I believe the purpose of watching the videos was so we get reminded that we are all able to become successful in math, and we have to believe in ourselves. Also the videos reminded us that group work is important. The activities helped us in many different categories like, visualization, patterns, and number sense. One of the first activities we worked on was the rectangle activity. We were told to draw an 11x13 rectangle and fill it with the least amount of squares. The smallest number I believe was 6 squares. The next activity we did was the square stairs task, where we had to identify the patterns we see. This was one of the most challenging tasks for me. Another task we completed was the hailstone number problem. We created “number strings” and came up with theories about the patterns we saw. At first I didn’t see any patterns in my number string, but after talking with the class, I finally noticed one. The problem I was really confused on at first was the painted cube activity. In this activity, we found our answers by visually solving the problems. It was really helpful that we used real sugar cubes instead of a drawing, because we were able to make more sense of what we were looking for. Most of the videos we watched last week had meaningful lessons for all mathematicians. The first one we watched was about how our brains grow, and we aren’t born a math person. Everybody has the potential of growing their brain. When we learn new things a synapse fires in our brain. On the second day we watched videos about how mistakes, and believing in yourself actually affect the way you learn. On the third day we watched a video about speed. How long we take to solve something doesn’t define how good we really are at math. Being able to understand the concept is more important than speed. It is better for our brains to think about the problem longer. The last video we watched was about the importance of visualizing. Visualizing a problem helps everyone learn better, because math is really about seeing patterns.
The video I connected with the most was the mindset video. Whenever I see a math problem, I automatically think I can’t solve it. I am like the girl in the black shirt in the video, because she didn’t have a positive mindset going into the test and during the test. I want my brain to grow, so I need to believe myself for that to happen. The second video that has a personal significance is the visualizing video. In my elementary school we weren’t allowed to use our fingers to count which frustrated me. Now as a tenth grader I use them, and it is very helpful for me to visualize the problem. Visualizing the problem is something that has always helped me do better in class, because I get to see the concept rather than think it.
The problem that I think I learned the most from is the squares to stairs problem. We had to answer three questions about the cubes that were stacked, in a form of a staircase. Our task was to see how the shape was growing, and to find patterns. I chose this problem because I thought I did really well, and after I completed this activity I felt proud of myself. I went into the problem believing in myself and since I had a positive mindset, I managed to work my way slowly to the solutions. Figure 1 had 1 cube, figure 2 had 3 cubes, and figure 3 had 6 cubes. The image below displays my work I did for the problem.
At first I thought it was going to take a long time to find what figure 10 would look like. I asked my table for help and they showed me the in and out table method. I didn't really understand why that method would work at first, but I used that to help me solve question one and three. They told me when you go up a number you add the x to the y. So if I was talking about figure 3, the x would be 3 and the y would be x+ the previous y ( 6). For question one, I got: 10x10 (including the one cube that is connected by the left and bottom row of cubes. This staircase would be made out of 55 cubes. To find the answer for c, I used the table method instead of finding an equation, unlike other people in my class. It took me awhile but I eventually got 19x19. I think my brain grew a lot these first two weeks of school, but this was the problem that confused me the most. I made a lot of mistakes, which means my brain grew when I learned how to solve them. A challenge I faced was when I wanted to give up. I felt like giving up when I was doing the in and out chart to find the answer for C. I realized it wasn’t that bad, and if I had given up I would have never felt the satisfaction of completing the work with my answers. This challenge reminds me of the speed video we watched in class. I was taking a long time to solve C, and now I know it isn’t a bad thing to do that. I was slow, but it was actually great that I was because I got more out of the process of finding the answer. A habit of a mathematician I used was the collaboration habit. Without my table, I don’t think I would have gone this far. In fact, they are the ones that showed me how to solve them. I think it is good to use your peers when you need help because they guide you.
I think last week’s math work helped me become more confident in class. Even though the videos we watched were cheesy, they reminded me things I needed to know. I am proud that I am a slow problem solver, and I have a positive attitude when it comes to believing in myself. I have never liked sharing my answers with the class, but I think I can work on it this year. Because of the problems that I actually tried hard to solve, I will try to participate more when I feel confident in my way of solving the problem.