This past week, we watched a series of videos focused around brain growth and worked on a few open-ended problems to get us on a strong start into the school year. These problems weren't meant to solve, but rather meant to grow and learn from. The videos that we watched before every problem, helped us to get rid of the idea that we supposedly can't do something. One message that I liked from these videos is to always try because trying will get us way further than quitting--there's no reason to quit. Keep moving forward. Another thing that stood out to me was that the only thing you need to be "good at math" is to have good bran power. By that I mean being able to think forward, and not be afraid of failing. There is no such thing as failing--with each "fail", whether you noticed it or not, you learned something new and with that, you can try again.
Work
The first problem we worked on, is called "tiling an 11X13 rectangle. The goal was to find a way to break up the rectangle in as few squares as possible. Here is how I progressed in class with this: As you might be able to see, I made a first attempt by cutting the largest square out of the 11X13 possible. The rest I divided as efficiently as I could. I was able to get 8 squares from that--the smallest number I was able to reach. From there I started dividing the rectangle using slightly smaller and smaller squares and quickly found out it was impossible to divide the 11X13 evenly since both are uneven numbers. After working on the problem in class, I thought of another way the problem could be worked out and got excited to go back to it (a rarity for me). I went back to it couple days ago, this time using decimals to divide up the 11X13. At the bottom of the page is my work for that My thought was that it would be convenient to perfectly divide the rectangle into four squares and figured that since half of 11 is 5.5 and half of 13 is 6.5, I could use decimal numbers to split it in half. I worked on this for a class period, but gave up in the end seeing as I hadn't found even one way to tile the rectangle into any less squares. Even though I didn't find out the most Ideal way to do this in very few squares, that doesn't matter because I still worked through the problem. One strength I used is a habit of a mathematician called "generalize". after working on the problem at school, I thought about it in my own time and realized something that should have been right in my face, that being that 11 and 13 are odd numbers and cannot be divided in two without using decimals. By taking this step back I was able to continue forward and learn more.
Reflection
I'm really glad we watched those videos (as corny as they were) and worked on those problems, especially in the first couple weeks of school. I got a lot from these and i'm glad I can go through the rest of this school year with a better look on mathematics. Two weeks into sophomore year and for once, I’m not dreading showing up to math class every day. My teacher has given us a perspective I finally understand. The school has told us this many times but I’ve now been able to put this into my own perspective and use it to my strength. I haven’t said once this year the sentence “I’m not good at math” because to be strong in math, you just need to have mental strength. You simply have to believe that by moving forward, not giving up, and not being afraid of failure, you can expand your knowledge and overall brain strength. You have to have grit. Before I thought I didn’t have a brain that functions logically and maybe I don’t. Maybe I see things more visually and understand the world around me that way, but I don’t need to have a logical mathematical brain to be good at math, and I guess knowing that is all I needed to enjoy the math we do here at school and I’m happy to have realized that so quickly this year thanks to seeing D’r Drew’s approach to learning.