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PreCalculus

I am certain that precalculus is all about learning patterns. I have found a lot of success in showing students the patterns that arise in precalculus topics. I have found if a student is able to work with, see, and talk about the equations, graphs, and concepts in precalculus their success in understand the subject increase dramatically. In fact I have found that students do better in the math classes they take afterward.

To show my reasoning let me discuss polynomials for a moment. Everyone who takes precalculus encounters the following equation: ax^2+bx+c=d. If the student is able to see, show, and talk about the coefficients and how they effect the graph, they will ultimately be able to do this for any polynomial equation they encounter. This will then lead to a better understanding of the polynomial in calculus. For instance, the coefficient a, affects the graph's width, or horizontal width, with this concept understood the student will understand how the polynomial with transform in calculus. This then leads to a better understanding of physics and the effects of acceleration on an object.

This basic concept must be worked with in the creation of many graphs, changing the polynomial many times, and discussing the concept out loud to ensure the student has grasped the concept. Thus once the student sees the pattern for themselves they will be able to quickly identify the polynomial and understand how it applies to many different problems.