Sophomore year of math so far has been filled with blue haired superheroes and houses made out of sugar cubes. All for the sake of reminding ourselves that we are all mathematicians. I came into this class ready to learn something new, but knowing that math is the subject I have always struggled the most with. In the last math class I had all of the work went right over my head. I was worried that it was going to happen again. So I promised myself that I will hard to understand what we learn. Even though math is the villain in my comic book, something changed when I came to class. My teacher started right off by saying that everyone learns at their own pace. Just because someone needs to learn in a different way, doesn't take away from the fact that they are learning. Even though I had heard this in my old class it was like I was hearing for the first time. I processed what I was told and it gave me courage.
After my teacher had gone over this we started watching video's and in between video's we had small activities that were made for us to learn knew ways of finding the answer to a problem. The videos were an add on to what my teacher had said to encourage all of us. The first video went over how there is no such thing as a math brain or someone without a math brain. Our brains are constantly learning and growing. We can do whatever we set our minds to. The first activity started with us looking briefly at a set of dots. We were asked the amount of dot's we counted and in what fashion did we count them. I was surprised to see that everyone had counted the dot's in a very diverse way. Some people didn't even count it they just saw a shape instead of numbers. It really taught me that we all look at problems in a different way. The next part of that activity was trying to get the fewest amount of squares in a 11 by 13 rectangle. The purpose was to find the way we all approach a problem. Some started with small squares and some big. In the end we were left with the same amount of 6 squares.
The next day we watched two video's. The first taught us that making a mistake is much more powerful than getting something right. When you get something right that is all that happens. Your brain doesn't grow because you already know. When you get something wrong you go back and learn the area's in which you made a mistake. So instead of frowning upon making a mistake we should cheer for it. Cheer on the knowledge we're gaining. The second video was about the importance of our energy. In order for us to succeed we need to believe we can. Our mindset will determine how much we care for completing a task. I strongly believe that this is true. When I was younger I would have such negativity when it came to math that I was in control of my failure. I was the one who decide that I just couldn't. The moment that I decide that I can do anything is the moment I became a mathematician. I also believe that your energy affects the people who are working next to you or with you. If you say you can't then how are they going to feel about the situation? Positivity isn't just for you, it's for the people around you. The activity that we did was looking at a set of growing figures. We determined on our own how they were growing. Just like the activity the day before, I was surprised to see how many diverse ways people watched the figure grow. The way I saw the figure grow was a new block was added to every naked top and right piece of the block. One way that interested me was the idea of is falling down like Tetris. After that we were asked a few questions. What does figure 10, 55, and 190 look like. We were challenged to not draw out the figures, but instead find an easy way. This problem was really hard for me, because I really tried to push myself in finding the answers without using visuals. It ended in me getting frustrated and just counting it all out. It taught me that it takes me a bit longer than other people to find the answers to a problem. It's always been something that has bugged me, but I need to get over it and realize that it's just the way I function. I go at my own pace and being proud of that is not a problem. Another thing that I got out of this activity is getting to know that there are so many ways to find the answer to a problem and even though I'm slow there's a chance I can find a new one.
After that day we watched another video about speed. This video pushed me even farther to understand that how fast I go does not determine my understanding of math. The video explained that math is much more than numbers and calculations. It's taking time to think deeply about what the questions are asking you and how many ways they can be solved. This isn't just a concept that helps me in math, it helps me in all my classes. Knowing that I need to take the time to understand it for myself and not for the answers on a paper is the most important thing I need as a student. For the activity we learned about the Hailstone sequence using the numbers 20-10-5-16-8-4-2-1. Something I really would have liked to do in class was try to figure out the pattern before we learned it, but we only got a small amount of time to make a conjecture (An idea you might think is true, but you do not know for sure: A word we learned to use that day in class). The Hailstone sequence is when you take a random number and if even you divide by two to get the next number, and if odd you multiply by 3 then adding one to get the next number. This was definitely my favorite activity in class mainly because I love patterns and finding new ones within them, which was the goal in this activity. I learned every pattern ends in 4-2-1. Also that big numbers are sometimes easier to finish than smaller numbers.
The final day we watched a video about visualizing. The video include counting on your fingers and how it's super important in the way brain visualizes numbers. Studies have shone that when adults are counting they are visualizing numbers in their heads. Still students are embarrassed to count on their fingers. Even today I'm still shy to count on my fingers, and as a person who can't do mental math, not being comfortable with it has caused some issues. Such as not being willing to find answers because it's embarrassing to say that you need to write it down somewhere or get a calculator. Growing up with this fear that I'll be called on in class to figure out a problem has ruled my life for as long as I know. It's not so prominent now, but I still get anxiety. Because of my learning disabilities I have another level of embarrassment. Instead of counting large numbers I'm counting small numbers that a lot of kids at my age could visually get answered in a few seconds, but I have to slow everything down for me to get the answers. So I couldn't really appreciate the video because it didn't relate to the struggles I have when it comes to visualization. The final activity that we did was using sugar cubes to make a 3 by 3 by 3 sugar square. Then instead of counting, it was our job to visualize how many sides were not being touched by other cubes or sugar. Our data concluded that
3 sides not touching:8
2 sides not touching:12
1 side not touching:6
We could know that this data was correct because when we add it all together it is the same amount as the 3 by 3 by 3 square. This question had me wondering what the out come of counting how many cubes that were touching each other instead of not, was there was going to be any patterns in the graphs? I first approached the problem by trying to solve it in my head, but that didn't really work out well. Then I looked up a visual of a 3 by 3 by 3 cube. I was then able to map out how many sides had either 3,4,5, or 6 sides touching the other sides. My data concluded that
3 sides touching:8
4 sides touching:12
5 sides touching:2
6 sides touching:1
I found that this adds up to the same amount of the 3 by 3 by 3 square. By exploring this different way to finding the answer it taught me that just an idea can open a whole other set of questions. This week was full of reminding myself that it is okay not to know the answer because math is so much more than finishing as fast as possible, it's understanding and gaining the knowledge I need.
