How I’m Spending My Summer Vacation

I’m editing. It’s hell. I haven’t looked at these papers in…awhile, and they’re hot messes that I can’t even believe I’ve showed to other human beings. But they’re getting better. Slowly. They can’t get published sitting on my desk.

I’ve got a new class starting Tuesday, one I’ve never taught before. It’s one of our Masters-level electives for inservice teachers: Calculus for Middle School Teachers. I have no idea how this one’s gonna go, but I’m excited, except for the part where it starts at 8am and lasts until lunchtime.  I’m sure you’ll hear more about it next month.

I’m also ripping apart my digital piano again. Just needs a little more sanding on one of the pins. This time I really think I’ve got it.

But I’d rather talk about something more recreational. I’m sure somebody must have taught me compass and straightedge constructions at some point in my life, but I don’t really remember it. As a young person I didn’t have this awe of the beauty of Euclidean constructions that mathematicians are supposed to have, and mostly was just annoyed with two column proofs like most other 15 year olds. I might’ve encountered them later on when I took a geometry class, but that was just to pad out my credits and I’m embarrassed to say I never devoted much energy to it.

At some point I ran across Euclid the Game, developed by Kasper Peulen, and completely fell for it. It uses a web-based Geogebra interface to guide you through a number of Euclidean constructions, more or less in the order they occur in Elements. Once you develop a construction, like an angle bisector, it adds it to your toolbar for future use, just like Euclid intended.

I know I’m a total sucker for gamification, but I think this goes beyond that: just laying out these constructions in an easy-to-follow, step by step, mistake-friendly way helped me to unlock the beauty and fun that others had found more obvious. If you find yourself teaching a geometry class, I can’t recommend this highly enough.

This is going somewhere, I promise. I visited my mom a couple weeks back. Her wife is a talented folk artist and quilter, and every once in awhile I get called in as a mathematical “consultant” for one of their projects. Lately she’s been making barn quilts and had an idea for a new one on an old salvaged sawmill blade. Could I figure out a way to reproduce this eight-pointed star design on the blade? They had a compass, but apologized for not having a protractor.

I almost felt like I was being set up. This was too perfect.

8 pointed star laid out on a sawblade, with compass and straight edge

Nailed it.

So there you go kids: when are you gonna use compass and straightedge constructions in real life? I used ’em on vacation in my mom’s garage. Get on my level.

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One thing I learned from Calculus, this time around

Turns out that this story actually doesn’t have anything to do with anything Erdos or Darwin said.
Erdos Photo by Topsy Kretts – Own work, CC BY 3.0,

Darwin photo from Public Domain,











This blog post is about how I gave an assignment that I regret and am embarrassed about. It all starts four years ago, when I gave my Calculus II students a review assignment in which they were supposed to solve calculus problems to earn letters for a key to decipher some quotes, which had been encrypted using a simple substitution. I looked for math-relevant quotes on the internet and had found the following:

“A mathematician is a device for turning coffee into theorems.”

“A mathematician is a blind man in a dark room looking for a black cat that isn’t there.”

The first was credited to Paul Erdös, the second to Charles Darwin.

This spring, I dusted off my old assignment.  At first I couldn’t find my original key, so I had to solve the cryptoquips myself.  I recognized the first quote as soon as I got the word ‘mathematician’.  The second I didn’t remember at all, and had to work out again.  As I remembered the second quote, I felt uncomfortable.  I realized that since the first time I gave this assignment, I had read a lot more about the idea of ableism—bias against people with disabilities.  I was not sure that it was okay with me (or with others) to use the word ‘blind’ in this way.  I have read that the term blind is correct and not offensive in referring to the condition of not possessing vision.  It is potentially offensive to use the term to indicate a condition of ignorance. Some people point out that the word blind has many meanings, only one of which is sightlessness; I can see what they’re saying, but my rule is to try to avoid any words in my own speech and writing in a way that I know could hurt someone, even if other people think the words should be okay.  In my interpretation of the quote, the man is supposed to be blind, as in physically not able to see.  However, the man does not actually exist; the quote in its larger structure is a metaphor, which uses blindness to describe something else entirely.

As I said, I felt slightly uneasy when I read the quote again, but at the time I didn’t fully work this reasoning through. I was in a hurry, and I trusted my past self, so I decided that this use was okay. I wanted to make sure that the quotes were actually correctly phrased, though, so I did a (very) little Googling. I learned that the coffee quote probably wasn’t from Erdös at all, but his fellow Hungarian mathematician Alfréd Rényi.  Ha, I thought, I will make that part of the assignment!  I will ask the students to do some research and figure out if these are real quotes and are correctly attributed!  This will be good practice in always carefully sourcing any quote you use. (I cringe now reading this thought.)

After I passed out the assignment, I started thinking even more about the second quote. I did my own assignment and started investigating more.  It turns out, the second quote was also misattributed. On Quote Investigator, I learned that the second quote has a long history, and is descended from one that involves racist language/images. The Quote Investigator entry has a trigger warning at the beginning. I thought, wow, this quote was a terrible mistake.  I didn’t make this assignment so that the class could discuss the power of language for good and ill, racism, ableism, or the problematic history and culture of mathematics. My Calculus II students are not likely to have been at all interested in ‘mathematician’ as an identity, and there was no reason at all to use either of these quotes to begin with.  What was I doing, sending my students into this complex terrain, when all I wanted them to do was practice their anti-derivatives? Especially when I had no idea how to unpack the whole thing? I now really regret using the second quote in class, this time and four years ago.

