The gauntlet has been thrown down.

Last week, fellow columnist Andrew Horton wrote about problems in the University’s mathematics department … my department. He spoke of archaic teaching methods and awful professors he encountered in his math classes, while singing the praises of the physics and mechanical engineering departments.

Frankly, it sounds like it’s time for a good old-fashioned opinions page showdown. Horton vs. Vandehey, one night only. No strawmen, ad hominem arguments or other hits below the belt.

To begin, let me dispel the impression that the instructional quality of the mathematics department is lagging behind that of other departments. For my witnesses, let me call upon you — my dear readers — and your class evaluations.

ICES form comparisons between mathematics and mechanical engineering (or physics) show that they are all about on the same foot: In some ways math is doing better, in some worse, but nothing horribly different. Mathematics generally has more instructors in the top 10 percent of faculty than mechanical engineering, but also has a couple more in the bottom 10 percent.

In fact, when it comes to exceptional teachers, the math department is a bit of a hog. A mathematician has won the LAS Dean’s Award for Excellence in Undergraduate Teaching every year but one since 2003. Five faculty members from math (but only two from mechanical engineering) have earned the Campus Award for Excellence in Undergraduate Teaching between 1995 and 2010. The math department is not, as Andrew implies, lacking in “instructors who are passionate about teaching.”

And all of this has been happening at a time when outside pressures have made it increasingly harder, not easier, to teach mathematics. Due in large part to increasing demand from the College of Engineering, the mathematics department is teaching 16 percent more Instructional Units than five years ago, while its ranks of active faculty have declined. Surprisingly, ICES scores for the mathematics department are generally better today than they were five years ago.

But this hasn’t addressed Andrew’s column itself yet, just the inferences one might draw from it. He makes two primary points: that the teaching methods of the mathematics department are outdated and that the very fact that he had any awful professors, let alone three in a row, should be a sign of something horribly wrong.

On teaching methods, Andrew seems unaware of some programs in the mathematics department already enacting the exact suggestions he made. The LAS Top Ten Initiative is increasing the number of so-called active learning courses that focus on problem solving in small groups. The mathematics department and College of Engineering have also worked together to create a calculus class specifically tailored to the needs of engineering students.

But lurking behind his arguments was one point that did make me start to twitch. Andrew criticizes “deriving theorems on the chalkboard in full formality.” Which theorems to state, which theorems to prove and how to motivate all these theorems are critical questions that the mathematical community should address, but Andrew skirts close to a just-teach-me-the-formula philosophy that makes my skin crawl. The formula might be enough 90 percent of the time, but when it fails, it fails spectacularly and utterly. (Just ask all the students who try to apply l’Hôpital’s rule willy-nilly to every limit they see.)

Andrew’s second main point is that the math department has some awful professors. I won’t deny it: I’ve had to TA for such a professor and basically reteach the entire class in my discussion sections.

The relevant question is why such professors exist and what can be done about it.

If we go back even just 40 or 50 years, universities placed much, much less emphasis on the teaching skills of professors. Once a bad teacher obtains tenure, the university’s ability to enforce high standards on them drops like a rock: some of these professors hang on to this day, and the university often can do little more than offer a good retirement package and hope they’ll take it.

Departments also have post-docs and visiting professors who are simply not around long enough for the department to hold any serious threat over them. They can’t fire someone at the end of the semester if they won’t be here next semester anyway.

In smaller departments this is less of a problem, but as the size increases, the presence of one, or even several, bad professors is almost a guarantee. Running into these teachers many times in a row isn’t a sign of a bad department — it’s sheer, dumb bad luck.

Should you be in such a class, please do not just sit on your hands, muscle through it, and then write something nasty on the back of the ICES forms (only the professors themselves read it). Do not just write a bad review on RateMyProfessors.com and leave it at that. Do not just grumble to your fellow students.

If you do those things, nothing will change for you, certainly not during that course. It might take years for enough data to accumulate to force the department to act.

Instead, get up, go to head of the department, the head of undergraduate studies or an undergraduate adviser in the department and Tell. Us. About. It.

We can’t fix something if we don’t know that it has gone wrong until six months later.

Joseph is a graduate student in Mathematics. He can be reached at [email protected].