Reducing Inflammation

University of Saskatchewan

Not all math mistakes are created equal. Certain math mistakes are so infamous among math teachers that they get monikers, and, for whatever reason, these monikers often sound like mathematical diseases. Take, for example, the mistake *log*(*a* + *b*) = *log*(*a*) + *log*(*b*), which has sometimes been referred to as *logarrhea.* Technically, though, diarrhea*squaranoia, logarrhea, sinusitis, functionitis, cancellitis, sumonia, rootobia, negativitis,* and *moveitis:* There’s too much inflammation.

When it comes to mathematical diseases, the *-itis* suffix is used rather liberally. As mentioned, there’s sinusitis, functionitis, and cancellitis, which, respectively, correspond to the mistakes *sin*(*a* + *b*) = *sin*(*a*) + *sin*(*b*), *f*(*x* + *y*) = *f*(*x*) + *f*(*y*), and (*a* + *b*) / *a* = *b.* Also, as I’ve found tossed around in online math teacher message boards and list serves, *-itis* has been used to form *negativitis* (which corresponds to the inexplicable appearance or disappearance of negative signs) and even *moveitis* or *movitis* (corresponding to errors associated with negative exponents, as well as moving negative numbers from top to bottom or bottom to top). The burr in my bonnet is the accuracy of the medical suffix. To be clear, *-itis* is a perfectly fine suffix, but it denotes inflammation. In other words, while tacking the medical suffix *-itis* onto the end of words creates some great-*-itises* came to mind.

Knowing the meaning of the *-itis* suffix, we see that the term *sinusitis* implies inflammation of the sin or the sinus. And, I suppose, it kind of works. One *could* interpret *sin*(*a* + *b*) turning into two sines*sin*(*a*) + *sin*(*b*)*log*(*a* + *b*) = *log*(*a*) + *log*(*b*)*sin*(*a* + *b*) = *sin*(*a*) + *sin*(*b*). Given the similarity in the nature of the mistakes, one might propose, in the name of consistency, renaming *logarrhea* to *logitis* (i.e., an inflammation of logs). However, this simply doesn’t sound as catchy as *logarrhea.* Conversely, one might argue that *sinurrhea* (i.e., the flow secretion or discharge of sinus) also kind of works, but then there’s the potential issue of too much *-rrhea* on our hands. Fortunately, I think I’ve come up with a replacement.

I contend that *lateralparentheticsinucentesis* should replace *sinusitis* as a more accurate descriptor of the mistake that is occurring. My proposed term is comprised of four key elements: *lateral* (to the left or the right side); *parenthetic* (referring to the brackets or parentheses); *sinu* (referring to sin or sinusoidal); and, *centesis* (puncturing and draining). Putting it all together, *lateralparentheticsinucentesis* refers, then, to how the sin (sinu) punctures the brackets and drains (centesis) to each of the terms in the parentheses (parenthetic), with the result on the other side (lateral) of the equals sign. Quite a mouthful, but in a land of many *-itises,* I contend that *lateralparentheticsinucentesis* is a still medically rooted but more accurate descriptor of the mistake in question.

Worthy of note: *Lateralparentheticsinucentesis* is, really, a general term. Initially, recognizing the two-*sinistroparentheticsinucentesis* and *dextroparentheticsinucentesis,* which referred to *sin*(*a* + *b*) = *sin*(*a*) + *sin*(*b*) and *sin*(*a*) + *sin*(*b*) = *sin*(*a* + *b*), respectively. Full disclosure: I am still unsure whether *sin*(*a* + *b*) = *sin*(*a*) + *sin*(*b*) would be best described by *sinistroparentheticsinucentesis* or by *dextroparentheticsinucentesis.* Once established, though, the other term would then naturally refer to *sin*(*a*) + *sin*(*b*) = *sin*(*a* + *b*). The issue is that I was unable to establish what was being referred to as the left side. In other words, a left side puncturing and draining of the sin to each of the terms in the brackets ends up on the right side. Similarly, the end result of a right-

Like *lateralparentheticsinucentesis,* renaming *functionitis* would fall prey to the left/*sinistro-* and *dextro-* prefixes were ruled out from the beginning. Of course, the effort that was put into *lateralparentheticsinucentesis* could have easily been applied to *functionitis,* which would have resulted in *lateralparentheticfunctioncentesis.* However, no matter how I looked at the word, I had issue with the latter part: That is, when joined together, the combination of *function* and *centesis* just didn’t sound right to me. I was also looking to differentiate the word from *lateralparentheticsinucentesis.*

As mentioned earlier, *functionitis,* meaning an inflammation of the functions, may indeed be an adequate descriptor of what is taking place during the mathematical mistake: That is, an “inflamed” *f* results in two *f*s. However, and now being on a bit of a roll with my amateur use of medical terminology, I established a new word to describe what is taking place during this particular mathematical mistake: *endoparentheticfunctionostomy.* Breaking the term down into its constituent parts, we have: *endo* (denoting something as inside or within); *parenthetic* (relating to brackets or parentheses); *function* (verbatim use of the word *function*); and, *ostomy* (the creation of an artificial opening, or *stoma*). Put together, then, *endoparentheticfunctionostomy* refers to the *f*s being distributed inside of the parentheses thanks to an artificial opening of *f*(*x* + *y*).

In comparison to *functionitis, endoparentheticfunctionostomy* has two things going for it. First, it reduces the number of *-itis*-based mathematical diseases. Second, breaking the word down helps one get a sense of the mathematical mistake that is taking place. However, renaming these particular diseases led me to wonder whether or not *disease* was an accurate or appropriate general descriptor for the errors they describe.

Initially, a distinction between disease, disorder, condition, or syndrome might not seem like that big of a big deal. As time goes on, however, terminology often gets more and more nuanced. Case in point: What were once known as *venereal diseases* (VDs) were renamed *sexually transmitted diseases* (STDs), which, although often used interchangeably, have since been distinguished from *sexually transmitted infections* (STIs). Similarly, the days of declaring that students are riddled with mathematical diseases are probably over, too. The question remains, then, of how to properly describe scenarios such as the above in math class. Having parsed the notions of disease, disorder, syndrome, and condition (to the best of my ability), allow me to make a suggestion.

Just because a student hands you a paper with *sin*(*a* + *b*) = *sin*(*a*) + *sin*(*b*)*log*(*a* + *b*) = *log*(*a*) + *log*(*b*) **and** *sin*(*a* + *b*) = *sin*(*a*) + *sin*(*b*) **and** *f*(*x* + *y*) = *f*(*x*) + *f*(*y*)*syndrome* on your hands. In the instance I’ve presented, I suspect the syndrome that I will denote as *parecentesis* (the puncturing and draining of brackets, which is another way to describe distribution of the undistributable) might be at play.

Other than a silly exercise, there might not really be much more to renaming mathematical diseases. Take, for example, *cancellitis,* where the notion of inflammation makes the least amount of sense, especially when compared to other *-itises.* At the same time*cancellitis* is such a great word and helps draws attention to an egregious mistake (e.g., ^{16}/_{64} = ^{1}/_{4} *because* the 6s cancel). I’ve tried, and I mean really tried, to rename *cancellitis,* to no avail. In the end, though, silly or not, I’ve realized that my efforts to rename the mathematical diseases have helped me start to walk a mile in students’ shoes. And, silly or not, any exercise that builds empathy for those making common mathematical mistakes can’t be in vain.