Philosophy for Teaching and Learning of Mathematics
This I believe:
What is mathematics? Until now, I have never thought too critically about this question. Throughout my educational career, I have been forced to analyze my beliefs about my role as an educator. I have written several papers defending my epistemology regarding the importance of differentiation, teaching across the curriculum, cooperative learning, utilizing Bloom’s taxonomy, addressing learning styles, assessing reading levels, setting workable goals and objectives, etc.. The list is extensive, but never once have I critically thought about my philosophy of mathematics.
Sadly, I believe my unenthusiastic conceptions about mathematics were formed over years of having to memorize formulas, processes and computations that never really made sense. I remember my feelings of validation when I asked my high school trigonometry teacher, “When will I ever use this in the real world?” His response was a stumped expression ensued by a nervous response that evidently was not too convincing. As I grow “into myself” and outside of the confines of the lackluster mis-teachings of my more formative years, I am starting to understand the beauty of math that was never taught to me.
Ironically, the beauty of mathematics that I’m starting to understand is forming through a process of relearning what mathematics is truly about. Throughout my elementary and middle schools years, I attended several (12 to be exact) different schools due to my father’s employment with the United States Navy. Rarely, did my school year end at the same school the year began. As a result, my knowledge base of mathematical concepts was as choppy as the ocean waters my father sailed on. In fact, the idea that there were even deeper “concepts” to the monotonous and rote memorization of various math facts was foreign to me.
A couple of months ago, I was standing in my oversized teacher shoes, in front of my marker board decorated with repeated addition groups of various colors attempting to “teach” multiplication when, the “big picture” suddenly rolled over my mind like the giant peach that saved James from the mean and debilitating Aunt Spiker. However, in my case, Aunt Spiker was years of public education that convinced me that math was only for smart people and I was not one of them. The epiphany I reached was that mathematics makes sense. Except, you have to understand the beginning of the story in order to figure out the ending. One cannot skim and scan the middle of the story, unless gifted, to predict the correct ending. It builds and builds on each other and it is meaningful yet undeniable complex (for me anyways—at this stage in the game). It’s not a matter of memorizing the techniques needed to plug 10 into x, it’s going beyond the superficial and understanding that the true essence of mathematics is to recognize that mathematics is a way of thinking. However, without a firm foundation, much of this “way” can be lost, and that is the experience of many.
Like with any new -found knowledge, it can’t be forgotten even if it would make your life easier. The vision and expectation I have for myself as a math teacher is one that facilitates to the best of my ability an atmosphere and learning experience that focuses on the “why” and the “how” not the “what” is the answer. The reasoning behind the “madness” is as important as the reasoning behind me wanting to become a teacher. If I don’t provide my students with the foundation to build their house, they will never live in a castle. They may grow to think they’re incapable of reaching their dreams because they, “just don’t understand” or are “not smart enough.”
This is my first year teaching fourth grade special education. I have taught history and economics at the high school level and thus, was never exposed to strategies called “doubles plus one” or “touch math.” Apparently, I wasn’t taught these strategies either. However, I learned rather quickly from the students what they needed to be successful. My first couple days of school were filled with questions like, “Can I have a number line?” My response, being “ a number what?” Yes, it’s true, I was that clueless. I quickly learned, that each of my brilliant little minds had a different way to compute math. Some depended on their number line like it was their lifeline, if I took it away they just might stop breathing. However, others weren’t reliant on that, they had red and yellow counters that did the job just fine. As I walk around my math class I can see each one of my students using a different strategy to solve a problem. I firmly believe that we all learn differently, and it’s important to allow students to have the freedom to choose what works best for them. And to my honor, as their teacher, I can facilitate their learning so that they might understand a more efficient way to solve a problem.
I recognize that I am at the tip of the iceberg. I have only begun to conceptualize how truly understanding math will transform my way of perceiving the world around me and how I teach in it. As the anti-smoking ads state, “Knowledge is contagious,” it is up to my generation of teachers to relearn, redo and reform the way we think about math.
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