An open letter to Gov. Scott Walker: stop perpetuating the myth of the lazy professor

I found this very nice blog post on the myth of the lazy professor. (no, I’m not avoiding studying for prelims by reading all of WordPress. Why do you think that?) I’ve spent four years at two different universities, and during those four years I’ve never met a professor who didn’t work 50-60 hours a week. The myth of the lazy professor ties in to so many of my favourite misconceptions about teaching. My mother is a high school teacher, and she gets it from politicians all the time: “teachers only spend 15-20 hours a week in the classrooms, they have such a nice cushy job”. That’s the opposite of true. A bare minimum of preparation before each class is about 20 minutes, then on top of that there is preparing homeworks, labs and exams. And then there is at least 5-6 hours of grading each week for each class, and on top of that talking to students and their parents, and doing various administrative tasks that keep popping up. 15-20 hours of contact time is a full-time job. More than that actually, if you want to do a good job and not just a passable one. Those 20 minutes of preparation will be more like an hour if you want to give a good, engaging class.

A college professor is only supposed to teach 50% of the time, and spend the rest on research, so the normal 6 or so hours of face time with students is spot on. Especially if you consider that advising graduate students and undergraduate students comes on top of the regular teaching. So to everyone who thinks that college professors have it easy: think again.

Oh, and as a side note: I find it funny that people love to tell teachers how easy they have it, but public speaking is consistently the thing most people fear. And yet people call out teachers and professors for having an easy job. I find it extremely frustrating, especially coming from people I know who work in industry. They can take weeks to prepare for a 20 minute presentation, yet are shocked that it takes 20-60 minutes to prepare a 50 minute class. There is a lot more to teaching than what you see in a classroom. Anyway, I’ll stop ranting now and let you read this excellent blog post.

The Contemplative Mammoth

Dear Gov. Walker,

Last week, you told professors at the University of Wisconsin that they needed to “work harder.” You were making a case that the Wisconsin state budget crisis could be ameliorated by increasing employee efficiency, and you suggested having faculty teach at least one more class. I’m not going to talk about whether or not the budget crisis is manufactured (some have argued it could be solved by accepting federal funds for the state’s Badger Care health program), or whether your real goal is really partisan politics, and not fiscal responsibility.

Ouch. Photo by fellow UW Madison geographer Sigrid Peterson.

Instead, I want to talk about the myth of the lazy professor, a stereotype that you’ve reinforced with your comment. I spent 2005 to 2012 at the University of Wisconsin, where I obtained a PhD in the Department of Geography; I am now an assistant professor at the University of Maine.

When you…

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Can we teach kids real math with computers?

As so many blog posts and articles with a question in the headline, this one follows Betteridge’s law of headlines. I disagree with the sentiments put forth in this following TED talk by Conrad Wolfram, the creator of Wolfram Alpha, and best friend of calculus students everywhere. Before you read on, you can watch the talk here:

Like I said above, I strongly disagree with the conclusion of Wolfram’s talk. The idea he promotes is that students shouldn’t have to bother with mechanical calculations, because there are now computers that can do mechanical calculations faster and more accurately than any human. Instead, mathematics should focus on teaching kids how to apply their knowledge in the real world, and how to make the computer do the difficult, numerical parts for us. We can do all these really cool things with math – math underlies Google, rockets, the financial market, and countless other things. However, since students mostly do mechanical calculations and occasionally see a very simplified model of a real world event, they never see how cool mathematics is and lose interest. I agree completely with this problem statement. However, his solution is entirely off-base.

Wolfram is making the same mistake countless elementary school teachers do by dumbing down mathematics to be strictly about applications. I personally realized early, like Wolfram points out in his talk, that the applications we get to see in school are silly. There has never been a time in my life where I needed to estimate the height of a building by knowing the length of my shadow and its shadow and applying similar triangles to it. This far, Wolfram has a point. But after that, once he starts talking about how we therefore should skip mechanical calculations and move on to realistic computer simulations of the real world, he loses me.

He believes that we are teaching math for three reasons: to prepare kids for technical jobs, to better navigate our modern world (mortgages, statistics and those kinds of things) and to teach kids to think logically. If this were really the reasons, then maybe Wolfram would have a point. However, there is no other subject that has to justify its existence in this way. When will you ever dissect a frog or need to recite Shakespeare? Probably never, for the overwhelming majority of you. Why does then math have to be all about what it’s good for, when no one questions why kids should have to read Shakespeare?

Consider what would happen if we were told in English class that we need to be able to read to interpret road signs, recognize the letters for a vision test and occasionally write a memo at work. And then we spend the next 12 years practicing vision tests, reading road signs and writing memos. How many authors, poets, and songwriters would we have if we were taught in school that English is strictly about such mundane applications? But that’s not what we do in English class. Instead we read Shakespeare, Austen, and WH Auden, and try our hand at writing poetry, and fiction, and plays. And today everyone and their cat has a blog, or is working on a novel, or wants to be a screenwriter.

We don’t learn math in school because math will be useful in the rest of our life. For the vast majority of you, you will not use derivatives any more than you use that close-reading of Romeo and Juliet. We learn math because it is a major area of study, and hence one that students should be familiar with to be able to decide what they want to do with their life. Don’t show kids more realistic applications of math in school, most people will still never use it: show them more math instead.

Teach kids graph theory, combinatorics, number theory, cryptography, probability theory, non-euclidean geometry, or propositional logic instead. Bring in some of the wonderful areas of mathematics that can be extremely accessible to kids if presented in the right way. Show them the breadth of mathematics. At the risk of sounding like a cliché: show them the beauty of mathematics; its power and adaptability. See how many kids will still want to study math after learning math, not applications of math like they do today.

