Meet David Gay

Professor

Graduate Program Coordinator

When did you start teaching in the WIP?

Fall 2013 

What WIP courses are you teaching/have you taught?

Foundations of Geometry 1 (Math 5200), a required course for math education majors and a math elective for math majors

Why did you join the WIP?

I’m 100% on board with the overall WIP philosophy and have tried to implement that philosophy in my teaching with and without WIP support. In particular, I strongly believe that nurturing effective discipline-specific communication skills in students is just as important as teaching specific content. I especially like to think about this in the context of a formal geometry course, where a key goal is to live and breathe the ideal of “proof” as exemplified by Euclid’s writings from 2500 years ago; I believe that classical geometry really laid the foundation for much of what is today considered rigorous logical argumentation, and that, of course, is intimately tied up with the whole project of writing. Well, there’s lots and lots to say about Euclid and writing and intuition and what it takes to convince someone that something is true, and engaging in this nexus of ideas seems to fit perfectly with the vision of WIP.

What have you learned from your experiences as WIP faculty? About teaching? About writing? About your students?

That teaching people to write (i.e. explain an idea) in the way that I think they should be writing is highly nontrivial and that it is actually incredibly difficult to clearly articulate what makes good mathematical writing and what doesn’t. It’s easy when they write well to begin with, but when students put garbled ideas together in garbled ways, it’s obvious they are trying to make sense, and frequently I can see the good idea that they are working with, but to clearly pinpoint what it is that’s wrong about what they are doing is really hard.  

What is your WIP teaching philosophy?

This is mathematics-specific, but in our discipline, there is a great deal of mystique built up around the notion of a “proof” which can be a real obstacle for some students. Understanding that a proof is really a social construct, namely something you do to convince someone else that something is true, but with the understanding that we can develop skills to be both more convincing and more skeptical, makes it feel less intimidating and something that can be achieved through a repeated process of writing, revising and talking to peers.

How do you put that philosophy into practice in the classroom?

Peer review is very important, where peer reviewers are expected to be extremely skeptical “devil’s advocates.” Having a carefully choreographed calendar of due dates for multiple assignments, revisions, reviews, etc., helps me as a teacher to make sure I stick to this plan and don’t revert to the standard process of me just telling them whether they are right or wrong and them just trying to game the system to get me to say it’s right whether or not they really know that it’s right.

What are your biggest challenges you face as a WIP teacher/in your WIP courses?

Keeping the pace moving so that the mathematics is engaging and we don’t get bogged down. Covering enough material to get to the really exciting topics. 

How do you address those challenges?

Sometimes you just have to decide that you’re going to jump ahead content-wise because the writing intensive activities are taking away from rather than adding to the excitement of the material, and you just agree to leave some issues unresolved and move on. This doesn’t mean that the work you spent on those activities was not valuable, but just that getting to a particular milestone you had in mind in advance is not really the right thing to use to measure the value of the activities.

What do you hope students take away from your WIP courses? How do students benefit from the writing-intensive nature of your course?

Well, it’s a mathematics course and I want them to take away first and foremost a love of mathematics. I want them to see that the writing process, although challenging, is rewarding and ultimately helps facilitate the experience of joy in mathematics. 

Why is it important that students write in your class?

Well, the discipline really requires students be able to write about mathematics as they do it—just “getting the right answer” is almost completely worthless; what is important is being able to communicate with other mathematicians about your solutions and explanations. Going back to Euclid, there is an interesting idea that in the classical Greek setting, “doing mathematics” was a performance art, and that Euclid’s great book, The Elements, should be read as a series of scripts for short performances of proofs. So the most important thing is that students learn to “do mathematics” which really means to “communicate mathematics,” and of course writing is an important component of communication. Incidentally, in my ideal world I would also figure out how to devote a significant chunk of course time and energy on visual communication skills, as well (basically, discipline-specific “graphic design”), but that’s a topic for another day!