What was the purpose?
The purpose of this week of investigation and video watching was to learn that mistakes are valuable and help us think deeply as mathematicians. I did many different activities with my class and watched videos that inspired me to work even harder on problems that challenge me to become a better mathematician.
Building Shapes
For the first activity, I did was called building shapes. In this activity a group of four students were given a rope that was tied together to make a circle and we had to make shapes using all of the rope. When my group and I got the rope we tried out different ways to make shapes but we were unsuccessful. We started drawing our ideas, cutting out shapes to figure out how to fold the rope and tried whatever idea came to mind. We eventually figured out how to make shapes such as squares, and stars. We checked to make sure that each side and corner was equal by measuring the length of each side and checking the corner with a piece of paper. On the first day I watched different videos in class about different math strategies such as drawing out problems and using different sources to help understand. On the second day I watched a video about how being slow at math doesn't mean that you're bad at math. It just means that you are a deep thinker and many mathematicians are slow but they are still very good at math.
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First Video
The first video I watched this week was a video about different ways to overcome a difficult problem. The message is that drawing out the problem, discussing the problem with other people and looking at different resources such as the internet or a text book are great ways to further understanding of a problem. This video is important to me because it is very true. From my experience as a student, I understood problems better by working in groups, writing out problems in different ways and looking up information on the internet.
Number Visual Pennies
For the second activity, my class was given a work sheet and told to look for patterns in the shapes independently then share out what we saw. We did for about five minutes and I realized that if you look at some patterns diagonally the number of circles would multiply. On the other side or the worksheet we were given five shapes the we must include in our solution. We were given 100 pennies that we must stack on the shape and use them so there are none left over. My group did very well in this activity. We found two solutions to this problem. We used a calculator to figure out exactly how many times we needed to stack each shape. We were correct with our math. We worked very well together and I feel like I have enhanced my collaboration skills with this activity.
I chose this problem as the one I wanted to explain in detail because I think I learned a lot about working in groups and using different methods to understand a problem as I wrote above. When working on the front page I counted how many circles are in each shape. I also noticed that if you went from a corner and went diagonally, the numbers would multiply. For the problem on the back, my group and I also used a calculator to figure out how to split the 100 pennies. It worked out well and we put the pennies in different shapes. An example of when I dealt with a problem was when my group was trying to figure out how to divide numbers to create equal stacked shapes using all 100 pennies. We tried some numbers but it didn't seem to work so we kept on doing it until we found something that worked. This is a great example of habit of a mathematician called Be Confident, Patient and Persistent. We didn't loose our confidence when our first try was unsuccessful. Despite not knowing where to begin we were patient when we thought of different numbers. We didn't give up and persevered until we found a solution and we found two!
I chose this problem as the one I wanted to explain in detail because I think I learned a lot about working in groups and using different methods to understand a problem as I wrote above. When working on the front page I counted how many circles are in each shape. I also noticed that if you went from a corner and went diagonally, the numbers would multiply. For the problem on the back, my group and I also used a calculator to figure out how to split the 100 pennies. It worked out well and we put the pennies in different shapes. An example of when I dealt with a problem was when my group was trying to figure out how to divide numbers to create equal stacked shapes using all 100 pennies. We tried some numbers but it didn't seem to work so we kept on doing it until we found something that worked. This is a great example of habit of a mathematician called Be Confident, Patient and Persistent. We didn't loose our confidence when our first try was unsuccessful. Despite not knowing where to begin we were patient when we thought of different numbers. We didn't give up and persevered until we found a solution and we found two!
Second Video
The message of the second video was that just because someone is slow at math doesn't mean they are bad at math. Many mathematicians spend a lot of time to solve a problem because they are thinking deeply. This video is important to me because I spend a lot of time on problems and sometimes I feel like I'm not good at math because I take longer than others, but this video made me more confident in my abilities and ready to try out new problems.
One Cut Geometry
For the third activity, my class was given patty paper and told to cut a triangle out of the patty paper without using the edges of the paper as a side for the triangle. We also only could cut the paper only once and we could fold or draw on it to help us find a solution. At first my group folded the paper however we could to experiment and see if we could come up with solutions that way. I tried all sorts of different ways to try to cut out a triangle but I would always end up with a square or a rounded triangle shape. After getting close to a solution by cutting out an almost perfect triangle, we drew lines in marker to help us fold the paper in a precise lining up each side in a way so one cut would be enough to get a complete triangle. I learned that its okay to take my time to solve the problem, its the process that matters.
Third Video
The message of this video was that there is no such thing as a math person. It is a myth because a person isn't born with a math brain. Brains constantly grows when a person learns and it opens up new pathways in the brain. Those pathways are new ideas to solve problems. If you practice a difficult problem a lot you get a stronger pathway. This message is important to me because when I was younger I believed I wasn't a math person because it seemed like there were people who were always better than me, but after experiencing different ways to learn math and became more open minded, I felt more confident in my math skills.
Square Mania
For the forth activity, my class was given a figure with many lines in it. We were instructed to find the how many squares are in the figure and agree or disagree with the statement next to each question. We first worked independently and wrote down our own answers. I would trace out the squares I saw in the figure and tallied the total number of squares i saw in the figure. When my class was told to share show them how we got our answers. When one of my classmates went up to explained there answers to the first question they had a different answer that was correct. They found two more squares. I looked over my work and realized that I did indeed miss it. This was a very good learning experience for me and taught me to check you answers even if you think you are correct.
Fourth Video
The message of this video was that if you believe that you can solve a problem, you're brain will grow more than if you didn't believe in yourself. There are also two different types of mindsets. A person with a fixed mindset is someone who thinks their intelligence or learning capabilities are something they cannot change. A person with a growth mindset believe they can learn anything. This is important to me because when I was younger, I had a fixed mindset and thought that I was always going to be bad at math but after learning about growth mindsets and being taught about it by my teachers, I grown to accept this idea and believed in my abilities more than I ever did before.
Fifth Video
The message of this video is that even when a person make mistakes, you're brain is growing. When a person make a mistake, synapses fire in the brain. Every time synapses grows it creates new pathways. Challenging problems are great for the brain because it works like a muscle. The more challenging it is, the stronger the brain gets. This video is important because I used to think that mistakes and challenging problems were didn't help me at all but I learned that challenging problems help me become a better mathematician. It is very important to know that mistakes are valuable and a key way to enhance your mathematical abilities.
Reflection
This week was a very good because it reminded me of good things to keep in mind when working on a math problem. I was reminded that mistakes are valuable and that its okay to take my time. Doing the activities were challenging to me so I'm sure my brain grew a lot this week and I worked with my classmates and improved on my group collaborations skills. Despite learning and being reminded of all these things, it is a very good starting point for what I should work on this year. This year I want to take these goal further and work on problems that are more challenging and become better at working in groups because it is a great way to learn about different perspectives and I will gain more experience that will help me in the future.