The purpose of these activities was to encourage new ways of approaching solutions to problems, new ways of thinking about problems, and to emphasize the point that making mistakes is good and paves the way for success in the future. We also learned how to work together as a team to obtain solutions to problems.
Day 1: Building Shapes
In class, we worked together in groups to build 2D and 3D shapes with a 7-8 foot loop of rope. The teacher played the role of the skeptic, and we as a group had to convince the skeptic that we had constructed a certain shape. We had to come up with our own methods of giving proof, and in doing so I realized the importance of convincing myself that work I did was correct and made sense. I learned that many times, my perception of things is not shared by others, so I need to come up infallible proof in order to prove that I am right.
In class, we worked together in groups to build 2D and 3D shapes with a 7-8 foot loop of rope. The teacher played the role of the skeptic, and we as a group had to convince the skeptic that we had constructed a certain shape. We had to come up with our own methods of giving proof, and in doing so I realized the importance of convincing myself that work I did was correct and made sense. I learned that many times, my perception of things is not shared by others, so I need to come up infallible proof in order to prove that I am right.
Day 2: Number Visual Pennies
For this activity, we used visuals and different patterns of pennies to arrive at the total of 100 pennies. There had to be the same number of pennies in each stack of the pattern. Everyone used different combinations of numbers of pennies to come to the total of 100 pennies. At first, my group came to a total of 98 pennies because we had forgotten that we were supposed to use all 100 of them. Then we noticed that the stacks were uneven on the visuals, so we corrected that and arrived at a total of 100.
For this activity, we used visuals and different patterns of pennies to arrive at the total of 100 pennies. There had to be the same number of pennies in each stack of the pattern. Everyone used different combinations of numbers of pennies to come to the total of 100 pennies. At first, my group came to a total of 98 pennies because we had forgotten that we were supposed to use all 100 of them. Then we noticed that the stacks were uneven on the visuals, so we corrected that and arrived at a total of 100.
Day 3: One-Cut Geometry
This activity was by far the most interesting to me. The objective of this was to draw a polygon on a square piece of paper and cut it out of the paper with one straight cut. We weren't allowed to use the edges or corners to aid us in this process. I particularly liked this activity because I enjoyed finding new ways to go about making the polygon. I felt that this activity really helped me find creative solutions to problems.
This activity was by far the most interesting to me. The objective of this was to draw a polygon on a square piece of paper and cut it out of the paper with one straight cut. We weren't allowed to use the edges or corners to aid us in this process. I particularly liked this activity because I enjoyed finding new ways to go about making the polygon. I felt that this activity really helped me find creative solutions to problems.
Day 4: Square Mania
In this activity, we looked at diagrams of rectangles made up of squares. We had to identify how many line segments were used in the diagrams as well as how many squares there were in the diagram. This was a little challenging because the number of squares and line segments were not always easily obvious. However, with some outside-of-the-box thinking, however, we were more or less able to solve the problem.
In this activity, we looked at diagrams of rectangles made up of squares. We had to identify how many line segments were used in the diagrams as well as how many squares there were in the diagram. This was a little challenging because the number of squares and line segments were not always easily obvious. However, with some outside-of-the-box thinking, however, we were more or less able to solve the problem.
Video 1: Strategies for Learning Mathematics
The message of this video was that learning math becomes easier when I draw things out, use teamwork to solve a difficult problem, experiment with new ideas, use different resources, and start small. If I use these strategies for learning, solving a difficult problem becomes a much less daunting task.
The message of this video was that learning math becomes easier when I draw things out, use teamwork to solve a difficult problem, experiment with new ideas, use different resources, and start small. If I use these strategies for learning, solving a difficult problem becomes a much less daunting task.
Video 2: Speed is not Important
What I learned from this video was that thinking carefully about the problem in front of you and understanding what you're doing is more important than fast calculation. Sometimes, making calculations too quickly can lead to mistakes, many of which could have been solved easily by simply thinking more carefully about the problem and going back to check work.
What I learned from this video was that thinking carefully about the problem in front of you and understanding what you're doing is more important than fast calculation. Sometimes, making calculations too quickly can lead to mistakes, many of which could have been solved easily by simply thinking more carefully about the problem and going back to check work.
