One of my favorite classes this year is actually study hall. It's not your average study hall though. For this class students bring their math questions for us all to wrestle together. I don't know if I love hearing them wrestle with math problems that they've never seen before or love sharing a challenge with them more. To be clear, these students are not in the same mathematics classes, also it's not a large class. I'm sure that both of these factors play a role in making this class particularly fun. What's not to like about watching a student in Algebra 2 wrestle with a precalculus concept they've never seen, but are excited to explore?
One of our recent challenges involved finding a beautiful way to use the process of completing the square to discover the quadratic formula. As you may know, the quadratic formula is not beautiful. It is messy, but gets the job done. However, mathematicians love to find the intersection of beauty and truth, and the origin of the formula from completing the square can be particularly beautiful.
While exploring this process of completing the square by literally completing a square shape, we were reminded that the famous algebraist Al-Kwarizmi would have neglected the negative answer, as a negative length for the side of a square doesn't make sense. This neglect reminds us that the origin of algebra is actually geometry. Geometry reveals our need for algebra, and now that algebra is developed, we use it to describe and learn geometry. Algebra is the language used to explore all areas of high school mathematics. It is universal and reveals to us our human tendency to imitate our creator through language. This short non-essential class is quickly becoming essential as both my students and myself learn how the created world is connected to the world of mathematics through language. Exploring mathematics not as segmented branches, but as intermingling dance partners reveals the glory of God in a whole new way.