Ingressive vs Congressive

May 13, 2021

I am starting to be a big fan of Eugenia Cheng. She has a bunch of thoughtful essays on mathematics, and I enjoyed How to Bake Pi.

Her latest book is X+Y: A Mathematician’s Manifesto for Rethinking Gender. The book has two parts. The first of which talks about how a mathematician might think about gender, which I found to be a stretch and not very strong. At this point, I was disappointed.

However, the second part introduces a fantastic idea. We have this idea about “masculine” traits (e.g. courage, assertiveness, etc) and “feminine” traits (e.g. empathy, humility, etc). Cheng says this is problematic because gender and these traits are actually different dimensions.

Her solution is to introduce vocabulary, which I find to be an extremely power idea. Her suggestions are “ingressive” as a replacement for “masculine,” and “congressive” for feminine.

Here are two examples from old Saturday Night Live episodes. Will Ferrell’s version of Janet Reno should be described as “ingressive” rather than “masculine,” since Janet Reno is a woman (how can it be “masculine” if she is a woman?). Similarly, Al Franken’s Stuart Smalley would be “congressive” rather than “feminine” (why would we say “feminine,” given that Stuart is male?).

Describing a woman as “masculine” or man as “feminine” has a judgment built into it (“You are doing it wrong!”). The words “ingressive” and “congressive” simply describe behavior without the judgment.

If you are interested, I encourage you to read the book. Again, I would very lightly skim through Part I; just read enough to get the context. Part II is where the good stuff is.

Cheng also makes a case for why mathematics is too ingressive, and she offers some examples of how to make mathematics more congressive.

I love this contribution, but I also wonder if this has already been proposed by someone in gender studies (likely with different vocabulary). Do you know of any work from that field that is related to what Cheng did?

Apple Watch as Dumb Phone

May 5, 2021

My phone for the past seven years or so has been an AT&T Z222 flip phone. I had a similar dumb phone prior to that for about a year, and I didn’t have a phone prior to then. I have been getting dumb phones to save me from myself. They are also a lot cheaper, both up-front and monthly.

I got a notice from AT&T saying that they will no longer support my Z222 in February 2022 due to their new 5G network. Soon after, the Z222 simply started not to work (it wouldn’t retrieve text messages, and the alarms started being unreliable).

I was looking for a replacement phone, but there weren’t great options. The options that were there didn’t get great reviews, and they were more expensive than I wanted (I prefer not to pay $80 for a dumb phone). I wasn’t happy with any of the options.

Enter the Apple Watch. This is really perfect for me. Here is how I did it.

  • An Apple Watch needs to be tied to an iPhone. This would seem to be a problem for me, but my wife has an iPhone. I can tied the Watch to her iPhone, and then I can have my own phone number through Apple’s Family Plan. The Family Plan is largely meant for kids (give the kid a watch instead of a phone) and elderly parents, but they will let anyone sign up.
  • This does everything I want it to do, and not much else. Cal Newport always recommended that you just use your smart phone for calls, text, maps, and audio. The Apple Watch does all of these things well. I can also look things up online if I need to, but I not about to go down any rabbit holes due to the fact that it isn’t pleasant to read for very long on such a small screen.
  • It has a low monthly cost. My Z222 was pre-paid, and $108 would last me roughly one year. My Apple Watch costs $120 per year (through Truphone), which is essentially the same (it is more some years, less others depending on how much I use the phone during the year). For roughly the same price, I get unlimited minutes now.
  • The Apple Watch is expensive up front—roughly $300. However, I use a running watch to track my speed and distance when I run, and the Apple Watch is only marginally more expensive than a replacement watch. So for $300, I get a new running watch, a cell phone, and probably save about $50.
  • I love new tech, and I think that it is just cool.

Now, I don’t talk on the phone a lot, and I don’t text a ton (when I do, the voice dictation works really well). So while this is a great option for me, it might not be for most.

I have been using the Watch as my cell phone since February, and it is the right solution to me. I am largely posting this because I had to work pretty hard to figure out that (1) there is a Family Plan and (2) it would work for me.

Discrete Mathematical Modeling Postmortem

April 21, 2021

I just got done teaching my Discrete Mathematical Modeling class. See here, here, here, and here for previous posts. Here is my summary of how the class went.

