Friday, August 27, 2010

My Math Life Story

Peak Experience:

My math life story peak experience was actually born from a feeling of complete inadequacy I had in regards to my mathematical achievements. Due to my older sister's ability to excel in every math honors course she took in high school, I entered my high school journey with the already implanted expectation that I also would join the math honor's train. This expectancy however, did not last very long. So after two failed attempts across two years to test into a math "AP" class, I finally accepted my place in a basic Algebra I course during my junior year of high school. I decided that I no longer was going to try to prove to my parents and the guidance counselor that I was, "smart," enough to get that special credit on my report card, and I was going to just try to experience math, for me. Now, it may have been the teacher, the book, or even just the material I was learning, but boy did I increase not only my mathematical competence but also my confidence in my abilities to succeed in math. That year I went from a stressed out basket case trying to memorize every definition, equation and concept (for the test) to a math student who became engaged in class discussions, accepted help from tutoring, and eventually became a peer tutor herself. It is from that, "basic," Algebra I class that I took away more knowledge, and more experiences from which I have now transferred to my college math courses and assignments. I learned that sometimes you have to take a step back and forget about the formalities and pressures surrounding others' expectations. I then allowed myself to learn something for me! In the end it did not matter if my high school transcript said, "honors," courses or not. I moved on from high school with an improved outlook on what it means to be a successful student, on my own terms. It is this message that I will pass on to my students as a teacher. I will make sure they know that it does not matter where you end up on that honor roll, it is the journey you take to get there, and the knowledge you develop along the way. Teaching them to be the best THEY can be, and always remember, stress will not equate success!


Nadir Experience:

With the good comes the bad! As you just learned, I never did make it into a honor's math course in high school. My negative experience comes from that reality in combination with my school's choice to place a football/baseball coach in the position of teaching the, "regular," geometry class. His idea of teaching us was assigning chapters to read and practice problems for us to do inside and outside of class. This was done without any form of formal teaching. My frustration levels grew each class period, as I was unable to learn successfully by reading from the textbook. Eventually I began to shut down, and lose motivation to retain anything I was assigned to learn. My math experiences began to be about completion rather than mastery. Geometry was obviously not important to this teacher placed there to teach, so why would it mean anything more to me? Geometry became more of a social hour with the occasional rush to memorize angles and definitions in order to pass the test. That experience truly made me realize that lack of quality and meaningful instruction really does have negative impact on students. A large amount of important geometric concepts were not learned by myself due to this teacher's lack of ability to teach and motivate. I was forced, 4 years later, to play extreme catch up in order to succeed in a college level geometry course. As teachers, we should never set our students up for a deficit that large and influential. I will take my job as an educator very seriously as a result of this experience, and never take for granted the job I am assigned to do. I wish only that my students take away peak experiences in my classroom, and any nadir experiences that may come along will be quickly forgotten or celebrated.


Turning Point:

I do not feel that there is just one specific point or experience that sparked an important change in my math life. If there was one, my memory has failed me! However, a series of turning points in my mathematical journey came during my elementary math courses I was required to take before entering my PDS. The courses were not really about teaching (or re-teaching) math but exposing a different side of it from what we were originally taught; to understand the why. This was a turning point because up until then, similar to my colleagues, I thought math was full of very concrete, "do this to do that," type of concepts. When trying to explain why something is what it is, you have to take a step back and really dissect the process you took to get there. It is from these dissections that I realized that math can also be very abstract, and solutions can be influenced by our own learning styles and perspectives we take. While you can teach a child that two plus two will ALWAYS be four, you can also give a child multiple ways to solve addition, subtraction, multiplication, and division problems. They can choose which way suites their learning style. By choosing their own way to solve math problems they are more likely to experience success! I do not know about you, but I was only taught one way to set up a subtraction problem, and one way to show my work throughout my early math journey. These series of turning points, which came from my participation in these courses, revealed a more dynamic side to math that I can pass along to my students.


Other Important Scenes:

Around the World," is not a productive game! My third grade teacher loved to force us to play this torturous game after we all passed our multiplication times tests. It is from these games that my math anxieties stemmed. It is also from this game that the stereotype of female’s inferiority in math began to emerge, of course now I wonder if it was a more of a competitive characteristic that led to the boys’ dominance of being the last one standing. I still remember the butterflies I felt in the pit of my stomach when my turn to stand in front of all my peers and answer the random multiplication fact was next. I would consider myself an average to slightly above-average student in third grade. I can only imagine the anxiety my peers felt who were struggling learners when forced to stand up in the spotlight and display their memorization of the multiplication facts. These are feelings that I will work hard as an educator not to expose in my students. Those types of competitive games should be left on the playground!