After my teacher had gone over this we started watching video's and in between video's we had small activities that were made for us to learn knew ways of finding the answer to a problem. The videos were an add on to what my teacher had said to encourage all of us. The first video went over how there is no such thing as a math brain or someone without a math brain. Our brains are constantly learning and growing. We can do whatever we set our minds to. The first activity started with us looking briefly at a set of dots. We were asked the amount of dot's we counted and in what fashion did we count them. I was surprised to see that everyone had counted the dot's in a very diverse way. Some people didn't even count it they just saw a shape instead of numbers. It really taught me that we all look at problems in a different way. The next part of that activity was trying to get the fewest amount of squares in a 11 by 13 rectangle. The purpose was to find the way we all approach a problem. Some started with small squares and some big. In the end we were left with the same amount of 6 squares.
The next day we watched two video's. The first taught us that making a mistake is much more powerful than getting something right. When you get something right that is all that happens. Your brain doesn't grow because you already know. When you get something wrong you go back and learn the area's in which you made a mistake. So instead of frowning upon making a mistake we should cheer for it. Cheer on the knowledge we're gaining. The second video was about the importance of our energy. In order for us to succeed we need to believe we can. Our mindset will determine how much we care for completing a task. I strongly believe that this is true. When I was younger I would have such negativity when it came to math that I was in control of my failure. I was the one who decide that I just couldn't. The moment that I decide that I can do anything is the moment I became a mathematician. I also believe that your energy affects the people who are working next to you or with you. If you say you can't then how are they going to feel about the situation? Positivity isn't just for you, it's for the people around you. The activity that we did was looking at a set of growing figures. We determined on our own how they were growing. Just like the activity the day before, I was surprised to see how many diverse ways people watched the figure grow. The way I saw the figure grow was a new block was added to every naked top and right piece of the block. One way that interested me was the idea of is falling down like Tetris. After that we were asked a few questions. What does figure 10, 55, and 190 look like. We were challenged to not draw out the figures, but instead find an easy way. This problem was really hard for me, because I really tried to push myself in finding the answers without using visuals. It ended in me getting frustrated and just counting it all out. It taught me that it takes me a bit longer than other people to find the answers to a problem. It's always been something that has bugged me, but I need to get over it and realize that it's just the way I function. I go at my own pace and being proud of that is not a problem. Another thing that I got out of this activity is getting to know that there are so many ways to find the answer to a problem and even though I'm slow there's a chance I can find a new one.
After that day we watched another video about speed. This video pushed me even farther to understand that how fast I go does not determine my understanding of math. The video explained that math is much more than numbers and calculations. It's taking time to think deeply about what the questions are asking you and how many ways they can be solved. This isn't just a concept that helps me in math, it helps me in all my classes. Knowing that I need to take the time to understand it for myself and not for the answers on a paper is the most important thing I need as a student. For the activity we learned about the Hailstone sequence using the numbers 20-10-5-16-8-4-2-1. Something I really would have liked to do in class was try to figure out the pattern before we learned it, but we only got a small amount of time to make a conjecture (An idea you might think is true, but you do not know for sure: A word we learned to use that day in class). The Hailstone sequence is when you take a random number and if even you divide by two to get the next number, and if odd you multiply by 3 then adding one to get the next number. This was definitely my favorite activity in class mainly because I love patterns and finding new ones within them, which was the goal in this activity. I learned every pattern ends in 4-2-1. Also that big numbers are sometimes easier to finish than smaller numbers.
The final day we watched a video about visualizing. The video include counting on your fingers and how it's super important in the way brain visualizes numbers. Studies have shone that when adults are counting they are visualizing numbers in their heads. Still students are embarrassed to count on their fingers. Even today I'm still shy to count on my fingers, and as a person who can't do mental math, not being comfortable with it has caused some issues. Such as not being willing to find answers because it's embarrassing to say that you need to write it down somewhere or get a calculator. Growing up with this fear that I'll be called on in class to figure out a problem has ruled my life for as long as I know. It's not so prominent now, but I still get anxiety. Because of my learning disabilities I have another level of embarrassment. Instead of counting large numbers I'm counting small numbers that a lot of kids at my age could visually get answered in a few seconds, but I have to slow everything down for me to get the answers. So I couldn't really appreciate the video because it didn't relate to the struggles I have when it comes to visualization. The final activity that we did was using sugar cubes to make a 3 by 3 by 3 sugar square. Then instead of counting, it was our job to visualize how many sides were not being touched by other cubes or sugar. Our data concluded that
3 sides not touching:8
2 sides not touching:12
1 side not touching:6
We could know that this data was correct because when we add it all together it is the same amount as the 3 by 3 by 3 square. This question had me wondering what the out come of counting how many cubes that were touching each other instead of not, was there was going to be any patterns in the graphs? I first approached the problem by trying to solve it in my head, but that didn't really work out well. Then I looked up a visual of a 3 by 3 by 3 cube. I was then able to map out how many sides had either 3,4,5, or 6 sides touching the other sides. My data concluded that
3 sides touching:8
4 sides touching:12
5 sides touching:2
6 sides touching:1
I found that this adds up to the same amount of the 3 by 3 by 3 square. By exploring this different way to finding the answer it taught me that just an idea can open a whole other set of questions. This week was full of reminding myself that it is okay not to know the answer because math is so much more than finishing as fast as possible, it's understanding and gaining the knowledge I need.