I did not do a good job with the course. I am not down on myself about it, since I don’t think that there was a way for me to do much better: I found out that I was teaching the course a in January, the class started in March (we are on block scheduling this year), and I had two intensive Calculus II blocks between when I found out and when I started teaching the course. I simply didn’t have a lot of time to plan. That said, I am pretty impressed with the level of planning that I was able to do, considering the constraints.

Moreover, I didn’t have a lot of time to adjust once the block started. In particular, I was the chair of a search committee, in charge of registration for my department, advising a student about to defend her thesis, finishing up an independent learning project with three students, and probably a couple of other things during the block. It was kind of a ridiculous confluence of big jobs. Again, I am proud of the way that I managed my time, but I was pretty constrained and I wasn’t able to do everything I wished I could have.

The interesting thing to me is that I wasn’t doing an objectively good job teaching, but I have enough teaching experience so that I could recognize this in real time—I think this was my first subpar teaching effort where I wasn’t subject to the Dunning–Kruger Effect. Here were my main issues.

  • I didn’t have enough time to prepare and adjust, as noted above.
  • In particular, the block schedule hindered my ability to adjust, even if I wouldn’t have had all of the other obligations. I didn’t have a good sense of how well things were working until 1.5 to 2 weeks in, by which time the class was halfway over.
  • My pedagogical content knowledge wasn’t where it needed to be. I hadn’t taught the class before, nor have I thought about modeling deeply before the class began. I simply wasn’t aware of what the students would find easy and what they would struggle with. This made teaching doubly hard—I didn’t know what to look for, and I didn’t always have the fastest way of correcting misconceptions. I didn’t know enough to be able to predict how students would react to the material, so I didn’t have tools available to help them.
  • Related; I mainly stole my modeling problems from trusted sources. However, the problems didn’t do what I wanted of them. In some sense, they weren’t as rich as I wanted them to be. Either I didn’t select the problems well, or my expectations for what problems could be was too high.

I have mainly been teaching the same classes for the past 13 years, and so I have developed a good sense of what to expect students to do. It was an interesting (and unpleasant) experience not be armed with ways to help students. It made me recognize how much progress I have made as a teacher in the last 20 years.

On the plus side, a lot of things went well.

  • Doing a version of ungrading was a really smart move on my part. This gave me a lot of flexibility that I didn’t know that I would need. When the class struggled with one particular project, I had the freedom to walk the class through it. This was really the best thing for their learning, and it didn’t mess up my grading scheme—I just gave them all credit for it. In my original plan, this would have meant that they only would have had four team projects instead of two, and I would have had to wring my hands about how to adjust my grading scheme on the fly. Students also reported that they appreciated the ungrading.
  • The next step in my evolution toward moving my courses toward the CURE end of the spectrum. The projects were open-ended, and the students had a great flexibility to look at problems in the way that they wanted. It was really exciting!
  • I felt like I did justice to the Justice theme. We did some modeling on the Flint water crisis and gerrymandering. Students had to do an individual project where they do modeling on a Justice topic. I thought that it would be difficult for students to find topics, so I supplied them with a default topic (model how to set up a wheelchair program in an airport. How many wheelchairs do you need? How much would it cost? What sort of system can you install to get the wheelchairs to where they need to be?). I was surprised that only two students did the default project, and I was very seriously impressed at the topics students came up with. Some student-generated topics were: how universal childcare would affect the wage gap between men and women in the U.S., how the availability of generic drugs would affect health of people who need them, and how to distribute stuffed animals to children who are detained at the border.
  • I enjoyed working with the students. They were game, and they came up with good ideas. I was a bit surprised at how many of them expressed that they really liked the class, given that I was a bit down on my own teaching.

I will teach this class again. It was really enjoyable, and I would love to do it with the proper amount of prep time.

Picture a Scientist

April 7, 2021

This is a short post to advertise the movie Picture a Scientist. This film does a nice job describing the difficulties of being a woman in STEM. These range from not being given as much lab space as men, to being assumed to be a janitor, to being terrorized and bullied while in the field in Antarctica. It is worth watching.


March 31, 2021

I read A World Without Email, and Cal Newport used it to finally convince me to use Trello to organize my projects (something his podcasts failed to do). The jury is still out, but I can definitely see the advantages of having all of your obligations visually laid out and limiting yourself to the number that you can work on at any one time.