My second scene comes a little later in my life. It was the first semester of my special education internship and I was placed in a fourth grade general education classroom. During this internship we taught a total of twenty lessons across the semester, dividing them up among math, reading, writing, science and social studies. For one of my math lessons I was told to teach the foundations for learning to divide. This lesson was taught over the span of two days, and by the second day my students were rolling along great and it was time to introduce them to the operational signs that are used to represent division. On the overhead, where everyone could see, I wrote a division problem using the traditional right parenthesis with vinculum, or this is what I thought. In fact I had actually wrote a square root symbol! I should have realized this sooner, but even after my students tried their best to expose this error to me, I continued with the lesson using a square root sign! It was not until my professor, who just happened to be observing me, told me after my lesson of my mistake. I was humiliated. I took the first opportunity to correct my error with the students and made sure they learned the correct sign that can be used when setting up their division problems. This memory just solidifies the critical idea that it is imperative that you plan, plan, plan and rehearse before teaching a room of children. Maybe have someone else look over my math lesson plans in the future as well!


Greatest Challenge:

The single greatest challenge I have faced along my math journey has been the time commitment I typically have to make in order to be successful in this subject. I feel throughout my life I always had to work just a bit harder at math than others, and no matter the problem, solution or expectation I always spent more time than my peers completing it. I have faced and overcome this challenge by dedicating more of time outside of school to understand math, as well as increased my engagement in discussions and math problems inside of school. I also sought the assistance of a math tutor outside of school during my high school years. This challenge never allowed me to slack off, because if I did I experienced failure (lack of accomplishment). With my math tutor, parents and sister, Allison, I gained the support and help I needed to be successful and accept this challenge with full embrace. This challenge has impacted my experience with math in the form of confidence in my ability. I have come to accept also that maybe it was my lack of confidence all along that created this challenge for me. When my confidence was low, the time commitment increased, but when my confidence was a little higher, the time commitment decreased. This mutual relationship has remained consistent throughout my childhood and on in to my adulthood.


Special Education Teacher:

I want to be a special education teacher because I believe that every child can. Not only do I feel every child can, but also that every child should be given equal opportunity to reach their inner potential and exceed expectations. One of my favorite quotes from a Christian song I love reads, “Impossible is not word, it is just a reason people give for not trying.” Throughout history that “word,” "impossible," has been used too much when speaking about and teaching children and adults with special needs. It is amazing the change that has occurred in this field and I want so much to be a part of that. No matter the disability, I feel that children are all born with special gifts. It is with these gifts that we as teachers can really make a difference in their lives, and it with these gifts that they can have meaningful growth. I want to celebrate the, “special,” in special education!

When it comes to teaching mathematics to my students I feel that their success will have to start within me. I need to be confident in what I teach them so that they in turn are confident in their ability. I believe that there is no one way to teach or learn. I will be sure that they are given the tools to solve the problem the way they can be most successful with. My vision of math instruction also includes cooperative and collaborative learning. Breaks in the lesson when my students can explore and learn together with their peers. I will do all I can to prevent math anxiety from occurring along their math life journey!

9 comments:

  1. Thanks so much for your detailed entry, Amy. Wow. I really learned a lot about your journey in mathematics in reading this. I can still feel the pain and anxiety that comes out when you remember your Around the World experience. It sounds like it's still a very raw memory for you. Have you had a chance to read Elizabeth's entry yet? She writes about her experiences with Around the World in a very different way.

    I also get a sense that your mathematical confidence came from learning math in a way that did not emphasize correctness or competition. Being in a "regular" track Algebra I sounds like it helped you understand the mathematical concepts at a very deep level. I'm only sorry that it was followed up by a horrendous year of Geometry. Unfortunately, what you describe in your Geometry class is more common than we'd like to believe. I'm sorry you had to go through that.

    Thanks so much for sharing this, Amy. I'm touched by what you wrote about your reasons for working with special education students. It sounds like your faith also plays a deep role into your desire to work with students with special needs.

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  2. Amy,

    Can I ever relate to your Around the World experiences! I was never good at that sort of game, both with the timing issue and being put on the spot.

    I can also relate to your horrible memory of high school Geometry. I had a teacher who always taught "above" us, who really should have been teaching college students rather than sophmores. Very hard class. I really learned most of my upper level concepts in Geometry from my remedial math courses, which taught me so much more than I have really learned all along.

