The skill I chose to focus on for this reflection is one I have struggled with throughout the semester, understanding infinity. It was really hard for me to think in terms of infinity in the different formulas we used, and was impossible for me to fathom the infinities of different sizes presented to me in class.
What helped me understand this concept was not an assignment we did in class, but two small pictures a friend from Calculus II showed me. Both pictures contained a circle on a graph with a diameter of 1. In the first picture (fg. 1) the circle had vertical lines drawn through the circle. In the second picture (fg. 2) the circle had lines drawn through it diagonally from a point just above 1 on the y-axis.
Figure 1
Figure 2
After showing me these pictures, he asked me this question: "If there are infinity lines drawn each of these ways across the circle, which has more lines?" My immediate response was: "Neither, they are both infinity." Another student came over from Calculus II, contemplated the picture, and said the circle containing the most lines was the one in figure 1, with vertical lines, because figure two had angles between each diagonal line, therefore taking up more space.
Understanding infinity came much more easily to me after this picture, and I hope this way of thinking helps you too.
PROBLEM-SOLVING SKILLS:
The problem-solving skill that I am strongest at is generating ideas. The beginning of this semester was a little rough for me because I was going asked to find my own ways around problems, and that was not something that I have had to think about before. The Problems of the Week helped me most with this skill because, every problem, I was encouraged to find my own solution to each problem. At first I relied on my classmates, but as the problems continued I got better at recognizing patterns and similarities between problems. I still struggle with this skill, but I think the POW's of next semester will help me even more with this. I also intend to listen to my peers so I can begin to understand more of their solutions as well.
Problem of the Week
In calculus we are challenged to problem solve, and this often comes in the form of our Problems of the Week. These are presented and we spend around a week trying to solve each one, Below you will find my best POW solution of the first four problems.