Analytical Thinking – Solving Multiple Problems at the Same Time

Being able to solve multiple problems at the same time using limited resources is a typical example of what we, the mathematicians, refer to as analytical thinking. This type of thinking involves careful analysis of the situation and formulating the optimum solution, if not the best one. This, ladies and gentlemen, is what we mean to give our students by teaching them mathematics; they will probably forget the law of cosines in trigonometry, but the analytical thinking skills they acquire on the way will be theirs to keep forever.

So now, the question is how are we as educators in an ever changing, technological world, going to accomplish this task?

Suppose it is 2:00 AM in the morning and you are driving your brand new convertible sports car on a major highway trying to get to your home in the city center which is 80 miles away. Suddenly, the weather changes and it starts raining heavily with a fierce thunderstorm making the rest of your journey very unpleasant. Struggling to drive for 20 minutes, you decide to pull over as soon as you see the nearest shelter next to the highway and wait until the weather gets better to drive.

You see three people there: the first person is the doctor who once saved your life (he is lucky to be there with his car that suddenly stopped working); the second person is a patient heavily injured in the thunderstorm; and the third person is “the one” that you would like to spend the rest of your life with and unfortunately, this is your one and only chance to meet her (or him), so you really have to take this opportunity to do so.

The question is: What would you do?

Here are a few further details: there is not enough time for an ambulance, which means the only hope for the patient is driving in your car to the nearest hospital; the doctor has stopped the bleeding for a while but the bleeding is very likely to start again because the first aid kit in the doctor’s car and that in yours do not have the necessary medical equipments (besides, there might also be internal bleeding). To make things even worse, there is room for just one person in your car aside from the driver. And, none of the mobile phones are working, neither yours, nor the others’.

This question was asked to one hundred people who applied for a management position at a major international corporation. Most of the applicants said they would take the patient and go. Some of the applicants misunderstood the underlying idea and said they would not even stop. A few of the applicants even came up with a shallow response saying they would take “the one”. In fact, only two of the applicants were wise enough to comprehend the hint in the question itself; the question was: “What would you do?” and not “Who would you take?”

The correct answer was: “I would give my car to the doctor to drive the patient to the nearest hospital, and stay there with ‘the one’ and use all of my communication skills to leave a good impression on her (or him) until the doctor would come back with the good news that the patient’s life is saved.”

You probably heard this question before, or different versions of it, because it is really not a new one. But here is a brand new question that I am asking you at this very instant: What is the purpose of this question? What do we mean to learn by asking this particular question to, say, John Doe, who seems to be a brilliant young man?

First of all, not everyone would be willing to share his brand new convertible sports car, so this question gives us an idea about whether or not John is willing to share his resources. Secondly, we understand how the stress factor is likely to affect John; will he keep sane enough and struggle to discover the best course of action, or will he simply collapse under so much stress to give up and go with the majority? Thirdly, when resources are limited, how will John respond to the situation? Remember, the mobile phones are not working while there is limited time and space for only two people in the car. These, indeed, are all what the question reveals about John. However, in the heart of the question lies the following inquest: There are multiple problems that John must very quickly solve at the same time, he does have to save a life but he must also please himself by meeting the lady of his dreams.