Reflection About Maths

I have always excelled at math and science. Sophomore year, I had to decide whether I would take regents or honors physics in my junior year. I was already going to take AP biology, and I had planned on signing up for regents physics so that I wouldn't get too overwhelmed by science courses. Everyone warned me that honors physics was a tough class. However, I ended up taking the honors because my friend didn't want to be alone in that course. This is one of the best choices I've made in my life. I loved my honors physics class. Physics allows me to apply my math knowledge into real world situations that I can visualize and even test experimentally. Additionally, it requires me to problem solve and think problems through meticulously, which I love.

I think it is safe to say math has always been a passion of mine. I remember learning to count to 1000 in first grade. When I was finally able to do it without any help, it was like swimming for the first time, eating the ripe tomatoes I grew myself, or putting together a new song on the guitar. The feeling of accomplishment cannot be recreated. As we get older, this feeling becomes more difficult to achieve. This only increases my motivation and determination to learn something new. AP calculus has been a roller coaster of learning. Despite the struggle and rigor, I learned valuable skills that will help me in my future aspirations. Taking the AP Calculus exam gave me a rush of accomplishment. I have built a knowledge base because I am constantly

For the past three years of my high school career, and now my fourth, I have made it an obligation to continually expand my horizons in regards to math; when I cannot fully grasp an idea or concept, rather than giving up, I relentlessly pursue the idea until it is understood. During freshman year, math did not come easily to me. I was forced to go in early some days because, simply, I did not comprehend the concepts. However, taking initiative with my school work, and constantly working through problems that were difficult can be deemed one of the best decisions I have made. Although my final grade may not have been an

After all, math was one of my best subjects. I had never really had an experience where I just couldn't understand the concept of a math problem, of how it was solved and why. Our teachers has warned us back in elementary school, that one day we would hit an invisible wall and not ease through classes. That one day we would struggle with understanding a problem, a concept or even a subject. I had never believed them, thinking this would never happen to me, that I could somehow avoid this wall of confusion and just walk right through. But there I was, utterly confused and frustrated at a simple problem that everyone else could solve. Why was I not seeing it? Why couldn't I understand the solution? I asked myself. For the first time in my life I really struggled to get an A in a class. I had my sister tutor me almost every day, preparing for a quiz and then the next, and the next. I came in to my teacher for lunch and he helped me step by step. I studied for tests, and worked hard. And my work payed off. I got a high A in the course, and a lot of experience from it. It taught me how to work hard for something, to earn a good grade when you deserve it, and it gave me the skills I needed to get As in the high school classes I am taking this

Algebra was awful! I did not realize why in the world I had to take it! I knew I would not use it ever in my field. Wrong again! I used it a lot in the BSHS program. I never connected Human Services with Business. Once I was challenged with courses such as Statistics and Financial Management, I realized very quickly that Math and Human Services Management relate.

In 8th grade, instead of baking cookies or cake in cooking class or drawing pictures in art, I took German 1 to put myself in the position to be placed in AP German my senior year. My freshman and sophomore years of high school I took Photography to work towards taking AP 2D Studio Art along with other AP/accelerated sciences, maths, and english classes. Certainly, there are other students that took just as difficult of courses that I did, but I pushed myself to excel in other courses that others may not have taken.

I would enjoy taking pre-AP Algebra II because I want to be ready for college courses. I love challenging myself, especially in math because that is my favorite subject. I will be willing to put as much time doing things for this class, like studying and doing homework. This year, because of geometry, I have figured out how hard classes can be, but also how much help all of the homework and study flashcards have given me. Also, I can easily complete assignments on my own because I have plenty of time to work on them and I enjoy working by myself. Taking pre-AP Algebra II would help significantly in the future.

As those who love physics or chemistry, or biology, are most likely to understand difficult and complex concepts and be successful in their respective subjects, I became more successful at understanding mathematical concepts as my junior year progressed and as my senior year began. Calculus became an infinitely easier subject and one that I could comprehend with relative ease, even easier than traditionally “easy” subjects for me such as history or language arts. I learned that I could fly through problem sets and enjoy it, and for the first time in my school life, I was the one answering my peers’ questions instead of being the designated clueless classmate. Learning to love something that is so essential to life made me enjoy myself and my life more than I had previously, and I no longer felt the self-doubt of not being “gifted” in mathematics in a group of mathematically “gifted” students. I feel markedly more confident in my mathematical abilities, both presently and in the future as a student majoring in

“There are students taking these courses three, four, five times,” says Barbara Bonham of Appalachian State University (Hacker). I do not believe that if the schools want their students to pass, and be successful that they should teach algebra. More and more students each year stop taking the classes because it will hurt their GPA (Grade Point Average).

Besides that, I also have enjoyed my science and math classes more so than any other subject. The satisfaction that comes along with the correct solution to a tricky math problem, the “aha” moment when you understand why something happens, those instances have been the most enjoyable moments in my classes. Especially when those subjects are paired with a good teacher, it's guaranteed to become my favorite class.

As a mathematics major, the concept that most people overlook is that I did not choose to study mathematics because I do well at it; I chose to study mathematics because it makes me smarter. In fact, all throughout junior high and high school I was in remedial mathematics classes and worse, I did not even place into a freshman year mathematics class in high school. I had to re-take 8th grade mathematics. However, something about mathematics excited me. Maybe it was the fact that mathematics never came easy to me and I wanted to prove to myself that not only could I pass mathematics classes, I could actually understand and excel at them. For me, mathematics is not about the arbitrary numbers, trivial solutions, meaningless formulas, or repetitive computation: it is about the progress of knowledge and human understanding.

Of course you could always work hard to learn the content, but it would be very useful to know more about high level mathematics. It could be very good for students to have a teacher that has a math major or minor along with their teaching degree. In the fifth grade classroom, the teacher is not the greatest mathematician, but is very honest with the students and shows her curiosity to find the answer.

During the observation time I was placed in a first grade classroom. Walking into the class I began to look around and smile, there was so much color all over the classroom I could not help but feel happier. The teacher immediately stopped the class and told us what they were doing that morning and had each student introduce themselves to us. They went around and stated their name and then went back to their math workbook. When they were finished with their math worksheets they were then able to pick something to do around the room. That included reading on their own, getting to use the iPad, working on the computer, etc. Some students were together while others chose to work on things independently.

In this paper I will be discussing the mathematical task framework, low cognitive demand and high cognitive demand by using two different articles. The research I will be using is from “Mathematical Tasks as a Framework for Reflection: From Research to Practice” by Mary Kay Stein and Margaret Schwan Smith and “Selecting and Creating Mathematical Tasks: From Research to Practice” by Margaret Schwan Smith and Mary Kay Stein. I have been given several different tasks that I have analyzed and put in high cognitive demand or in low cognitive demand. I will explain why I have chosen high or low cognitive demand for each task with using different approaches such as memorization, procedures without connections, procedures with connections, and doing mathematics.

In junior High School, things started to turn around for me. Although I was still placed in lower level classes, I developed a love for learning. In the years to come from Junior High to High School, I had a strong urge to make up for lost time. One class I started to excel in was the one I used to have the most trouble with, Mathematics. It seemed as though the once boring and complex equations now seemed meaningful and simple. As I progressed into 8th grade, I was able to advance to normal classes. I felt that the hard work I put in was finally paying of. At this point, I felt that I could handle a higher level. At the end of 8th grade, I took the necessary procedures and tests to try and get into honor - level courses in 9th grade. After taking a summer course of Algebra 1 and several tests I was able to succeed and take the classes. The experience was great. I felt that I was finally going the right direction