Geometry POL Prep Semester 1 Reflection
Geometry Skills
This semester that I believe I have mastered is my ability to problem solve and use critical thinking to solve different things during math. These could be anywhere from the POWs, the explorations, and homework. But, more than anything I think that the POWs really brought out my ability and somewhat made me use my skills of both problem solving and critical thinking in order to solve them if I wanted to do well. One of the ways that I am sure I have mastered this skill is by my reasoning and explanations I have in my POWs. (see buttons below) In all of my justifications for my POWs I am thorough and clear when explaining how I got my answers; this proves that I have thought deeply about my answer and how I’ve done my work to get to the final answer. The POWs I feel show these skills I have mastered the best are POWs three and one. This is because they both go into detail as to how I solved the problem and I feel that is important to be able to understand your work better, and for other people to understand your work as well.
The explorations that we’ve done this year have changed my experience as a math student this year by opening up my mind and helping me understand the content better. They were beneficial to me because when we had group conversations on each exploration I think they really helped me to wrap my mind around what we were learning; I would get to hear how other people did the problems when I did not understand, and I would compare my work to others to find a new way of doing the problems to make it easier for myself. However they did make math class a lot more challenging for me. This is because when I did the work on my own at home, there were some concepts I did not understand sometimes, so I forced myself to get as far into the problem as I could until I got to and answer or until I truly could not solve the problem without help. But, doing this and the explorations helped me learn because it made me learn how to not give up on a problem just because it was hard knowing that I was going to be talking about it the next day with the class, and it was okay because even if my answer was wrong I knew I would get the help of my classmates to be able to know how to do it in the future.
The hardest math problem that I encountered this semester by far was the pumpkin dimension problem, as part of our pumpkin carving project. I found this problem to be particularly challenging for me specifically because of the math skills it involved that I had a hard time doing. The way I eventually solved this problem was I asked another classmate who had similar dimensions to my pumpkin to show me how to do the math, so then I could do it myself; which helped me a lot in the long run.
Problem Solving Skills
After reading “The Habits Of A Mathematician” I strongly feel that the skill I have mastered more than anything is the being able to translate ideas using other forms or representations - language, symbolic, visual, etc. I feel that I am best at this skill, again because of my POWs in each of my POWs most commonly seen, I think, in POWs one and seven. (see buttons below) I believe I demonstrated this skill by using an alternative visual method to help me work through the problem, because I was able to easier see the work I was doing, this skill has helped me understand math work in the past because I am a very visual person, and being able to see what I am doing only helps and benefits me to work better. However, one of the skills I know I could improve in and have room to stretch in is my ability to formulate a plan - anticipate major intermediate steps. I noticed I could improve in this the most because generally, when I start to work on math problems, I just jump at it not knowing what I’m doing and not having an sort of strategy to help me through. The way I think I was held back from practicing this skill this semester I feel was to my lack of motivation with my work. Since math has never been one of my strong points in school, I think I have a lack of will to try to do it well, so I just rush to get it done instead of thinking about how I’m going to do it.
This semester that I believe I have mastered is my ability to problem solve and use critical thinking to solve different things during math. These could be anywhere from the POWs, the explorations, and homework. But, more than anything I think that the POWs really brought out my ability and somewhat made me use my skills of both problem solving and critical thinking in order to solve them if I wanted to do well. One of the ways that I am sure I have mastered this skill is by my reasoning and explanations I have in my POWs. (see buttons below) In all of my justifications for my POWs I am thorough and clear when explaining how I got my answers; this proves that I have thought deeply about my answer and how I’ve done my work to get to the final answer. The POWs I feel show these skills I have mastered the best are POWs three and one. This is because they both go into detail as to how I solved the problem and I feel that is important to be able to understand your work better, and for other people to understand your work as well.
The explorations that we’ve done this year have changed my experience as a math student this year by opening up my mind and helping me understand the content better. They were beneficial to me because when we had group conversations on each exploration I think they really helped me to wrap my mind around what we were learning; I would get to hear how other people did the problems when I did not understand, and I would compare my work to others to find a new way of doing the problems to make it easier for myself. However they did make math class a lot more challenging for me. This is because when I did the work on my own at home, there were some concepts I did not understand sometimes, so I forced myself to get as far into the problem as I could until I got to and answer or until I truly could not solve the problem without help. But, doing this and the explorations helped me learn because it made me learn how to not give up on a problem just because it was hard knowing that I was going to be talking about it the next day with the class, and it was okay because even if my answer was wrong I knew I would get the help of my classmates to be able to know how to do it in the future.
The hardest math problem that I encountered this semester by far was the pumpkin dimension problem, as part of our pumpkin carving project. I found this problem to be particularly challenging for me specifically because of the math skills it involved that I had a hard time doing. The way I eventually solved this problem was I asked another classmate who had similar dimensions to my pumpkin to show me how to do the math, so then I could do it myself; which helped me a lot in the long run.
Problem Solving Skills
After reading “The Habits Of A Mathematician” I strongly feel that the skill I have mastered more than anything is the being able to translate ideas using other forms or representations - language, symbolic, visual, etc. I feel that I am best at this skill, again because of my POWs in each of my POWs most commonly seen, I think, in POWs one and seven. (see buttons below) I believe I demonstrated this skill by using an alternative visual method to help me work through the problem, because I was able to easier see the work I was doing, this skill has helped me understand math work in the past because I am a very visual person, and being able to see what I am doing only helps and benefits me to work better. However, one of the skills I know I could improve in and have room to stretch in is my ability to formulate a plan - anticipate major intermediate steps. I noticed I could improve in this the most because generally, when I start to work on math problems, I just jump at it not knowing what I’m doing and not having an sort of strategy to help me through. The way I think I was held back from practicing this skill this semester I feel was to my lack of motivation with my work. Since math has never been one of my strong points in school, I think I have a lack of will to try to do it well, so I just rush to get it done instead of thinking about how I’m going to do it.