Fermi questions emphasize estimation, numerical reasoning, communicating in mathematics, and questioning skills. Students often believe that "word problems" have one exact answer and that the answer is derived in a unique manner. Fermi questions encourage multiple approaches, emphasize process rather than "the answer", and promote non-traditional problem solving strategies. So before smartphones, people might take a straw poll in the moment or over a couple of days, find someone more knowledgeable on the subject, or try to reason it out. Instant access to Google may have just short-circuited this process.
The classic Fermi question is "How many piano tuners are there in New York City?" The best way to figure this out is a series of estimations. Here it is, from on the website Mathforum.org, hosted by Drexel University.
HOW MANY PIANO TUNERS ARE IN NEW YORK CITY?
How might one figure out such a thing?? Surely the number of piano tuners in some way depends on the number of pianos. The number of pianos must connect in some way to the number of people in the area.Approximately how many people are in New York City? 10,000,000
Does every individual own a piano? No
Would it be reasonable to assert that "individuals don't tend to own pianos; families do? Yes.
About how many families are there in a city of 10 million people? Perhaps there are 2,000,000 families in NYC.
Does every family own a piano? No, perhaps one out of every five does. That would mean there are about 400,000 pianos in NYC.
How many piano tuners are needed for 400,000 pianos? Some people never get around to tuning their piano; some people tune their piano every month. If we assume that "on the average" every piano gets tuned once a year, then there are 400,000 "piano tunings" every year.
How many piano tunings can one piano tuner do? Let's assume that the average piano tuner can tune four pianos a day. Also assume that there are 200 working days per year. That means that every tuner can tune about 800 pianos per year.
How many piano tuners are needed in NYC? The number of tuners is approximately 400,000/800 or 500 piano tuners.
What a great exercise! In order to think something like this through with people, you need to think creatively, communicate with others, and estimate reasonably.
I raised this topic with a friend of mine who teaches high school mathematics, and I quickly saw that I touched a chord. S/he said that many of her students don't want to try to reason out problems. Rather, when they run into trouble as they begin working on a problem, they simply turn to someone who knows (including the teacher) and ask for the answer. According to this teacher, not enough students are interested in working on their thinking skills, but are more focused on getting the answer quickly and efficiently. Is this the "google effect" at work in the classroom?
I believe that the issue here is close to the heart of the future success of education in the United States, and ultimately, The United States itself. While students, and many of us in a busy, stressful, day-to-day existence, don't think twice about using Google or the internet in general to answer a question, I believe that it can become a crutch. You may wonder: what is the point of figuring out something that someone else already has figured out? My answer: it trains your brain to solve or resolve problems and issues. The United States had tremendous success in the 20th century due to its willingness to tackle difficult problems, such as putting a man on the moon, advancing medical science, and maintaining an unwavering commitment to (the continued evolution of) individual rights in this country. None of these things were easy, and they were messy and met with continued failure. Many things in this country, and the world, have had nonlinear progressions towards improvement and resolution.
That's the point. When students leave high school and college, they will be met with difficulties and problems, personally and professionally. The answer won't be found via Google. What kind of car should you buy, or should you even buy one? Should you buy a house in this current real estate market? Where should you invest your money? Should you look for a job at a new company or seek to move up where you are right now? Who should you vote for in the next election? Where is the next best opportunity, either in your job or your personal life? All of these questions -- and more -- are things that we encounter in the post-collegiate world, and none of them have simple answers. The best we can do is examine the choices, pros and cons, and their possible outcomes, and make the best choice possible. You just might end up doing some math! Until Google can do THAT for you, you will just have to think for yourself.