I have been using it for a couple of weeks, and it is (1) helpful but (2) I am not sure if it is helpful enough. My old system of using text files worked well enough, and they don’t require me to use one more tool (even if it is a good one). Still, I am going to try it for six months or so to see if it sticks.

Ungrading in Discrete Mathematical Modeling

March 24, 2021

My Discrete Mathematical Modeling course has started, and we are off to a good start. Here is what we have done so far:

  • We had a fantasy basketball auction, where the players were bid on only by formulas.
  • We did several Three Act activities.
  • We introduced the ideas of expected values, discrete dynamical systems, and linear programming (OpenSolver crashed, so we didn’t finish the linear programming problem).
  • We talked about Justice.
  • We talked about course policies, including grading.

This course has a Justice theme, and Justice involves power. I wanted to be very aware of the power I held over students, and I wanted to eliminate as many unjust parts of being a teacher as I can.

One thing that I did was to introduce something that is inching closer to ungrading. This is very similar to what I did in my capstone classes these last couple of years. Essentially, I gave them a list of assignments that they need to do. They can keep revising them until they get credit for them. If they do all of the assignments to completion, they get at least a B in the course.

This makes sense to me as far as the course goes, too. Modeling is similar to research, in that the students won’t end up at a predictable place (and they shouldn’t).

Scheduling and Hiring

March 17, 2021

We are in the middle of hiring two one-year term positions. We skipped interviewing at the JMM because (1) we intentionally set our deadline to be late (March 1st) so that we can minimize the competition with tenure-track jobs, and (2) there is a pandemic.

To replace JMM interviews, we are meeting via Zoom. Scheduling several interviews sounded like a nightmare, and I did not want to do it by email. Instead, I turned to an old friend: (I am not paid by; I just like their service).

Here are the steps I took.

  • I had my search committee (five total people) send me times when they are available.
  • I manually figured out all of the times when at least two of us were available to interview.
  • I created a new calendar within my work Outlook that was specifically for hiring.
  • I blocked off all of the times in this Outlook calendar where two of us weren’t available.
  • I linked this Outlook calendar to
  • I emailed (using Python) all of the applicants a welcome message and the link to

This whole process took me less than an hour—the toughest part was figuring out that I needed to create a new calendar in Outlook (other than that, this was a 15 minute job).

Then the magic happened. By the time I sent the email and check my calendar, two people had already scheduled interviews! The rest followed within about 24 hours, with almost no effort on my part (I just had to update the search committee’s shared document with the times of the interviews and the assigned interviewers).

The only drawback that I can tell is that there was not an equal work load among the search committee members. One member had significantly fewer interviews that than the others. I can live with that, though.

There are a bunch of other tools out there that will do the same, but I am very familiar with already, and I don’t need any more features than it offers for free.

Justice and Modeling

March 10, 2021

I am starting to think very seriously about my discrete mathematical modeling class. This is good, because it starts in a week-and-a-half.

This course has a Justice them, which means I need to make about 25% of the course be related to Justice. I have some ideas about content—we could make models for voting theory, gerrymandering, wealth distribution.

Additionally, we can think about Justice mathematically. For instance, one skill that I can bring is a love of definitions—several Justice experts I have conferred with haven’t thought a lot about how to define Justice (“I know it when I see it.”). In this way, I can be like Keith Devlin in getting people to say what they are talking about (I am thinking about using some combination of utilitarianism, libertarianism, and Rawl’s theory of Justice).

However, I am wondering if there could be a meta-thing, too. For instance, I could do universal design for learning (which I will do as best I can), but be very transparent about it.

I am also wondering if we could talk about student Justice. For instance, there is a huge power dynamic between student and teacher. Could I play with this? It would be scary (which I am okay with), but are there ways I could cede power to the students to make for a more just learning environment?

What ideas do you have? Nothing is too crazy for me.

Benefits of the Block Schedule

March 3, 2021

Our school year is almost 75% done, and I have some definite opinions about our hybrid model on the block schedule. Here is the outline of what we have been doing:

  • (Hybrid) Due to social distancing requirements and a lack of huge classrooms on campus, some amount of students need to be remote and Zoom into class each day (usually between 0% and 67%, depending upon class enrollment and classroom; I have had classes of 50%, 50%, and 33%). The students mostly rotate who is in, although there are a small number of students who are permanently remote for various reasons.
  • (Block) Students are taking (and professors are teaching) one class at a time. These classes meet for 15 days over 4 weeks, and we meet for 3 hours in a row on Monday, Tuesday, Thursday, and Friday. Most of our classes are 4-credits, but some are 1- or 2-credits; these meet on Wednesdays. There are four blocks per semester; students usually have a class every block, and professors typically teach in three of the four blocks.