Video 3: Brains Grow and Change
Many people think that to be good in math, they have to have a "math brain," but this is not true. People are good at math not because they have a "math brain" but because they focus on practicing new skills and learning more things in math. Learning a new skill and practicing a new skill creates and strengthens pathways in the brain, so really, all you have to do is get some good practice in the areas you're struggling with and really make sure you understand them.
Many people think that to be good in math, they have to have a "math brain," but this is not true. People are good at math not because they have a "math brain" but because they focus on practicing new skills and learning more things in math. Learning a new skill and practicing a new skill creates and strengthens pathways in the brain, so really, all you have to do is get some good practice in the areas you're struggling with and really make sure you understand them.
Video 4: Believe in Yourself
In this video, I learned that when faced with a difficult problem, I can either choose to think "Oh I can't do this, this is too hard for me," or I can choose to face it with the intention of trying my best. Many times, I doubt my math abilities when I encounter a topic that I understand very little about; I think that I will never be able to understand it or that I won't get any better in the subject. But, if I have a growth mindset, then I will do what needs to be done in order for me to understand the challenging subject so I can further improve in math.
In this video, I learned that when faced with a difficult problem, I can either choose to think "Oh I can't do this, this is too hard for me," or I can choose to face it with the intention of trying my best. Many times, I doubt my math abilities when I encounter a topic that I understand very little about; I think that I will never be able to understand it or that I won't get any better in the subject. But, if I have a growth mindset, then I will do what needs to be done in order for me to understand the challenging subject so I can further improve in math.
Video 5: Mistakes are Powerful
In elementary and middle school, I was always told that making mistakes was a waste of time and I always had to get the correct answer every time. What I didn't know was that making mistakes is really good because now I know what not to do and my brain has grown during the process of trying to solve a problem and making a mistake. Through my mistakes, I can find new ways to solve problems and learn more throughout the experience.
In elementary and middle school, I was always told that making mistakes was a waste of time and I always had to get the correct answer every time. What I didn't know was that making mistakes is really good because now I know what not to do and my brain has grown during the process of trying to solve a problem and making a mistake. Through my mistakes, I can find new ways to solve problems and learn more throughout the experience.
One-Cut Geometry:
In this activity, I had to cut a polygon drawn in the middle of a square piece of paper using only one straight cut. The polygon I decided to use this on was a scalene triangle. We were allowed to fold the piece of paper but were instructed not to use the edges and corners of the paper. The reason I chose this problem to write about was that I feel like I did the most creative thinking here; especially in my mistakes. My main approach to solve this problem is as follows. I first drew the scalene triangle in the middle of the paper, and seeing as it's a right triangle, I decided to draw another scalene triangle under the first one to form a rectangle. I then cut out this rectangle and cut it diagonally, thus making 2 scalene triangles. I thought I could get away with this because I thought we were only instructed not to cut a triangle out, and that the same rules didn't apply to a rectangle.
In this activity, I had to cut a polygon drawn in the middle of a square piece of paper using only one straight cut. The polygon I decided to use this on was a scalene triangle. We were allowed to fold the piece of paper but were instructed not to use the edges and corners of the paper. The reason I chose this problem to write about was that I feel like I did the most creative thinking here; especially in my mistakes. My main approach to solve this problem is as follows. I first drew the scalene triangle in the middle of the paper, and seeing as it's a right triangle, I decided to draw another scalene triangle under the first one to form a rectangle. I then cut out this rectangle and cut it diagonally, thus making 2 scalene triangles. I thought I could get away with this because I thought we were only instructed not to cut a triangle out, and that the same rules didn't apply to a rectangle.
One challenge I faced was not knowing what to do after my first attempt at solving the problem failed. With help from my group, I was able
to figure out how to solve the problem by folding the paper.
to figure out how to solve the problem by folding the paper.
One Habit of a Mathematician that I used in solving this activity was Conjecture and Test. I had an idea that could possibly solve the problem, so I tried it, hoping to find a solution, but I realized that I made a mistake. My mistake helped me find another way to find solutions.
Reflection: This week, I was eager to learn new things and to participate in class. I think the Week of Inspirational Math was an interesting experience for learning, making mistakes, and growing. I learned to look at problems in new ways, that making mistakes is a really good thing, that I can be good at math if I work hard and really practice in areas that are difficult for me.