Philosophy

As I reflect upon my previous years of teaching, I quickly recall how my first year forever changed my approach to mathematical education. After only a few months into my first year, I quickly realized that what I was doing was not working. I found myself telling my students how to do each problem over and over again. In other words, I would show them all the different rules and they would have to memorize and recall what to do and when to do it. This was next to impossible because the number of rules and properties never seemed to end. Let me give an illustration to prove my point. Think about a Rubik's Cube. I have learned how to solve one, but only by memorizing the many different algorithms. Sure I can solve it, but I do not really understand how each algorithm works. Often in math classes, we find ourselves doing certain steps, but we do not know why. We simply do it because the teacher said that’s how it works. I gave this example to each of my classes and they resonated with the idea right away. They knew exactly what I was talking about because so many of them had been taught this way in the past. We as educators need to teach procedural fluency, but in conjunction with conceptual understanding. To put it better, “knowing is the what, understanding is the why.” We need to teach the “why” along with the “how,” for students to truly understand.

If we want our students to understand why math works the way it does, they need to explore and discover it for themselves. To supplement them in doing this, I have my students use different tools such as algebra tiles, interlinking cubes, geoboards, tangrams, pattern blocks, graphing utilities, etc. These things give us something to talk about and promote classroom discourse. We discuss math in small groups, as a whole class, and we learn from each other. So my goal is to use tools along with real-world problems and contexts to drive instruction. Therefore, students are able to learn the concepts at the deepest level possible. This is the philosophy I base all mathematical instruction upon in my classroom.