Normalcy Versus Eccentricity: Case Study in Math Applications

The story is told of a man driving on the I-5 freeway, who received a cell phone call from his panicked wife. The woman warned her husband, "I am scared; I heard a news report that there is a crazy driver driving the wrong way on the freeway, right in your vicinity!" "It's not just one," replied the man, "there are hundreds of them!" In my math classes, it is oftentimes an interesting experience to pose unexpected questions to my students and make note of their replies. My math students are accustomed to classes commencing with a warm-up quiz via Kahoot. In lieu of a traditional multiple-choice practice quiz, I recently preceded a pre-calculus lesson on conic sections with a single-question philosophical question distinguishing a "normal" versus an "eccentric" person. This would lay the groundwork for the formulae on ellipses, especially that of eccentricity of an ellipse. I challenged students to select and justify which scenario is the more reasonable: "The distinction (between a normal and eccentric person) is mathematically describable", or "I'm normsl and everyone else is crazy; the Voices told me so." Students seemed divided in opinion, with perhaps a slight preference of the latter scenario (eccentricity being arbitrary). One student pointed out that since every individual is unique, complete normalcy is unattainable. Another student suggested a mathematical quantification of normalcy is possible from the standpoint of allowing deviation from the norm within certain limits. This was highly reminiscent of the normal distribution function, despite the fact that such a function is beyond the scope of this course. Why do I discuss this particular application concept here? We math teachers often contend with students who opt to avoid or minimize work done in math classes. Justifications for such inaction are disturbing. "I hate math." "I can't do math." "The subject is boring." "The subject is dry." Then, of course, we have the evolved versions of the "homework dogs" that back in the 1980s would pop up in front of unsuspecting students, snatch and eat their homework, then vanish into the parallel universes from which they had come. In this generation, we have instead computer bugs that delete files from students' computers, render computers totally inoperable for weeks at a time, mysteriously delete submitted assignments from drop boxes and delete all evidence of tests taken and messages sent to teachers about missing items. I have heard all of this, and more. Give me any excuse for not working; I have probably heard it, or some slight variation, at some point in time. In addition to establishing and maintaining standards of thoroughness in math classes, it is highly advisable to convey to students the applications of the content material to their everyday lives. This is not always easy. Many math lessons are invariably "dry," as they often involve proofs, mechanics, simplifying expressions, and so on. However, whenever possible, if one can effectively relate mathematical concepts to real life scenarios, there is the greater likelihood of better engaging the students. Humor can be very helpful. Oh- by the way, I am not eccentric in the slightest degree. I am perfectly normal. You are all crazy. The Voices told me so.