, 4
Exhale counting 1, 2, 3, 4
Repeat the breathing
Breath in counting 1, 2, 3, 4
Pause and hold your breathe counting 1, 2, 3, 4
Exhale counting 1, 2, 3, 4

Navy SEALs use it.  First responders use it.  Professional athletes use it.

Try it.  I will!  I will teach it to my kids.  Let me know how it goes.  Maybe instead of fear being a master, we can turn fear into a very good and wise friend.

How to Get Your Mind Right

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I used to have a personal trainer who would always shout before a lift, “Get your mind right!”  I am no longer with him.  He annoyed me.  First of all, he never explained what it meant to get my mind “right”.  Second, he shouted.  Neither situation is optimal for muscle growth—or problem solving.

Now, of course, having spent enough time teaching math to teenagers I understand how important it is to get your mind right.  If they are going to learn anything and succeed well enough on the SAT to go to the college of their choice, they are going to need to know how to get themselves in the most optimal mindset for examination success.

“Getting your mind right” is context specific.  The mental state necessary to lift a heavy weight is not quite the same as the mindset for solving an algebra problem.  But whatever the optimal mindset is for the domain of the challenge, it is important to be able to quickly get yourself into that state.

None of my students has ever lacked for cognitive ability.  But when they encounter a problem with more than ten words that is accompanied by an unfamiliar picture, they collapse in discomfort.  Instead of being able to marshall all the processing power of the one hundred trillion neurons they possess, their anxiety starts telling them lies like “I’m just stupid”, “I’m not good at math” or “this is impossible”.  None of this has ever been true.  But once in a panic, any of us can be convinced of any untruth—even if the liar is our own brain.

My erstwhile trainer was actually right about one thing.  When he shouted “get your mind right” he probably meant concentrate and focus.  Indeed, the correct mindset to solving any problem—or lifting any weight, for that matter—starts with focus.  All other considerations must be put aside to focus on the challenge at hand.  Only then can the awesome power of those trillions of neurons can be brought to bear.

In order to learn and solve problems I need my students to be focused, creative and open.  This is the optimal problem solving mindset.  But without the first, the last two are largely irrelevant to problem solving.

So how do I get my students to learn how to focus?  The opposite of focus is distraction.  What distracts them when faced with a problem?  Their cell phone?  The ambient noise?  Background chatter?

My students are distracted from focus by exactly the same things that distract us all: our own thoughts and feelings.  And the most powerful and, therefore, distracting thoughts and feelings are the ones associated with anxiety and fear.

So getting my students to get their minds right is simply a question of teaching them how to handle their distracting thoughts and feelings, which means helping them learn how to handle their anxieties and fears at the precise moment these anxieties and fears are at their maximum—like in the middle of a four exam that will determine the course of the rest of their lives.

Simple, right?

I’ll show them how to do this—right after I learn how to do it for myself.

That said, I do have an idea how to do this.  It’s not original and I certainly did not come up with this on my own but I’ll gladly share what little I know about this—next week.  Here’s a hint: one of the foremost experts in this is in the neighborhood and is very friendly.

How to Solve Any Problem

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Today would have been my mother’s birthday so instead of thinking about what I can give her, I will ponder and expand on one of the gifts she gave me.  Like my mother—and her father before her—I became a teacher.  My grandfather taught civil engineering.  My mother taught the law and english.  I’ve taught software engineering, martial arts and salsa dancing.  Today I teach SAT math to teenagers.

Those are all very different domains.  One domain involves erecting structurally sound edifices.  Another is about erecting a sound legal defense.  Yet another is about figuring out how to knock out your opponent before he knocks you out.  But whether it is math, or writing, rhythm or fighting, success in all these domains requires one ability above all else: the ability to solve problems in real time and at a faster rate than the problems arrive.

The question I am considering is this: is there a common way to solve problems across all domains?  This is on my mind as I try to teach teenaged students how to do algebra under time pressure.  I know that any human being can learn to do anything given a good enough reason.  What is the reason I can give my skeptical students for engaging in the struggle for finding the value of x?  That it will help them get into a good college and, therefore, get a good job?  Those are good reasons, but that motivation is hard to sustain in the face of the allure of texting their friends and liking a post on social media.  Could there be a more compelling reason to learn algebra?

Algebra is math.  Math is really nothing but a language governed by a precise and limited set of rules.  In other words, it’s a system of logic.  Solving a problem in math is nothing but an exercise in solving a problem of logic.  And solving a problem of logic is nothing but problem solving.  In other words, the steps you would need to take to solve a math problem on the SAT are not fundamentally different from the steps you would need in order to construct a bridge, defend a client from a lawsuit or lead a partner through a complex combination while keeping in time with Tito Puente.

Maybe you disagree.  A sound rejoinder to all this is to point out the dearth of mathematicians competing on Dancing with the Stars.  A fair point, but bear with me.  I think I’ll have you convinced as I pursue my not unambitious goal of developing the universal steps for solving any problem in the universe.  Or barring your full agreement, at least you will be entertained.  This will be fun for both of us.

So, without further ado, let’s get to the first step.  It’s an ironic first step given how much I’ve talked about logic.  In the years I’ve taught children how to solve math problems I’ve yet to encounter one who wasn’t fundamentally smart enough to solve even the most complex problems.  Cognitive ability has never been the issue.  More often than not, however, the young student will see all the words in the problem and immediately conclude that they simply cannot solve the problem or that there is no solution possible.  In the face of unfamiliar difficulty, the student simply collapses and surrenders.

Given that, the first step to solving any problem is not a step of logic but one of emotion.  Step 1 of solving any problem in the known universe is to get your mind right.  You need to believe that there is a solution to the problem you are facing and that you can find it.  Without this first step, all the other steps are irrelevant.  This is not so much a statement of confidence as it is a statement of faith.  The students who hang on to this faith are the ones who wrestle with the problem until they find the solution.

So whatever problem you face, you need to believe that there is a solution and that you can find it.

How to Solve Any Problem

Step 1: Get your mind right