Learning Limits
During this semester I have for the first time really struggled in math class. Calculus is full of concepts that were hard for me to grasp. Concepts like on type of infinity being bigger than another based on the speed at which it reaches infinity. This concept was hard for me to grasp because the concept of infinity is already hard enough to grasp and the idea of one infinite range being larger than another is even harder. An example of one infinite range being larger than another is comparing the decimals between 0 and 1 to the whole range of natural numbers like 1,2,3,4,5... both of these are infinite ranges but one of them is larger. The range of decimals between 0 and 1 is bigger than the infinite number of natural numbers because when dealing with the range of decimals between 0 and 1 you can put as many numbers as you want in between two of them whereas with natural numbers you cant put anything in between 2 and 3 because those are the closest natural numbers.
Another concept that took me some time to learn was limits. The reason that I wasn't able to grasp this concept right away was because I didn't know how it applied to real world problems. I did not do very well on the test that involved limits but after we applied them to finding derivatives, limits started making a lot more sense to me. One concept that helped me grasp limits was when we used asymptotes in graphing problems. When doing this you find the limit of the graph as it approaches its asymptote. This helped me learn limits because it gave me a reason for why I should learn them. So then I learned how to simplify an limit equation until I could insert the limit into it and get the answer of what the limit would be. This process of how I learned limits showed me the I learn well when I can apply what I am learning to a real situation.
Another concept that took me some time to learn was limits. The reason that I wasn't able to grasp this concept right away was because I didn't know how it applied to real world problems. I did not do very well on the test that involved limits but after we applied them to finding derivatives, limits started making a lot more sense to me. One concept that helped me grasp limits was when we used asymptotes in graphing problems. When doing this you find the limit of the graph as it approaches its asymptote. This helped me learn limits because it gave me a reason for why I should learn them. So then I learned how to simplify an limit equation until I could insert the limit into it and get the answer of what the limit would be. This process of how I learned limits showed me the I learn well when I can apply what I am learning to a real situation.
Communicating thinking in a clear and accessible way
During the beginning of the year I struggled with answering the problem of the week correctly but I was consistently able to clearly communicate my thinking. A good example of this was on the second problem of the week that I answered. I incorrectly answered the question but in my reflection of the problem I realized my mistakes and communicated my thinking behind the mistake and clearly corrected my mistakes. This also reflects my ability to recognize and resolve my errors. Even though I have done well with these two problem solving skills I have had trouble generating ideas and starting the problem solving process. In order to overcome this I have been trying to break down the problems into smaller parts in order to have an easier time solving them.