During the week of inspirational math we learned many different lessons and did four mini activities. I chose one to write about. My reflection and experience is below. Enjoy.
Video Watching Purpose
I believe that the purpose of this week was to learn about how our brains grow because of mistakes. I now understand that you learn more from making mistakes other than getting the answer right. It is good that we learned that because now I feel confident in my math skills, even if I don't always get the right answer. During the mini activities I realized that everyone gets to the answer a different way. Two people can get to the same answer but do the math two different ways.
Overview
We watched five videos and did four mini activities. Each video had a different message about math in it. They were about brain growth, Mistakes, open mindedness, time it takes to solve a problem, and counting with fingers. In the video about brain growth it focused on how the mind grows when you make errors, and the video on mistakes said that making mistakes is more effective than automatically knowing the answer. Open mindedness is a skill that everyone should strive to have. It means that before you even read the problem you have the confidence to always try your best. In the time video they focus on teaching us that your ability to do math isn't affected by the time it takes you to solve a problem. The final video talked about how counting with your fingers and visualizing the math is a good thing to do. All the assignments we completed showed us (in different ways) how everyone gets to the answer to a problem differently.
Message
The most significant message I took away is that "No one is born a 'math person'". This is meaningful to me because I have always been told that everyone is a math person and that made me feel like I was an outcast. This makes me feel like I can do math and be confident in my work. The second line that I took away from the video is that "How fast you are doesn't change how good you are". This changed my perspective because I always thought that being good at math meant that you can solve problems fast. I will remember this for future years to come and try to live my math life by this.
Squares to Stairs
The problem I chose was squares to stairs problem. In this problem we were first given a picture. It was a pattern and we had to write how we saw it growing. After we wrote our pattern down, we had to answer three questions; 1. How would figure 10 look? How many squares would be in it? 2.How would figure 55 look? How many squares would be in it? 3.Can you use 190 squares to make a stair like structure?
I chose to write about this problem because I thought I did a good job at explaining my work and ideas. I also felt that my ability to solve this problem was good and my understanding was great too. It looked neat so I chose this problem to share.
I looked at the figure and I saw it growing diagonally so I showed that using colors. Once I finished that, my group and I decided to move onto the questions. For question one, we drew out the figure and added up 10+9+8..., and so on until we got to one. Once we added them up we knew the amount of squares in the figure. There were 55 squares in the figure. For question two we decided that drawing out figure 55 would take way to long, so we only did the addition. 55+54+53+52+51+50+49..., all the way down to one. There are 1540 squares in figure 55. For the third question I looked back at figure 10 and decided it would be easiest to add up until I got 190. I started at 55, because that already covers the first ten figures.Then added 55+11+12+13+14+15+16+17+18+19. We stopped at nineteen because we hit the number 190. So, the answer was yes you can make a staircase with 190 squares and it would be figure 19.
The third question stumped me for awhile. I was confused on how to know if 190 squares could fit into a figure. After not being able to figure it out, I asked my table group how they solved it. They reminded me of how we found the answer for question two and I realized that we could add the numbers. I eventually got the answer and was glad that I overcame the problem.
Out of all the Habits of a Mathematician I believe that I used conjecture and test the most. I thought of a way the problem might work and just tried it without thinking twice. This is helpful for many things and it was helpful to me.
Once I chose this problem to talk about I wanted to extend it and see what would happen in a different situation. I chose to see the difference between making the figures with 1x1 squares v.s 2x2. We already did 1x1 as the actual problem, so I needed to text 2x2. I drew a figure that went as high as 10. The figure looked different and ended up having 60 squares, instead of 55, like the other figure 10.
Picture we were given. (Above)
Extension (below)
The way I saw the figure grow. (Above)
Work for the three questions. (Below)
Reflection
Watching the videos will help me this year because I now believe in my ability to solve math problems before even seeing them. Another big thing is now not feeling ashamed for counting with my fingers for addition. Every time I am stuck in math class, I know that my brain is growing and it is a good thing to get the wrong answer.
If you would like to watch the videos or see the assignments in more detail check out the link to the right.