School teaches us how to think about ourselves, our lives, our world. In different classes, we learn different techniques: analyze, problem solve, investigate, communicate. Each technique is crucial to developing students as thoughtful, informed members of society, and all are developed through mathematics. The typical explanations of why all students are expected to study mathematics often reference the possibilities of the STEM fields, or simply that its value is inherent; we learn math because math is important. As a student, I was never taught anything beyond this, but I enjoyed my math classes, so I persevered in learning mathematics in order to use it in my future career. I had planned to be an engineer until I found that my calling was to teach. However, neither of these typical explanations recognize the true value of studying mathematics; both represent a narrow and unconvincing perspective, which will not reach the majority of students or inspire them to persevere through its complexity.
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I believe that students learn best through actively experiencing and creating knowledge for themselves, and so I make every effort to include hands-on, experimental projects in my classroom that deepen the context and student understanding. A process which they discover themselves will have more meaning and lead to more productive results than the “most efficient” technique whose steps a teacher lists on the board as the student copies them. Students producing divergent ideas signals to me not that my students are necessarily failing to understand, but rather that they are thinking deeply about the task and the process needed to solve it. Mistakes are opportunities for growth, because they create opportunities for discussion, asking “Why do you think that your strategy didn’t work?” I have found that greater learning occurs through thought -provoking questioning that promotes examination of the reasoning behind that misunderstanding as opposed to directly correcting the error or funneling students toward the “correct” answer. This strategy emphasizes student authorship over their mathematics, while also creating opportunities for students to learn. I believe that all students have the ability and drive to learn mathematics at a high level, but often feel alienated from the subject when it becomes strictly procedural and removed from reality. Despite the common understanding of mathematics as strict repetition and memorization of procedures, students in my classroom understand mathematics as a process of discovery and understanding. Students and teacher alike ask not “What is the answer?” but rather “How did you find your answer?” and “Why did you do it that way?”
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