First calculus semester reflection
Content Skill
One valuable skill that I have gained from this past semester in Calculus is critically thinking my way through advanced and difficult problems. In Calculus you are given problems that require multiple and difficult steps to solve. In order to work through some of these problems, I had to think critically through the steps to reach an accurate solution. Some things that have helped me with the development of this skill are worksheets that include critical thinking problems, projects in which we had to critically think of how we could accurately represent the math behind the structure (pendulum), and POW's, which required of me critical thinking to be able to find a solution. In one specific situation that I strongly showed critically thinking skills was my first POW (below). For this POW, we were instructed to think of a creative solution to a rigorously challenging problem. The task was to find the number of possibilities of no two people standing up next to each other if eight people were in the circle and they each had to flip a coin once and if your coin landed on ‘heads’ you would stand up and if you landed on ‘tails’ you would stay sitting down.
This was an extremely difficult problem to work through, however, this was the first time I would be able to apply my critical thinking skills, or rather the first time I had to start the path to growing my critical thinking skills. For this POW, I was able to think out of the box and around the familiarity of this problem to find a simple solution, a Fibonacci Sequence. To come to this solution, I had to think critically and start with the seemingly easiest process, mapping out the problem. I started to go through each possibility, but then I realized that there must be an easier way to figure out the solution. My main objective was to come up with a simple solution in order to get to the answer through a faster and easier process. Below in my explanation, there is more information on where the Fibonacci led to.
Overall, I can see my growth in critical thinking and the skills I have acquired in order to apply to the world of mathematics. Through my POW and along with our pendulum project. I will admit, that because I wasn't here for the entirety of the project, I did not get the chance to work on it as much as I wanted to, however, I still do think that I was able to develop critical thinking skills by thinking of ways that we could incorporate trigonometry into a physical structure. I think building and applying the trigonometry to the project also enhanced my problem solving and critical thinking skills. We had to understand the trigonometry, we had to apply the trig, and finally we had to describe how the trig behind our structure made the pendulum work.
One valuable skill that I have gained from this past semester in Calculus is critically thinking my way through advanced and difficult problems. In Calculus you are given problems that require multiple and difficult steps to solve. In order to work through some of these problems, I had to think critically through the steps to reach an accurate solution. Some things that have helped me with the development of this skill are worksheets that include critical thinking problems, projects in which we had to critically think of how we could accurately represent the math behind the structure (pendulum), and POW's, which required of me critical thinking to be able to find a solution. In one specific situation that I strongly showed critically thinking skills was my first POW (below). For this POW, we were instructed to think of a creative solution to a rigorously challenging problem. The task was to find the number of possibilities of no two people standing up next to each other if eight people were in the circle and they each had to flip a coin once and if your coin landed on ‘heads’ you would stand up and if you landed on ‘tails’ you would stay sitting down.
This was an extremely difficult problem to work through, however, this was the first time I would be able to apply my critical thinking skills, or rather the first time I had to start the path to growing my critical thinking skills. For this POW, I was able to think out of the box and around the familiarity of this problem to find a simple solution, a Fibonacci Sequence. To come to this solution, I had to think critically and start with the seemingly easiest process, mapping out the problem. I started to go through each possibility, but then I realized that there must be an easier way to figure out the solution. My main objective was to come up with a simple solution in order to get to the answer through a faster and easier process. Below in my explanation, there is more information on where the Fibonacci led to.
Overall, I can see my growth in critical thinking and the skills I have acquired in order to apply to the world of mathematics. Through my POW and along with our pendulum project. I will admit, that because I wasn't here for the entirety of the project, I did not get the chance to work on it as much as I wanted to, however, I still do think that I was able to develop critical thinking skills by thinking of ways that we could incorporate trigonometry into a physical structure. I think building and applying the trigonometry to the project also enhanced my problem solving and critical thinking skills. We had to understand the trigonometry, we had to apply the trig, and finally we had to describe how the trig behind our structure made the pendulum work.
Problem - Solving Skills
Generating Ideas
Generating ideas allows me, as an individual, to integrate my creativity and ingenuity into math. I am strong at generating ideas because throughout my life, I have always tried to work around a problem with creativity and ingenuity, always generating new ideas. I always try to look at the problem a different way than the obvious one, making me realize other simpler solutions to the problem rather than working through a rigorous process to get to the answer. Throughout this semester in Calculus, I have had many opportunities to grow my ability to generate new ideas. One activity that has helped me throughout this year are the POW's. The POW's provide rigorous opportunities for me to critically analyze and think through the problem creatively to lead me to a solution. One specific POW that I thought I showed strong ideas was the POW above. I realized early on that the obvious way to solve this problem would be very time consuming. I wanted to look at the problem from a different angle, come up with a shorter, more simple solution. This is how I originally came up with the Fibonacci sequence solution. However, the generating of ideas really didn't really take off until I showed my idea to Kyle and we started to build off of it. The original idea didn't work, but we were able to find a way to set up the Fibonacci sequence in order to reach an accurate solution. This is just one example of many activities that have helped me: projects (pendulum), problems ranging from simple algebra to conceptual derivatives, and seminaring about the math community and world. I hope to continue my ever increasing skill in generating ideas next semester by doing more projects, POW's, and more conceptually challenging concepts. I am always open to increase my atmosphere of skills in any way and considering how many skills I've already gained just this semester in Calculus, I am very excited to see what will be in store for next semester.
Generating Ideas
Generating ideas allows me, as an individual, to integrate my creativity and ingenuity into math. I am strong at generating ideas because throughout my life, I have always tried to work around a problem with creativity and ingenuity, always generating new ideas. I always try to look at the problem a different way than the obvious one, making me realize other simpler solutions to the problem rather than working through a rigorous process to get to the answer. Throughout this semester in Calculus, I have had many opportunities to grow my ability to generate new ideas. One activity that has helped me throughout this year are the POW's. The POW's provide rigorous opportunities for me to critically analyze and think through the problem creatively to lead me to a solution. One specific POW that I thought I showed strong ideas was the POW above. I realized early on that the obvious way to solve this problem would be very time consuming. I wanted to look at the problem from a different angle, come up with a shorter, more simple solution. This is how I originally came up with the Fibonacci sequence solution. However, the generating of ideas really didn't really take off until I showed my idea to Kyle and we started to build off of it. The original idea didn't work, but we were able to find a way to set up the Fibonacci sequence in order to reach an accurate solution. This is just one example of many activities that have helped me: projects (pendulum), problems ranging from simple algebra to conceptual derivatives, and seminaring about the math community and world. I hope to continue my ever increasing skill in generating ideas next semester by doing more projects, POW's, and more conceptually challenging concepts. I am always open to increase my atmosphere of skills in any way and considering how many skills I've already gained just this semester in Calculus, I am very excited to see what will be in store for next semester.