Virtually all of the applications Wolfram talks about are applications of calculus. This is one of the main problems I see with mathematics education: most kids even at university see nothing but trigonometry and calculus. When I tell people I’m a mathematician, they have no idea what kind of research there even is to do in math. Do I just sit around all day and take derivatives and integrals of things? Figure out new ways to calculate areas of triangles? We would never accept an English curriculum that only teaches kids how to read technical texts. Why do we accept a math curriculum that only teaches mechanical calculations?

I agree with Wolfram that the focus on mechanical calculations of derivatives and integrals is too strong and probably scares off quite a few students. But don’t substitute it with more calculus using computers as tools: substitute in more math. Show students the whole breadth and beauty of mathematics that is out there, and that only very few of us ever get to come near. Show students that, and see what happens to the number of kids who still like math in high school and onwards.

Ribbon graphs of link diagrams

This has been a weird week. Grad school seems to go in waves: first I feel really stupid and like I understand nothing, and then suddenly I’m on top of everything. Up until now, this rollercoaster has been out of sync in all of my classes, but this week I’ve been on top of everything. I wonder how long it will last. I even understand what we’re doing in analysis (intro to functional analysis), though that will probably change when we start with abstract measure theory next week…

Update: It did not change when we did abstract measure theory. Shocking, I know. I found the abstract stuff so much easier to do than the concrete Lebesgue measure. When we did abstract measure theory, I didn’t get confused by all the things I do know about the real numbers and I could focus on just understanding measures on sets, rather than mixing in all the weird things that happen with real numbers. Much more fun.

I have a vague recollection of promising a post on the topic of my conference presentation, so here it goes. First of all, you need to know what a knot is. A normal knot, that you tie your shoes with, is not mathematically interesting. It can be tied, so it can (mathematically at least) be untied. Instead, to define a mathematical knot we tie a knot in a piece of string, and connect the ends. That’s the intuitive definition. There are some tweaks to make it behave nicely, but you get the general idea. A link is a knot with several components.

The title of this post mentions link diagrams. We can find a link diagram of a link by simply projecting the link “nicely” onto the plane. I’m fudging a lot of the details about knots, because they are not the main topic here. I might do a post later on knots where I explain all the details properly. Here “nicely” should be taken to mean that one can recover the original knot from the projection.

Now that we have a vague idea what a link diagram is, we define a ribbon graph. A ribbon graph is a collection of discs called vertices, and a collection of discs called edges. The edge discs intersect exactly two vertex discs along an arc on each vertex, and no edges intersect. An easier way to think about a ribbon graph is as a graph embedded in a surface, and then we cut out a thin neighbourhood around the graph to obtain a ribbon graph.

Next, I’m going to tell you how ribbon graphs are connected to link diagrams. We take a link diagram, and eliminate each crossing just like when constructing a knot polynomial, choosing a negative or a positive splicing at each crossing. We can choose whichever of the two ways to eliminate each splicing we like. When all the crossings have been eliminated, we are left with a number of disjoint circles. These will be the vertices of our ribbon graph. Connect the vertices where there were crossings with edge discs, and you will end up with a ribbon graph. Since we could choose any splicing we for each crossing, there are up to possible ribbon graphs associated with each link diagram.

The natural questions to ask is then: how are these connected? What can we say about the ribbon graphs of a given link diagram? If two link diagrams have the same set of ribbon graphs associated with them, how are the link diagrams related?

My undergraduate advisor already answered both of those questions for links in . It turns out that the ribbon graphs arising from the same link diagram are partial duals of each other. For the second question, it turns out that the link diagrams are related by a very simple “flip” move. In my undergraduate thesis, I proved that the same results holds for checkerboard-colourable link diagrams of links in . This is roughly what I presented at the conference a few weeks ago, to a room full of grad students. Here is a link to the paper on ArXiV.

It was a very nice conference, by grad students, for grad students. The organizers did a really good job putting it together, and there were a lot of interesting people there. It was all very friendly, in part I think because we are all so early in our careers. There were none of the “let me interrupt to talk about why my research is superior disguised as a question for 10 minutes”, which was nice. I also saw quite a few interesting talks, in particular one on the Erdös-Ko-Rado conjecture that I might try to turn into a blog post on a later date. No promises though, since apparently things keep popping up that keep me from blogging for weeks at a time. It should be easier for me to write regularly now that term is over, but no promises on the topics.

What if mathematicians wrote travel articles?

I’m posting an update of my own tomorrow probably, after my analysis final with some of the material I talked about during the conference I attended a few weeks ago. In the mean time, I found this post very enjoyable (in fact, Izabella Laba’s entire blog is very enjoyable).

The Accidental Mathematician

Some time ago I suggested that scientists might not always make the best writers. I guess I wasn’t the only person ever to make this profound observation. Slate has since published this piece on how political scientists would cover the news; see also here. As hilarious as these are, I would say that there’s more to the picture. The story below is inspired by this one (hat tip to Terry Tao). Believe it or not, there are actual reasons why we have to write like this sometimes. I’m as guilty as anyone. In fact, I’m in the middle of revising one of my papers right now…

In this article we describe the plane flight that Roger and I took to San Francisco. The purpose of our trip was to meet Sergey, our collaborator on the paper “The structure of fuzzy foils” (J. Fuzzy Alg. Geom. 2003) who also co-organized…

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