In some ways, this was a “teachable moment”—a real-life example of how mathematical culture is (obviously) every bit as problematic as culture at large, how innocuous-seeming assignments and utterances can carry enormous baggage, and how well-meaning people can make potentially hurtful mistakes, especially if they try to hurry through and never question their past judgments. As I mentioned, I don’t feel that I have the tools and background knowledge to lead the best discussion on all of this.  But I felt that, tools or not, I needed to say something about the assignment in class. I messed up, and I needed to acknowledge that.

I gave this assignment out on Monday.  On Wednesday, the last day of class, I told my students that I was sorry and why.  They didn’t have anything to say about it. Except one student who asked, “Are we still going to get credit for doing the assignment?”  I said yes, and after waiting a while to see if anyone wanted to talk more, we moved on to Lagrange Multipliers.  From the response, it seems possible that none of the students found the assignment offensive or distracting, and probably nobody would have brought it up with me if I had just kept quiet. However, I don’t think that would have been the right thing to do. In my classroom, I have power. I am the expert, I give the grades, I get to decide what is okay, and I choose what I/we talk about.  I could tell myself, “If nobody brings it up with me, nobody was hurt, no harm done.” But that ignores the real power imbalance in the classroom. Since I am in the professor, students would likely not feel comfortable telling me that something I said hurt them. It is hard to speak up. If I can’t bring myself to admit mistakes and speak frankly about difficult things, how can I hope that my students will find the courage to do this, or to tell me when I am wrong?

I feel that it is my job to manage the classroom climate and call out disrespect. If a student said something I viewed as potentially hurtful in my classroom, even/especially to another student, it would be my job to identify that as unacceptable, whether the other student spoke up or not.  This is actually my number one job, as a person, much more important to me than teaching mathematics: in any situation where I have power, I must use that power responsibly.  Whether or not any student in this particular classroom was bothered by the assignment, I was bothered by the assignment, which is proof that it had the power to hurt. Therefore it was my job to speak up.

I have told a couple people about this experience since it happened.  Honestly, nobody really seems to know how to respond to me. I can’t tell if people are appalled that I ever thought that quote was okay, or if they think I’m being ridiculously politically correct, or if they think I am moralizing about what they should do in their classroom. I guess the fact that the same thing could provoke any of these reactions shows how complicated this terrain is. After thinking about it for a long time, I came to the conclusion that using the quote was not right. Now that I see it that way, I can only respond from that place. I am not saying that everybody has to see it that way or else be a bad person.  I am just doing my best to do what I think is right.

That assignment wasn’t what I wanted my students to remember about Calculus II.  But it is one thing that I will not forget about this class. The math classroom does not exist in a vacuum, and of course we need to reckon with the same issues as the larger culture.  For me, right now, that means re-examining everything—including old calculus assignments.

Thoughts? Ideas? Please share in the comments.

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Student (Mathematical) Modeling Competition

Note that if you mention to professors outside the sciences that you are judging a student modeling contest, you may want to be a little more specific.

This spring, Hood fielded a team for the SIMIODE math modeling competition, graciously hosted by our friends across town at Frederick Community College. And due to some scheduling issues, the professor who served as coach for the team couldn’t be there the whole time, so I stepped in for the afternoon portion. Even though mathematical modeling with differential equations is about as far out of my wheelhouse as you can get, it was a really fun day, and I got to see some really creative solutions to some challenging problems.

Students working on modifying their model, photo courtesy of Lucy Yagodich

The competition begins a week before, when teams are presented with their choice of three situations to model. The two popular choices in our session were one on modeling high school group dynamics, and another on designing a chute in a recycling plant that would separate paper and cardboard from the rest of the recycling stream. They spend a week coming up with an appropriate model for their chosen scenario, writing an Executive Summary, and creating a ten minute presentation. On the day of the competition, the students submit their summaries for judging. Also, to keep it interesting, the students are presented with a slight twist to their problem, and given a few hours to incorporate that twist into their model.

After a lunch break, the students compete in a short Math Bowl, give their presentations, and the judges assign honors based on the summaries and the presentations. It was an intense day for the students, but they all seemed to enjoy the process, and got valuable experience about how design and communicate models of real world situations. And while the students are busy, the accompanying faculty can participate in some professional development centered around teaching modeling.

Student Presentations, Photo courtesy of Lucy Yagodich

Our students didn’t take the highest honors, but they got some valuable experience right before graduation. And all the faculty members involved enjoyed coaching their teams and watching all the presentations. All solutions and presentations are available on the SIMIODE website.

The next competition is coming up this fall, from October 19th to October 27th. Many schools have already volunteered to be host sites, and if you don’t see one near you it’s not too late to become a host. SIMIODE provides all the materials for the professional development and the student activities, so all you need to provide are space, lunch, wifi, and some facilitation.



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