What is Math, and Why Bother with it?
Greetings, and welcome to the pure joy of math!
This website was created by a mechanical engineer, university instructor, airplane pilot, astronomer, robot-builder and real rocket scientist – me! When I was in high school, I was so excited about math that I not only starting my own profitable math tutoring business, which was marketed mostly to my friends, but I also attended extra math classes in the evening at a local college where I was the only one with a curfew of 9 p.m. I have the happy opportunity to teach you everything I know about math over the next set of hands-on lessons – something that’s not usually a part of math unless it’s a game, and those get tiring after awhile, usually because they aren’t related the real world.
I promise to give you my best stuff so you can take it and run with it or fly!
When I first started out writing content on this topic, I was amazed at how the math camps and programs out there for the brainiacs who had way above-average math skills operated. There was even one where the kids were solving math problems that even adults didn’t know how to solve.
I also found a handful of remedial math camps and programs for kids failing math during the academic year who needed to spend their summers making up for lost time. And those were overstuffed with busywork-style worksheets and endless rounds of drills, none of which were stimulating or designed to make kids think.
I found no place for kids in the middle of the spectrum, who want to continue honing their math skills in a fun and challenging way. That’s really sad, because that’s where most of the population is. There was absolutely nothing for the kids in the middle of the road, because the current math content out there was either designed for the super-smart kids or the ones falling way behind. That’s when I decided to do something about it.
While we’re not going to solve the world’s current unsolvable math mysteries, or spend time with remedial work, what we are going to focus on is content that is fun, innovative, creative, and designed to make you think. And there’s no silly cartoon-animations, fake problems designed to look real (how many pink elephants fit in the bathtub?), or endless rounds of busywork. You get enough of that elsewhere, so you won’t find it here. What you will find is real math, just like real scientists use every day, so you know what to expect when you get out there in the real world. (Like I said: no pink elephants.)
So, that leads us to the first real question: What is math?
Math can be compared to a very useful tool, like a hammer, or a collection of tools like a set of screwdrivers. A lot of kids get frustrated and bored with math because many textbooks concentrate a lot on teaching the small, meticulous details of each and every type of tool. That’s one of the fastest ways to kill your passion for something that could have otherwise been really useful!
Don’t get me wrong – you do need to know how to tell a hammer from a screwdriver. But can you tell me when to use the hammer instead of the screwdriver? It’s really important to focus on how and when to use the different tools. This is my practical approach to teaching the subject.
Most kids think math just means numbers, when the truth is that math is much more than just numbers and being good at multiplying! There are three main areas in math (at least when you first start out). Some kids enjoy adding and dividing, and for them, math is all about numbers. However, if you’re really good with shapes and how they relate, then you might enjoy geometry. And if you are good at solving puzzles and people think you’re unbeatable at certain games, chances are that logic will be a great match for your skills.
We’re going to discover what math really is, and how we can use it in our everyday lives in a way that’s really useful.
This website is chock-full of demonstrations and hands-on activities for two big reasons. First, they’re fun. But more importantly, the reason we do activities is to hone your math skills, which usually don’t show up in the science arena until way later, like in high school or college. One of the biggest mistakes teachers make when teaching math is that they don’t connect it back to the real world. They treat it like a bunch of problems on paper that need to be solved, as if the story ended there.
But you already know where math is around you: it’s counting back change at the grocery store; it’s figuring out how much fuel you need to make it to the next gas station; it’s fitting all the boxes into the back of your truck; it’s how to beat the kid down the street at chess. It’s everywhere, if you only know where and how to look.
The skills in math take time and practice to master. But it’s important not to get so lost in practice sessions that you lose sight of the goal. Imagine learning a new sport, and you were always practicing, practicing, practicing… and never got around to playing a game, never kept score, never heard the crowd cheer or felt the sense of pride that comes from scoring a goal. You actually need both: practice and performance, and most teachers only settle for practice and forgo the real reason you need to learn this stuff in the first place: to be able to handle the science side of things later on down the road.
One thing I didn’t realize about math (but you probably already know) was that it’s not always right. What I mean is that sometimes math gives deceptive answers that have to be interpreted for them to make any sense. For example, I remember one time I was doing a calculation and my answer to the problem actually resulted in two answers. One answer was 53 feet, and the other was 6 inches. Both answers solved the set of equations I was trying to solve. Now, how did I know which one was really right? I mean 6 inches is different from 53 feet. I had to look back at the original problem, and as soon as I did, I realized that the answer was 6 inches, since there was no way I was going to find a 53-foot badger.
Ideally, you’d learn both science and math skills together in tandem, so you could see how one affected the other; how one was used in a way that made the other possible; where math leaves off and where science takes over, and how they intertwine. In fact, when I was studying aeronautics in high school, I also took advanced calculus in addition to flying lessons!
For example, you could really see how to model a car on paper as a mass-spring-damper system and write an equation to describe the motion the driver feels while driving down the road, solve that differential equation, plot out the solution on a graph, find the points where your solution exists, and run back and put a big X on the car where you want the wheels in order for the ride to be as smooth as possible for the rider (turns out that those points are at the center of percussion, kind of like the “sweet spot” on a bat when a baseball batter hits the ball in exactly the right spot so there’s almost no force felt at the grip). But it’s not always possible to teach math this way because not every teacher will have these skills.
To sum it up: math is a tool that helps scientists model the real world down on paper so we can make the problems easier to solve. Once we solve them, we have to bring them back to the real world by making sense of what we did on paper. That’s usually where we find out how good of a job we did in the first place. That’s why I always do my math problems in pencil, and I write everything down so I can easily find my mistakes.
Math by itself is an art, but math combined with science is pure joy and fulfillment, the kind I want to share with you. I’m going to give you a lot of different activities to help you develop your math techniques in learning how to think. Good luck and enjoy!