Week of inspirational Math
For the first week of tenth grade, we went over five videos and four conceptual math problems. Each of the videos had a message about the ways the human brain learns math, and each of the problems was open ended, so we were able to use our new skills on the ideas presented. The purpose of these activities was to make us confident in our math abilities, as well as challenge our thought process. The videos taught us that doing things like going slow, counting on fingers, and making mistakes are not only good, but important for learning. With the problems, the answers were less important than the concepts, and the concepts were not to hard to grasp. The goal was to build off of the concepts given alone and with groups, and we were able to do that well.
I chose two of the math videos that relate to me personally. The first is about the importance of mindset when doing math. People with a positive mentality towards difficult math problems showed more brain growth, while people with a fixed mentality restrained their brain growth. This fact makes me happy because usually I believe in myself, and I always try to make other people believe in themselves too. The other video I chose talks about visualizing math. People always tell children not to count on their fingers, but it's actually good to be able to visualize the numbers. I was always embarrassed to count with my fingers or use other childish math tactics, but now I know that it’s okay. Watching these two videos and their messages made me feel a lot more validated.
The problem I chose to explore further was called the squares to stairs problem. The problem includes a set of figures that grow in a special way. It starts with a single square. The next figure adds one square on top of the original and another to the right. The figure after that adds three squares in a similar manner. This pattern continues onward towards infinity. We were asked three questions about the figures. They asked about what figure 10 and figure 55 would look like and whether or not you could make one of these formations with 190 squares.
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I could already tell that we were using the habit of a mathematician Look for Patterns. Having seen these patterns before, my first instinct was to write about how the figures were growing. Whether you saw it as adding a row, column, or diagonal line of squares to the shape, everyone could agree that the figures were growing by adding two, then three, then four, etc. After making a T chart of the figure number versus the number of squares, I chose to graph it. The graph I got showed me that the growth was exponential. I got really excited about this discovery, so I attempted to show my group mates my graph, but they were busy trying to draw or manually count up to figure 55. My mind knew that if there was a chart and a graph, then there must be an equation. I knew how to make linear equations, but I forgot about the implications of exponential equations, besides the fact that they usually include an exponent. I struggled with remembering exponential equations for a long time before the period ended. The next day, the whole class went over the problem, and I was surprised by a lot of things. The first surprising thing was the answers to the questions. I already knew the amount of squares in figure 10, but I never figured out an equation to solve the other two questions. Many people drew figure 55 or counted 1+2+3+...+53+54+55 manually to get 1540 squares. One student found that the figure with 190 squares was figure 19 using manual methods. What I wanted to know was the equation for this number set, because I had never figured it out. I was shocked to see that neither of the equations that the class came up with had exponents. The teacher then explained that the number set was not linear or exponential. He told us that this was a polynomial equation. I had never heard this term before this problem, but the concept made sense to me. He said we would learn more about them next semester. I chose this problem because it was the one I got the most invested in. When I answered a question, I would get very enthusiastic. I’d be eager to tell my table what I had discovered. Even after getting the wrong answer, I never wanted to give up.
After doing everything for the week of inspirational math, I realized that I was really getting excited about doing everything. The videos taught me what I can to to keep my brain growing, and the math was just the right amount of difficult and understandable to keep me engaged and positive. This was the perfect way to start the year off. Can’t wait to see what’s in store for the future!