Language

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.