Purpose of Week of Inspirational Math: The purpose of this week of investigations and video watching was to get an idea of how to problem solve and work with others. We went over many different examples of how to be a mathematician. The video that stood out to me the most and encouraged me to learn was about growth and fixed mindsets. The video showed a scenario of two girls working on a math problem and both of them were stuck. One of them believed in herself and was able to form (or strengthen) a pathway in her brain which would help her progress in Math in the future because she was encouraging/developing a growth mindset. The other, struggled too but didn't believe she'd solve the problem, meaning she wouldn't learn as much in the future. This was kind of the main idea for every video we watched. Each video was shown to remind us, the students, that math is supposed to be challenging and mistakes are powerful!
Overview: Building Shapes: Each group of four was given a rope tied into a knot so it made a loop. With the four people in the group, the goal was to create as many shapes possible. The options were: a square, a cube, a 5-pointed star, a tetrahedron, an octohedron, and a square pyramid.
Number Visual Pennies: On one side of the sheet of paper (the photo with more visuals on it) the goal was to find patterns we saw and share it with the class. There were no wrong answers, the question was to say what you noticed. The opposite side of the sheet (the photo with less visuals on it) was a bit more complicated. We were given 100 pennies then were asked to interpret what we thought the instructions meant. Eventually, the class came to a conclusion that the instructions were asking us to use each visual (the groups of 3, 5, 6, 7, & 9) to divide the pennies evenly. A better way of understanding this is to break it down. Here's an example of what we were asked to do: if you have 3 slots to place 60 pennies and had to divide the pennies evenly among the slots, how would you divide them? Into 3 groups of 20! To solve this problem, we worked in groups of four and shared ideas out loud to the class.
One-Cut Geometry: The point of this was to draw a scalene triangle on a small sheet of paper without using the edges of the paper as part of the triangle and cut it out using a single cut.
Square Mania: This was all about line segments and counting! The first question states how there are 17 squares within a shape made up of 10 line segments. Upon first count and glance, you'd only see twelve. Maybe the squares overlap. Maybe the line segments continue on to make more boxes. Maybe there are only 12 boxes. It's completely up to interpretation and how someone chooses to see a problem. There is always more than just one answer to these kinds of questions.
Day 1: Strategies for Learning Math The first video we watched videos that introduced us to the habits of mathematicians by explaining different strategies for learning math. The first strategy is to draw out the problem which could potentially fall underneath multiple habits of a mathematician like: conjecture & test and describe & articulate. The second strategy is teamwork which enforces the habit of collaborating and listening. The third strategy is to experiment (conjecture & test). The fourth strategy is to look for different resources (be confident, patient & persistent). The fifth, and last, strategy is to start with a smaller case (start small, take apart and put back together, and generalize.)
Day 2: Speed is Not Important The second video encouraged me the most because it was explaining how solving math problems quickly doesn't matter. I've never been quick at solving problems and, usually, it slows me down in class or I end up behind but this video reassured me by taking my time and challenging myself, makes me learn more than if I were to already know the answer to a problem
Day 3: Brains Grow & Change The third video focused on how much your brain can grow and change. The first part of the video is the teacher expressing to a student that she can be good at other things (one of those things not being math). The middle and end of the video are counteracting that belief that you can't become "good" at math. I liked this video a lot because it showed how it takes a lot of time and effort to become better at problem solving.
Day 4: Believe in Yourself The fourth video is my favorite because it brings up the idea of a "fixed mindset" and a "growth mindset" that no one really talks about. I see a huge divide in people who try to solve problems and know that they can and people who try to solve a problem and automatically think they'll do it wrong. I've always had a fixed mindset but this video taught me that having a fixed mindset can take a toll on how much I actually learn so my goal is to have more of a growth mindset by the end of this school year.
Day 5: Mistakes are Powerful The fifth video was a reminder that math is supposed to be challenging, not everyone's going to understand and answer math problems correctly right away. I liked this video as well because not many teachers tell their students that mistakes are okay or teachers will expect their students to know more than they do. I appreciated the message that this video sent because I forget that I am capable of learning from my mistakes.
One-Cut Geometry Problem: Write-Up The one-cut geometry problem is the challenge of creating a shape within the exterior of a small sheet of paper. There are only two rules to this challenge: you cannot use the edges of the paper as a line of your shape and you cannot cut your shape more than once. The first challenge was creating a scalene triangle (a triangle with different lengths on all three sides), and then the second challenge was creating a square.
I tackled the first challenge in the only way I knew how. I overlapped every line of my scalene triangle on top of each other until I only saw one line on the paper and cut. This didn't give me the results I wanted, even though I was very close, I was left with an equilateral triangle. This happened with almost every triangle I cut out. I began to collaborate with my group members and one of them found a specific way to end up with an equilateral triangle every single time. Another one of my group members figured out how to create a square very quickly. I was still stuck on figuring out how to make a scalene triangle without depending on simple human error. Of course, the lengths of all 3 sides can be less than a centimeter off but is there a way to make the differentiating lengths more defined?
The only challenge I faced while attempting this problem was making a proper scalene triangle. I tried this problem out a few times by myself and still didn't get the conclusion I wanted. I was able to figure out how to fold the paper to get a square and an equilateral triangle but how is a scalene triangle possible?
I liked the work and inspiration given this week because it encouraged me a lot. I liked the videos the most because they went against everything I've been told by my previous teachers and they reassured my thinking process. In general, I like Math because most of the time, I find myself going back to a certain problem that I can never really wrap my brain around until all of a sudden it just makes sense. From studying for a test, to practicing a math problem that I will later present to my peers, to a problem peaking my interest and catching myself researching it. I just enjoy having that "Ah-ha!" moment and being able to write it down to look back on later where I get to talk about it with other people and I think this entire week has been a full representation of that feeling. As far as my work goes, I enjoyed having 4 problems to focus on and being given the opportunity to pick one that sparks my interest and that I really wanted to understand deeper. I enjoy writing, so being able to thoroughly write out my thoughts on a problem can push my thinking even further. It gives me the chance to ask more questions and maybe inspire new ideas.