Today, my husband is guest posting on the blog to talk about math. Yes, this is primarily a writing focused blog, but math is another one of those subjects that, when taught poorly, can be perceived as un-fun. Indeed, if you’re good at writing, you may have the impression that math will be especially hard for you, but Steve is here to show you that’s not necessarily the case.
Greetings all! My name is Steve Dowell, and I’m a mathematician and teacher from Culpeper, Virginia. I was asked to talk to you all about a subject that I encounter almost everyday: Math Anxiety. Most people seem to have an innate fear of anything number related. They are able to do the basic tasks necessary for modern life: adding numbers, balancing check books, paying bills. Ask them to do anything more complicated than that, though, and they are at a loss. “I’m no good at math,” they say or, my absolute favorite, “Math? I was never good at math in school. I hate math!” The funny thing about this is that I never hear people say this about history or social studies; tell someone you’re an architect and they might say, “That’s neat.” Say you’re a math teacher or a mathematician, and they almost always reply, “Math? I was never good at math in school…”
From my own experiences as a teacher, I can tell you that the reason people hate math is because someone told them to hate it. They had a bad teacher tell them they were no good at it, or they were taught it in a boring way. They may have been forced to memorize times tables, or recite order of operations mnemonics. They may have been told that it’s okay to be bad at math or that being bad at math is a good thing. They may even have been told that they are not expected to or are not physiologically able to understand math; many generations of aspiring young women have been told this, and the damage it has caused is still present today.
I aim to change this. You, reader, are just as good at math as I am, and I’ll prove it to you. Not only will I show you that you are a mathematician at heart, I’ll also help you overcome and understand that dreaded Math Anxiety. And I will do this all by teaching you Calculus.
“Hold the phone, Steve!” you’re probably thinking, “Calculus? Isn’t that super hard math?” Actually, no, it’s not. Not if you understand the rules. Not if you understand what mathematics is and why you shouldn’t be anxious about it. You see, mathematics is nothing more than a language, like English or Spanish. When you do math, the same part of your brain that processes language is used. Like languages, math has its own grammar, its own vocabulary, its own syntax. And like any language, if you know the basic rules, you can begin to understand what’s being said.
Calculus is the mathematical study of change. The two main concepts in calculus, the Derivative and the Integral, both tell you how a system is changing. The derivative tells you how things change at an instant, sort of like how your car’s speedometer tells you how fast you are going at any given moment. The integral tells you how a system changes overall, like how your car’s MPG rating tells you about it’s average fuel consumption. The neat thing about both is that they use the same exact process to model this change. If I reverse a derivative, I’m doing the integral, and vice versa.
Now that you hopefully have a basic idea of what these things are, I will show you how to use them. But before I do, I have to explain what is one of the most important concepts in all of mathematics: the Limit. The limit can be tricky if you take it too literally. What it basically does is tell you what happens in a system when I get really close to a specific place. One example of this in everyday life is the freezing point of water. When the air temperature is 32º F, we know it might ice or snow; that’s what happens when we get close to that point. Anyone who has experienced winter, though, can tell you that even if the temperature is 34º F, it might snow, or it could be raining at 30ºF. The limit just tells you what happens near a fixed point.
Now, both the derivative and integral require the limit in order to work. To calculate a derivative, you need to know what a system is doing at two points, which you then bring close together using limits. The idea is that you bring the two points so close to each other that the difference between them is too small to be measured anymore. By doing this, you essentially figure out what the system is doing at one point or how it is changing at that location. For the integral, you do something similar. Instead of points, though, you use rectangles. You shrink a rectangle until it is really thin (again, using limits), then take the area of it. To calculate the integral fully, you add up the areas of a bunch of these really thin rectangles (this method of calculating an integral is called a Riemann sum).
This is all there really is to calculus: the rest of the discipline is devoted to tricks and rules to speed up both processes. If you spent some time learning the basic rules, the rest of the field becomes a whole lot easier to manage. All branches of math work this way. If you study the rules, you too can start speaking and writing in the way mathematicians do: through the language of logic and proofs. There really is nothing to fear or be anxious about! So stop saying you’re bad at math, or thinking that you can not understand it. Think instead that you were never taught the right rules and that if you put a little effort into it, you too can be mathematician. You probably already are.