When I was in 3rd grade, my class took a trip to the planetarium at the Natural History Museum to see a presentation about fractals. I didn’t know what in the world a fractal was, so I was expecting a view of the stars in our galaxy, a short discussion, and an early dismissal. We all sat down in the large round room, craning our heads up to look at the domed screen on the ceiling when the presentation began. I was astounded by the intricately beautiful designs that swirled above me. It amazed me that these incredible patterns were made from a single, simple mathematical equation; not only were they stunningly detailed, they continued on forever. Even more astounding to me was the fact that these were imitations of characteristics found in nature, such as leaves or ice crystals. I learned that mathematical equations could describe things that were wild and unpredictable as the sight of tree branches growing in natural splendor. So just like Tom Zhang, who found his fascination and comfort in his work on the twin primes, I can find solace in the labyrinthine depths of fractals.

After a long, stressful day at school and a hard volleyball practice I enjoy taking a run around my neighborhood in the cool evening air. It clears my mind of worries of the day, and sometimes I find my mind calculating how far I've come and how much distance I have left to go, much like your swimming. I judge my distance by landmarks, for example, I know that once I pass a certain house around a cul de sac, I have gone 0.5 miles and have 4.5 left to go. My calculations aren't nearly as complicated as the ones you described, and I have a few ideas how I can expand them in order to further improve my math skills. I can start wearing a watch while I run, and therefore approximate my pace, and then try to change it in order to meet my goal. There are many ways in which I can use math secretly, and hopefully my strategy to use it while I run will improve my mental math skills.

Grade can also be defined as slope, or the ratio rise over run. The percent grade of the slope can be determined by calculating the rise over run and then multiplying by 100. The method of finding the slope relates strongly to trigonometry because of the formation of the right triangle. If the grade of something is seen as a triangle, you could use the Pythagorean theorem in order to find the rise or run. Sine, cosine, and tangent can also be used to determine the sides or angles.

I had never thought of grade describing the hills and rises that I, as a native of our beloved and ridiculously hilly Albuquerque, have gone over time and time again. I often run in my neighborhood, and I always dread the incredibly steep inclines. I can now see these hated hills as grades; I learned that one particularly brutal hill has a grade something near 20%. The number seems small, but not when I'm running up the hill like it's a flight of stairs. It is very interesting to see a way in which the trigonometry we learn in the classroom relates directly to my daily life.

I agree that Americans are very illiterate in mathematics. For the longest time I used to think that a square was the same as a cube, it took me a while to realize the three dimensional nature of a cube compared to a two dimensional square. It may be that we Americans are so illiterate in math because of technology. Most people are used to being given an equation, simplifying the equation a bit, then plugging it into a calculator, pushing enter, and circling their answer with absolutely no idea how they got it and where it came from. Because of this, we don't know the specifics and definitions of some aspects of mathematics; when given a problem involving a percent, people blindly follow the formula to solve it and plug it into the calculator, never really knowing that there can't be more than 100%. If a problem was written incorrectly and it involved 120%, people would accept it with no question. Overall, I think that technology simplifies math for us maybe too much, therefore we do not know facts such as it is impossible to have more than 100% of something, and what the difference between a square and a cube is. We need to start learning the reasons and processes behind the answer we circle on our papers, and I believe if this starts to happen, we will greatly improve America's illiteracy in mathematics.

Very interesting story! I think this post is about how most people tend to look at math in the beginning, and how their opinion changes as they move throughout the learning process. In the story, when you first begin to grow the houseplants, you are unsure of yourself and expect that you will fail. I occasionally find myself feeling this way about math, I tell myself that it will be too hard and too much for me to handle, and that there is no way I will succeed. But in the story you surprised yourself, you exceeded your own expectations. Then, as you began to follow your neighbor's advice, you grew and succeeded even more, driving yourself past what you had thought were your limits. I think I should apply your experience to my upcoming year in math class, so that I can push myself past what I thought were my limits.

I have not always particularly enjoyed math. It doesn't come very easily to me either, and I often find myself having to go over the same thing many times for it to stick in my brain. I believe I learn math best when I take good notes in class and really try to learn the lesson, then maybe when I get home to go over that day's  lesson again in order to really learn it so that I can implement that knowledge while I do the homework. Overall, math has always been a challenge for me, but maybe if I come at it with the attitude that I can make it past what I think are my limits, I can  grow and exceed my own expectations as a math student.