Many people and commonly students believe that mathematics is the process of computing numbers in routine ways to obtain a specific desired result. They get frustrated when they can’t find a method in a textbook telling them a step by step procedure that fits the problem they are presented with. If that is what math is, then it should be easy for everyone. It would be like finding the map to a destination and following it. Many people try to do math this way and as a result can’t grasp the skills, beauty, or concepts of mathematics. This is because their idea of math is distorted. The idea of what mathematics is in society to do is so engrained that it is difficult to bring out the true mathematics. Football use to be the same way until society has shaped and molded it to be extremely accepted and now the majority of people participate in it.
Society needs to learn and experience what it really means to do mathematics. It is not solving problems on a worksheet or memorizing formulas. Mathematics is logically reasoning and thinking through a situation or question. For instance, I was flying on a plane and as we were landing I said to my friend, “I wonder what all has to go into landing a plane. The speed, the angle, the distance needed to stop.” This is an example of a mathematical question. After thinking the question, a mathematician would do mathematics by using his “tool box” to figure out the question either estimating an answer or finding exact ones. Now when I say “tool box” I mean an assortment of idea of where to start and mathematical knowledge that has been utilized previously that may help solve the problem. This may mean that the problem needs worked through several times before reaching a logical answer. Mathematics does just stop at an answer like commonly happens in schools. The next phase can vary but for this particular question a mathematician might investigate how the answer changes depending on the size or weight of the plain. Does the weather have anything to do with it? To answer some of these questions some research might need to be done to collect data, unless you have a bunch of planes in your backyard. With your data you can analyze it, look for patterns and reason through what the numbers mean. This part of the question involves some interpretation of the numbers. Depending on the mathematician this may look different. After answering some of these questions a mathematician might look at his work and ask, Could I find an answer in a different way? Why does this work?” Doing mathematics is playing with numbers and questions in an individually creative way.
Not everyone has the same mathematical questions or the same creative ways of finding answers, but everyone has these mathematical questions. Society just doesn’t recognize them as mathematics because they do not have a sense of “live” mathematics (that is, mathematics that isn’t staged in a textbook). If we can get society to just have conversations about these questions in a space where they would categorize their experience as mathematical (such as schools and workplaces), we could change the definition of mathematics.