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Math is a process. It is not a finite set of knowledge passed down from God to teachers, who then speak great truths to their idle students. These
students, from the day they were born, learned by experience: falling hurts, dirt is not fine dining, and big brothers are malicious. But for many
students, this process ends when they enter the math classroom. It is my strong belief that students learn best in a democratic and dynamic learning environment that reflects the exploratory nature of mathematical thinking. In addition, math should not be given from teachers to students, but cooperatively discovered, allowing students to own the mathematical process, making it both more real and more attainable in the eyes of students. These two points represent a difficult and challenging level of excellence for me to obtain, but it is the challenge of such an important job that I believe will make me a successful mathematics teacher.
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One important belief embraced by most schools is in civic responsibility, that schools need to teach and encourage democratic thinking and behavior.
Democracy, because of it’s emphasis on individual power and influence, promotes conflict, discord, and some type of peaceful resolution. The hope is
that through debate and discussion, national and local policies can be made in a fair and unbiased manner. This type of environment needs to also extend to math classrooms. As a student, I remember the classes that I had no say in, that revolved completely around the teacher. Most of my friends cared very little about these classes, as they would carry on just the same with or without my friends. The problem with this type of classroom is that it is too formulamatic and unrepresentative of the creative thinking process that is required to tackle difficult and challenging math problems. Unfortunately, the converse situation is not easy to implement. Students in high school are still maturing and not necessarily capable of making wise, informed decisions all the time. Therefore I believe that a conditional democracy is best suited for classroom teaching: students are allowed to speak their mind, and hence influence the process of learning, but I as a teacher would maintain ultimate control over what direction the class takes. It is therefore important for me to sincerely consider the will of my class before making my decisions, so as not to make my “little democracy” seem contrived and illusory.
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In addition to a democratic classroom, albeit conditional, it is important that math classrooms are dynamic learning environments. In more traditional
learning environments that I have been a part of, students are filled like vessels, in a system that Paulo Friere called the “banking system” of
education. These type of classroom, unfortunately, rarely yields any level of understanding for students, for the class’ main goal is not to relay reasons, but facts and stats. Specifically in math, students memorize mechanical routines instead of thought processes. Unfortunately for students, they will not be given simple word problems whose form easily match a routine they’ve used before after they leave school; they will have to modify their past knowledge in a way that makes sense of the new problem. Understanding the mathematical process of approaching problems would allow students to deal with situations which have no cookie-cutter formula for the answer. This type of thinking is exactly what a dynamic classrooms helps create.
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My belief in the dynamic classroom stems from my faith in cooperative and discovery learning. As cooperative learners, students learn from each other.
In groups, students are in the position to help each other with problems. Students are more likely to pay attention to other kids their own age, so any chance to make students the teachers can help get ideas and concepts across. Additionally, cooperative learning encourages strategy development and delegation of authority. With some probing, students can be pushed to brainstorm for several minutes all the different ways to address a problem and begin to think about which way would be easiest, fastest, and/or most accurate. This all goes towards thinking about math as a process instead of a fact of life. This kind of process can dead end for several reasons, including an uninteresting problem or a lack of past experiences where students thought on their own. But through the discovery process and well timed probing, students gain some real insights into mathematical thinking.
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As most students first learned by “discovering” the world around them, it only makes sense that students should also discover mathematics.
Discovery learning requires me to withhold knowledge from my students, hoping that with minimal direction, students will be able to find the answers to math
problems on their own. This type of teaching is effective precisely because it forces students to create knowledge on their own. Information is more
meaningful to anyone if it is either useful or it “belongs.” When students derive the quadratic formula, it no longer belongs to it’s
ancient discoverer, but is now an intellectual possession of the students. It is highly unlikely that any of my students will spontaneously derive the quadratic formula, so it is important that I give my students pushes along the way. The trick is not giving too little guidance to leave students lost and unsure of where they are going, while at the same time not giving too much guidance and doing all the work for the students. In addition, it is very tempting for some students to leach off of the explanations and discoveries of other students. Finding the right balance and making sure each student participates equally are formidable tasks that will definitely challenge me in my first years as a teacher.
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The challenge at hand can seem daunting at times; three or more classrooms of thirty, unmotivated students everyday, waiting to trash my idealistic dreams of how an effective classroom can be run. But it’s exactly this challenge that makes teaching such an important job, and my competitive instinct is helping me think of ways to deal with less than ideal classroom situations. I’m not going to claim that my vision for the classroom is perfect, but I do believe that a dynamic classroom, rooted in the democratic process, using cooperative and dynamic learning, and, most importantly, teaching math as a living process instead of a static fact, are keys to creating a successful learning environment for my future students.
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