    -Jennifer

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  3. Amy--I really enjoyed reading why you want to be a special education teacher. See what the student can do rather than what they cannot do is essential to success in our chosen field. I believe your faith in your students will help you in becoming a great teacher. Unfortunately, we mostly see teachers who are just trying to get through the day, rather than actually thinking of ways to help their students. We see teachers who are tired of their jobs and therefore no longer care about the success of the students. I know it is easy to say now that we will always put our students first, but generally that is not what we see in the schools. I sincerely hope we all continue to think first of our students and their success.

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  4. I agree with Allison, your desire to instill confidence in your students when teaching math will be an attitude that sets them up for success not only in your class, but in their future classes as well!

    Your statement about how we as special educators should never set our students up for a deficit (way back in the Nadir Experiences section), is so true, and is perhaps, the most difficult aspect of our future jobs. Whereas many of our Cohort F blogs were filled with stories detailing experiences where our math teachers forgot one crucial part of teaching, that is, the instruction itself, when we step into the classroom, the more demanding learning needs of our students will necessitate that such as laissez-faire approach to classroom instruction does not exist in our rooms. For many students in general ed, playing “catch up” for a year of poor instruction is sadly, part of the educational process; however, when working with students with learning disabilities, as we’ve already seen in Dr. Robertson’s class, playing “catch up” already exists due to their different learning needs so all instruction we provide should be provided with the intent of reducing any discrepancy between their starting point and that of their peers in general education.

    It's obvious after reading your blog that from the moment your students step into the classroom, you're going to set them up for success by providing support and encouragement throughout every step in their learning process!

    P.S. (In response to your comment on my blog...) I had to go to the Laptop Help Desk in order to figure this out, but when you want to add a picture to your blog there is a certain button that you push (it's a white box with a blue interior to the right of the word "link" on the bar above where you write your posts) before you actually put the pictures onto your post. I realize this explanation isn't great--I'll show you Wednesday at Dr. Patton's class, if you want!

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  5. I really loved reading your post! Although you've told us a bit about how mathematics was a struggle for you growing up, I never knew how hard you worked to feel successful in mathematics. It really shows how strong-willed and determined you are! My favorite part of your story was why you want to be a special education teacher. I know many of us in this cohort feel this way, but you put it to words beautifully! I also need to remember to ask you what song that line is from because I love it! You need to make a poster of that quote and hang it in every classroom you're ever in :)

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  6. Impossible is nothing. So true and it does not surprise me that this comes from a Christian song (not a slam). I gain strength from this fact everyday. I like this line released by the NBA:
    "Impossible is just a big word thrown around by small men who find it easier to live in the world they've been given than to explore the power they have to change it. Impossible is not a fact. It's an opinion. Impossible is not a declaration. It's a dare. Impossible is potential. Impossible is temporary. Impossible is nothing." This phenomenon will sustain both of our efforts as teachers of students that many others would give up on.

    Eric

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  7. You obviously had a difficult time in your Geometry class, and I do not blame you! I don't believe that many students could take something as abstract as Geometry, or any other type of math, and learn from their textbooks. We've learned that so many students need to work with their hands, listen to explanations, act out the problem solving methods, etc. to know better than to just hand a student a textbook and say, "You're on your own, kid." Yeah right, like that will work for everyone!

    It's also clear that you're coming from a good place while approaching this course. You seem to be willing to learn, willing to change your mental model of what a math class has been for you into what it should be for everyone. I believe this openness will help you succeed and be proud of your accomplishments even if the going gets tough this semester.

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  8. I too want to comment on your nadir experience. It's unfortunate that you had a teacher who didn't seem to care much about the subject he was teaching. In eighth grade, I experienced a similar issue when our class was taking algebra by CD. It was a trial program and while I was able to grasp the material, I watched as classmates just clicked through the pages and my teacher sat at her desk checking e-mails. Since she was ineffective at monitoring student progress, overall mastery of the concepts was not evident by the class test scores.

    With these negative experiences, we can learn to be even better teachers for our own students. It seems as though you have kept a positive outlook and are willing to set your students up for success. Yay! While math may be one of my favorite subjects, it is important that I take on your mentality when teaching subjects I find difficult, such as writing. I must seek out what my students are passionate about so that I can make the subject matter, no matter what it may be, applicable to their lives and interesting too!

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  9. Like you, a turning point for me was also in the math class we had to take. It made me think a whole lot more than I wanted to and I really didn't take it into consideration until I got into the classroom. Because math had been simple for me, I was really frustrated when I couldn't convey my thoughts to my students.

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