This week was all about making us feel comfortable where we are as a mathematician. We learned so many different ways that mathematicians are confronted with problems and how to work to overcome those problems. We need to be confident, logical, creative, and determined all at the same time to really succeed as a mathematician when confronted with a challenging problem. Everyone can learn anything as long as they believe in their ability to learn and understand something. Each day of the week involved a video which taught us these tips and an activity which required to use those tips to be successful.
Day 1:
Video Link: ajv.me/hth-2017-18/math-2/activities/wim/day1video/ This video was about a few strategies that could help you while working on a math problem. Some of these strategies were drawing out visuals to help you understand the problem in a different way and working with other people to get to a solution. These were great ways of helping us learn how to work through math in different ways. I could apply all of the strategies to my work which will help me when I'm feeling challenged or stuck.
Activity #1 - Building Shapes
In this activity, we used a circular piece of rope that was connected the entire way through the rope. With this rope, a group of 3-5 people would try to create geometric shapes like squares, stars, cubes, tetrahedrons, and more. It was actually a difficult task to make most of the shapes but my group managed to make a few like the square, the tetrahedron, and the cube. We tried most of the shapes multiple times and most of them resulted in the shape not taking shape. That's okay though, because I learned that effort and always giving your best is the most important skill to have while facing challenges.
Day 2:
Video Link: ajv.me/hth-2017-18/math-2/activities/wim/day2video/ This video was about how fast you can solve math problems and how the thinking of "being fast means you're smart," can negatively affect you. This isn't true at all because thinking long and hard about a math problem gives you more time to think of multiple solutions which might lead you to the right solution. Overall, you shouldn't be discouraged when you can't solve problems at a fast pace because math isn't meant to be solved at a fast pace. I've never had too much of a problem with this thinking but being able to help others now that struggle with this will be rewarding and fulfilling.
Activity #2 - Number Visual Pennies
In this activity, each group had 100 pennies in which you had to find a way to make each stack of pennies for each group of circles, have the same amount of pennies in each stack. For example: a set of 4 circles on the sheet of paper would need to have the same number of pennies in each stack out of 100 pennies. That would come out to have 25 pennies in each stack. My group found 3 different ways to do this which all included different amounts of pennies in each stack for each set of circles.
Day 3:
Video Link: ajv.me/hth-2017-18/math-2/activities/wim/day3video/ In this video, it talked about the growth of brains while working on math problems. The harder you work at a math problem and try to find solutions, your brain will grow immensely. Synapses in your brain will fire and create new pathways for the new knowledge you've extracted. This is why challenging yourself is a good way of learning more than going over topics you've already mastered. This video connects to me because I usually don't like to take on super challenging situations but with this new perspective on this topic, I'm starting to feel more comfortable with challenging situations.
Activity #3 - One-Cut Geometry
In this activity, we had to draw a scalene triangle on a singular piece of patty paper. Once we drew the scalene triangle, we had to cut the entire triangle out in one cut. There were so many ways to fold the triangle to make sure that the triangle would be cut out in one cut. What I chose to do was try and fold all of the lines on top of each other and then cut through that to cut out the entire triangle. The majority of this folding was pretty random as my goal was just to get all of the lines on top of each other. This was successful one time which really showed me that if you keep trying, you will get to a solution eventually.
Day 4:
Video Link: ajv.me/hth-2017-18/math-2/activities/wim/day4video/ This video talked about believing in yourself and your abilities to complete math problems. Without any confidence, you won't be able to continue if you can't find a solution. This can result in giving up and really not wanting to take on challenges as a whole. Without any challenge, well you won't be learning to much more than the range of knowledge you already have. I overall, need to have more confidence in myself and this video really shows in what ways I can do that for myself.
Activity #4 - Square Mania
This activity was the activity I felt most proud of so I will go into detail about it. Square Mania was about looking outside of what was obvious and looking deeper into the problems you were shown. I felt proud of this activity because to find what I needed to find, I had to think a lot about different ways I could find the amount of squares it was asking for. I tried counting the amount of squares, drawing the amount of squares, and even used angles and lines to find the hidden squares in the problem. For example, the first problem asked to see if there were 17 squares in this rectangle. At first I only saw the 12 obvious squares and didn't know where to go from there. Then I remembered about thinking outside of the box and looking at the problem in a different way. With this, I used the angles in the rectangle to look in a different way at the problem which helped me find 5 more squares that were made of 4 smaller squares. This then equaled 17 squares which meant that I had found the solution that equaled the question to the problem. Finding all of these different ways to solve the problem made me feel as though, I had used what we had learned throughout the week and applied that to finding a solution for the problems. This activity also made me use a Habit of Mathematicians which was Start Small. At first I started with the smaller more obvious squares and then looked at the problem on a bigger scale to find the 5 remaining squares.
Day 5: Video Only!
Video Link: ajv.me/hth-2017-18/math-2/activities/wim/day5video/ This video covered the topic of making mistakes in math class and how mistakes are beneficial to learning and growing as a mathematician. Making mistakes shows that you are being challenged with a problem and can use that knowledge in the journey to find the solution you are looking for. Making mistakes shows that you want to grow as a mathematician and expand your knowledge from what you already know. Besides, you will learn from those mistakes and get closer and closer to the right solution. Keep making mistakes. This video connects to me because not getting things right, really hurts my confidence in my abilities. Knowing this will give me more confidence throughout the entire process of solving the problem.
Reflection:
This week really shaped my thinking in a good and positive way. Throughout the week, I felt more comfortable steeping out of my comfort zone and being more involved throughout the group's efforts to solve a problem together. I also generally feel more inspired knowing that the different ways to become a better mathematician are by taking things slow and being okay with messing up. There still is a lot for me to learn and apply to my work but hopefully this week really changes how I approach my work throughout the year. I want to put more effort, and participate more this year in ways I haven't really done before.