Personal Growth
Reflections:
Throughout this unit I had opportunities to work together with teammates, present ideas to the class and write about my thinking on different problems.
The main difference in the way I learned the mathematics in this unit and that of any other unit was the amount of justification required for each answer I came up with. Simply finding the answer was never really enough, I had to demonstrate a far deeper comprehension than that.
Another thing I like about this unit was how it pushed me to develop my own procedures for solving problems. The unit itself was laid out in such a way as to present a complicated puzzle for me to solve. As I unpeeled each layer of the puzzle, I developed another important skill required to solve the big problem as a whole. By the end of the unit, I found it easy to outline my procedure for solving a linear programming problem because I had already created each step of my procedure through smaller problems.
The way we worked in teams was very different than many of the groups I've worked with in the past. In these groups, because so much deep thinking and exploration was required, every person not only had a role to play, but had a valuable insight into how we could solve the problem as a whole. No one member would then carry the team, so it really felt like we collaborated as one unit to reach our conclusions.
What can I work on?
The biggest aspect I need to work on is proving my ideas to be true. My brain seems to slow down once I've found an answer to the problem, but I need to go beyond that if I want to justify my reasoning to others. I think I can help this tendency by looking for multiple answers to make the problem true. By doing so, I can look at problems from different perspectives, and think deeper about how others might interpret my findings.
Throughout this unit I had opportunities to work together with teammates, present ideas to the class and write about my thinking on different problems.
The main difference in the way I learned the mathematics in this unit and that of any other unit was the amount of justification required for each answer I came up with. Simply finding the answer was never really enough, I had to demonstrate a far deeper comprehension than that.
Another thing I like about this unit was how it pushed me to develop my own procedures for solving problems. The unit itself was laid out in such a way as to present a complicated puzzle for me to solve. As I unpeeled each layer of the puzzle, I developed another important skill required to solve the big problem as a whole. By the end of the unit, I found it easy to outline my procedure for solving a linear programming problem because I had already created each step of my procedure through smaller problems.
The way we worked in teams was very different than many of the groups I've worked with in the past. In these groups, because so much deep thinking and exploration was required, every person not only had a role to play, but had a valuable insight into how we could solve the problem as a whole. No one member would then carry the team, so it really felt like we collaborated as one unit to reach our conclusions.
What can I work on?
The biggest aspect I need to work on is proving my ideas to be true. My brain seems to slow down once I've found an answer to the problem, but I need to go beyond that if I want to justify my reasoning to others. I think I can help this tendency by looking for multiple answers to make the problem true. By doing so, I can look at problems from different perspectives, and think deeper about how others might interpret my findings.
For my students:
This reflection portion of the portfolio is your opportunity to think about your own thinking. Certainly, this can be a very challenging exercise, but it present a great chance to structure the way you think about mathematics (and life in general), and to improve upon the processes you already have in place. I would ask that you spend some time to delve a little deeper into your own thinking than would normally feel comfortable, and I'm confident that if you can do so, you'll see real benefits in your expanded logic and problem solving abilities.
Good luck!
This reflection portion of the portfolio is your opportunity to think about your own thinking. Certainly, this can be a very challenging exercise, but it present a great chance to structure the way you think about mathematics (and life in general), and to improve upon the processes you already have in place. I would ask that you spend some time to delve a little deeper into your own thinking than would normally feel comfortable, and I'm confident that if you can do so, you'll see real benefits in your expanded logic and problem solving abilities.
Good luck!