[MUSIC] As we've discussed, the first step in our four step process of problem solving is understanding the problem. In this lesson, I'm going to contextualize the step, and then give you some examples. After this, you'll get the chance to watch some experts talk through the importance of this step for the whole problem solving process. And some of the strategies that they use in order to really understand what a problem is. So why do we need to understand a problem? As Polya suggests, it is foolish to answer a question that you do not understand. If you don't understand what the terms of a problem are, you will struggle to find a solution no matter how good you are at problem solving. For example, if I asked you what the answer to A + B was, regardless of how good you are problem solving you couldn't give me a real answer. The only answer you can give is that A + B = A + B. This is because you do not understand what A or what B are and therefore do not know what the product would be if you added them together. As Polya says, it would be foolish to even try. However, if I define the term A as 6 and B as 3, then I understand the problem to be 6 plus 3 and I can easily give you the answer of 9. Let's look at another example. Say I mix together heated dihydrogen monoxide and dried camellia leaves. What would I get? In this case, heated dihydrogen monoxide is hot water, and dried camellia leaves are also known as tea leaves. So if you guessed regular black tea, you're right. As you can see, the first step in understanding a problem is being able to adequately define both the terms of the problem, and what the problem is asking you to do. This becomes difficult when you're given word problems rather than numerical ones. Problems can often appear to be very difficult, when in fact they only require the simple application of a known formula or theory. Understanding what these problems require you to do is the difficult part. Some strategies that can help you with this are for example, visualizing the problem and drawing a representation. Focusing on the units of measurement or defining key words and phrases. In the next few lessons we will explain what these strategies are and give some example problems with solutions that use them. Another aspect of understanding the problem is understanding what the real problem is. This is unfortunately not as simple as just finding definitions or drawing something. As the following humorous example from Faulkner illustrates. A student and his professor are backpacking in Alaska when a grizzly bear starts to chase them from a distance. They both start running, but it's clear that eventually the bear will catch up with them. The student takes off his backpack, gets his running shoes out, and starts putting them on. His professor says, you can't outrun the bear, even in running shoes. To which the student replies, I don't need to outrun the bear. I only need to outrun you. As Folger and Leblanc point out, the student defines the real problem as simply a matter of out running his professor. The bear will stop running once he has caught one person. Once he's defined the real problem figuring out a strategy that leads to a solution is simpler. Another way to look at this is from a medicine perspective. Imagine you're a dentist treating a patient with a toothache. This kind of toothache is usually caused by cavities or abscesses. So you clean their teeth and have a look. However, you can't see any problems. The only other explanation you can think of is a gum infection, so you prescribe some medicated mouthwash. A few days later they come back, this time in more pain. So you take another look and prescribe a different kind of antibacterial mouthwash and some painkillers. A few days later, they're back again. While you are trying to figure what is wrong with their teeth, another dentist comes by. She takes one look at the patient and prescribes a new medication. For those of you who guess C, you are correct. In this case, the toothache was a symptom of fluid build up in the sinuses caused by sinusitis. Figuring out that the sinusitis was the issue, means that the solution, sinus decongestant, was simple and easy. The real problem in this case was not a tooth problem, but a sinus one. Over the next few lessons we will introduce some strategies that you can use to help define and understand what the real problem is. Of course, it's important to remember that you should pick and choose the strategies best suited to your problem solving style and the problem itself. [MUSIC]
