Quadratics: A Story of Freedom and Constraint

When I was younger, I always wished I could fly. I wanted to be able to take to the skies to escape at times, and other times I wanted to fly towards some exciting yet far off event. Grounded? Nope, I'm going up into the clouds! Kevin is having a sleep over at his house Friday night? I know how I'm getting there!

Some say NASA was started by someone who was running from his mother's broccoli.

What I really wanted was freedom. Freedom to do what I wanted whenever I wanted, consequences be damned! I looked up and saw birds flying around the sky and yearned for that ability. I'm sure everyone has felt that urge in their life, and I'd bet it was a driving force that took to the Wright Brothers from their bicycle shop to the shores of North Carolina.

Nowadays, I spend most of my time working with math equations and science theories. One of the first lessons that is taught in physics is learning how to deal with projectiles. An object is thrown into the air from an initial height with a velocity and angle of velocity. It seems insufficient, but that information is all that is needed to explain the flight that object is about to embark on. You see, once the object is flying through the air, the only force acting on it is gravity, so a parabola can perfectly describe the motion of the projectile.

You take that acceleration, add some velocity, throw in an angle. Baby you've got a stew going!

Using the standard form of a parabola, it is very easy to relate this information into a mathematical equation. Using the form ax 2 + bx + c, a is half the acceleration, b is the initial velocity, and c is the initial position. From here, all the rules of quadratics apply. You can convert to vertex form, you can find the roots of the equation, and you can even find the focus point of the parabola.

There is an inherent dichotomy in using parabolas and quadratics to explain projectile motion. This act, seen by everyone person who has ever lived as ultimate freedom, is coincidentally constrained. It is the opposite of freedom! It turned out that my visions of flying freely through the air could not have been more predetermined.

The laws of science and math, which I have spent the majority of my life studying and pursuing, de-mystified one of my dreams. Life, it seems, has it's own sense of irony.

The Far Side - Gary Larsen

Role Of A Teacher

I want to be good at what I do. Whether that's teaching, playing video games, or raking leaves in my yard, I want to excel. I want to look back on what I have accomplished and feel proud of what I have put in and what I have gotten out. I believe that before you can ever start excelling, you need to know what it means to excel. Setting a goal is the only way to check whether or not you have actually succeeded, so now is the time for me to set goals for myself as a teacher.

Success

What do I want to accomplish as a teacher? I want my students to think of me as a good teacher. This naturally makes me think about what makes a teacher a good teacher. I think back to the good teachers I had and want to emulate them. The most memorable lessons I learned in high school fell into two categories:

1. The teacher was talking about something I was genuinely interested in and simply helped me explore a subject I was curious about. I was self motivated to learn, but that self motivation can be hard to find. It was not until I was (somewhat) mature and could really push myself. I think the best teachers are able to help students motivate themselves until students mature enough to push themselves.
2. The teacher's own excitement for the topic was so infectious that the lesson became an experience that I will never forget. To this day, I still remember the importance of the Interstate Commerce Clause, and that is simply from the excitement my AP Government teacher brought every day. 

Put simply, I believe that the role of the teacher is to help guide students to areas that interest each individual student while motivating and molding the students to become life-long learners. It is up to myself as the instructor to help students find topics and areas that they are interested in, show students how to pursue areas that interest them, and set the students up to continue learning and succeeding for their entire life.

I think this is absolutely vital in a math and physics class room. These topics can be really confusing, and a common complaint heard in these classes is, "When am I ever going to use this?" I need to help the students relate to this new information and apply it to their own lives. A day comes for every student where they walk out of a classroom as a student for the last time. From that point on, they will never "learn" new information in the same way again. If they are not prepared to learn on their own outside of a classroom, they will stop growing as an individual. It is my top priority to make sure students do not end up like this.

If I can do all that, then I'll feel like a successful teacher.

I would also accept seeing the Lions win the Superbowl. That would be an OK consolation prize.

What I Expect To See Every Fall