My Ideology
When asked what I do for a living, I commonly respond with, "I am a mathematician." Unfortunately, this usually begins a plethora of self-defacing responses. The most common of these is something along the lines of, "Wow. I was horrible at math." It's a sad commentary on society when the subject that is the basis for two of the most important skills in life, problem solving and critical thinking, is shuttled into a compartment of people's ego normally reserved for shame and fear.
The willingness that people have to admit their weakness with and fear of mathematics is astounding. If someone were to tell you that they were a race car driver, would you tell them that you could barely find the brake pedal on your car? If a friend told you that they ran a house cleaning business, would you proudly claim that you could not even wash a single dish? If your cousin told you she got a job at a clothing store, would you state with cool confidence that you could barely dress yourself? I would hope not!
Mathematics is one of the few subjects in which the majority of society deems it okay to say you are not good at it. Some people even sound proud about the statement, laughing at themselves in the process. Little do they realize that the joke is on them as high paying jobs in engineering, technology, and science pass them by because of their fear. Moreover, it's my opinion that the inability of people to think critically is creating a caste system in our country further increasing the gap between the "haves" and the "have nots."
"Why do we have to learn math?"
"When am I ever going to use this stuff?"
"What do I need to get a C in this class?"
"How many questions will there be on the exam?"
"Why is there so much homework?"
These, and many other questions, are often posed to professors of mathematics, much to our chagrin. The first two are great questions which I will attempt to answer here. The last three are not great questions, but I will address these as well.
Why do we have to learn math?
We study mathematics because it develops logic skills. Mathematics affords us a playing field where we can test our problem solving skills without having to build a bridge and hope it doesn't fall. Most citizens can get by without much of the mathematics that they learn in school and so it creates this false argument that mathematics is useless. I could use the same argument for many subjects - english, history, and social science, to name a few; however, without a basic knowledge in these areas, I would find it difficult to maintain more than a simple conversation with someone.
The study of english allows us to know how to communicate in the professional world without looking like complete idiots (try using the text-lingo lol, lmao, or wtf on an application for employment and you'll be standing in the unemployment line for the rest of your life). Sure, I don't really care about the intricasies of conjugation of verbs or what the phrase "past participle" means, but to contribute in a meaningful way to society, I should know the basics of the language. If I don't, then I am likely going to be leeching off of others for the rest of my days. Likewise, I know it's not necessary for me to remember that the first "Diet of Worms" was held in what is now called Germany in 829 A.D. (a fact that I will have ingrained into my brain until I die, for some odd reason), but a general sense of the flow of history affords me an understanding of the conflicts currently going on in the world and within our own country.
Mathematics, in its purest form, is philosophy and logic. Therefore, when I am asked why we study mathematics, I do not respond with, "One day you will need to find the roots of a quadratic equation using the quadratic formula and you'll thank me!" Instead, I tell the person that mathematics is the process of understanding how to solve complex problems - whether these problems involve numbers or not. In fact, contrary to popular belief, mathematics is not the study of numbers - it is the study of quantity, space, structure, and change. It is through the study of mathematics that we develop those skills of problem solving and critical thinking required to do some of the great feats of humankind - from building the Great Wall of China, to building your house.
When am I ever going to use this stuff?
This is a tricky question to answer. If your future career is in a science field, then you will likely need a combination of the topics you are going to be learning. If your career lies elsewhere, then mathematics can still play a major role. Businesses can benefit from data analysis, revenue optimization, and pricing design - all of which can be done once you obtain some "mathematical maturity."
I am constantly finding mundane uses for mathematics in my daily life. In fact, I once gave a project to a precalculus classes requiring them to find the best vehicle for me based on six variables (fuel cost per mile, average per mile repair costs, average per mile maintenance costs, financing costs, insurance costs per mile, and expected vehicle depreciation per mile). I gave them one car and they had to do research to find five other cars to compare with. I promised I would purchase the vehicle that was the best buy according to their calculations. To this day, my Honda Insight is still going strong at 55 miles per gallon!
The other questions
This brings me to the bad questions. Most of these center around how to pass a class. Let's first discuss why we even have classes and how you should approach a mathematics course.
For one to truly prove they understand something, they must be able to demonstrate their knowledge in that subject. There must exist some form of assessment of not only their skills in using the material (e.g., a doctor being able to perform a procedure), but their conceptual grasp of the deeper meaning and implications of the subject (e.g., that very same doctor being able to make a diagnosis of, and design a treatment for, an illness that may be rare or unheard of).
As you journey through a course in mathematics and explore the concepts presented to you, try to think of the significance of the subject. While you may think that mathematical manipulations portray a semblance of knowledge, realize that you must delve deeper into the hidden meanings and mysteries of mathematics to uncover a true understanding of those manipulations. Then, and only then, will you have mastered a concept.
Notice in those statements that I do not tell you explicitly how to get a C. It's implied - understand what you are doing and do not mimic. The number of questions on an exam is exactly enough to elicit a sense of understanding from you. There is so much homework because I need to assess whether you are copying the steps I do or whether you know what I am doing.