# Day 57: Jeff, Math teacher, Upper School

As a math teacher, I don’t often get the opportunity to have the same kinds of open-ended arguments with my students that my colleagues in the English and History departments do. The nature of mathematical instruction at the high school level is such that, at the end of the day, there are right answers and wrong answers. We will often have lively debates in class — Is a line longer than a ray? Can a polygon have equal sides without having equal angle measures? — but students are not really asked to deal with ambiguity, as these questions ultimately have a correct answer. I suppose this is one of the appeals of mathematics and the hard sciences; solutions can always be found, truth is absolute. Still, a part me of wishes that there were more opportunities to let students take different sides of a mathematical argument without ultimately having to tell one side, “Sorry, you’re wrong.”

I learned this week that these opportunities for mathematical debate do exist if you know where to look for them. In my Introduction to Calculus class, we’ve been learning how to find the local maxima and minima (or in layman’s terms, the peaks and valleys) of an algebraic function. While there are two methods that can be utilized – the FDT (First Derivative Test) and the SDT (Second Derivative Test) – I’ve always thought that the FDT has a slam-dunk case over the SDT, and consequently have always focused on it in my teaching, almost to the exclusion of the other. During a discussion after class one day, however, I was surprised to learn that a colleague of mine also believes that this issue is a no-brainer, except that in his mind, the SDT is clearly superior! As we playfully but heatedly argued the merits of our preferred method, I realized this was a perfect chance to model for my class that things in math are not always so cut-and-dry.

And so, on December 6, 2012, my esteemed colleague and I ended up dressing up in our tackiest suits and arguing our points in the math trial of the century: FDT v. SDT. For our “witnesses,” we called to the stand various functions (students were asked to speak on behalf of these functions), and peppered them with questions during direct and cross-examination: Isn’t it true you don’t exist at x = 0? May I call you g(x) ,or do you go by any other names? You don’t even know where your own points of inflection are? There was some rolling of the eyes, but in general, I think the students responded positively to the underlying idea that both methods had their relative strengths and weaknesses. I eagerly anticipate reading the students’ follow-up assignments, in which they must pick a side and support their choice with written and quantitative evidence. For once, I’ll get to find merits in the opinions of people with opposite perspectives without having to tell one side, “Check your work, you forgot to distribute a negative.”

*Jeff lives in White Plains with his wife Dana and his dog Chipwich. He thinks he pretty handily won the trial, but is busily preparing for the re-trial, as his opponent is appealing the verdict.*

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