Additionally, I am teaching remotely, so I am on Zoom rather than in the classroom.

Here are my thoughts.

  • I do not like the hybrid arrangement, although I recognize that it is necessary this year. It is significantly more difficult to have to teach to two groups of students who are having two different experiences (in-person and remote) simultaneously. My school is wondering what to do about teaching hybrid once the pandemic is over. For instance, a student who just had surgery might not be able to attend class in-person, but they might be able to join remotely. Frankly, I hope we don’t allow it. I think that the costs of splitting the professor’s attention are too high (I am fine using our technology to record class for the remote student, but having to provide a simultaneous experience for the student lowers the quality of instruction for everyone).
  • Teaching hybrid has made me a better instructor, though. I liken this to playing basketball at the Y all day, but playing left-handed. That won’t be a good day of basketball, but I would ultimately learn skills that would help me be a better basketball player in the long run. In particular, I had to think very carefully about how to run class to maximize learning, and I couldn’t have done this in the same way if I hadn’t been forced to live with this constraint. I write more on this below.
  • I love the block schedule. In a normal semester, I would have 75 students at a time. I can’t honestly tend to 75 students simultaneously and give them all the attention they deserve. I can come pretty close if I have 25 students, which I do on the block schedule. I can check in with them near-daily, I can keep tabs on how they are doing and what they are struggling with, and I am developing better relationships. I was a little surprised about having better relationships with students, because (1) I usually have a good relationship with my students, and (2) I only have 15 classes with them. But the experience is intense, and I am their only professor during that period. I love this.
  • My students are doing better than usual. Students can’t productively procrastinate doing the work for my course by doing work for another course, because there is not other course. Students can focus on one thing, and they are doing it well.
  • My best students are doing more work than they normally do, in a very particular way. My grading system allows students to clinch a certain grade after doing enough work, and the best students sometimes do this before the very end of the semester. These students, being rational, usually don’t do much math after that point, since they are busy finishing up three other courses that now need more of their attention. On the block schedule, though, there are no other classes, so these students are just going deeper into the mathematics—even though it doesn’t help their grade! I would have guessed that these students would have just relaxed, but they keep learning. My students are awesome.
  • We are not implementing the block schedule very well right now. This is completely unsurprising, and I am not blaming anyone. My school did a miraculous job getting on the block schedule at all, and the sub-optimal parts are on the fringe. First, not every professor thought enough about how to teach 3-hours classes (some are lecturing for three hours, which is particularly awful if you are watching on Zoom). Second, the block schedule is designed to have breaks between the blocks, and we only have three-day weekends. This is exhausting for students and faculty, both of whom could use more of a break between blocks, but necessary due to the fact that we are trying to keep students on campus during a pandemic (block breaks encourage travel). Third, our 2-credit classes, currently on Wednesdays, seem not to be getting enough attention from faculty and students. It is working okay enough, but I want there to be a better system than what we have. Finally, we aren’t doing science labs optimally. I sometimes have Calc II students who are taking calculus in the morning and a chemistry lab in the afternoon. The block schedule is designed to allow students to focus on one course, and having to schedule labs (and 2-credit Wednesday classes) dilutes that benefit.

In particular, here are the skills that I have learned this year that will make me a better professor in the future.

  • Knowing that I wouldn’t be face-to-face all of the time, I started documenting everything about my course for both students and course assistants. This way, students can get most of the answers they need about the course when I am not there. I should have been doing this for years.
  • I am mostly doing my mini-lectures in small groups now (in Zoom breakout rooms). This is where I have been heading for the past decade, but I leveled-up this year. This feels so much more personal, and students can ask me questions more easily when there are just five students instead of 25. After I am done, I can ask each person by name if they have any questions. The drawback is that I might have to give the same mini-lecture four times in a class, but the benefits are worth it—what is efficient for the professor’s time might not be efficient for student learning.
  • I started doing serious modeling projects in my class, and I give students a chance to work together on them in class. The two main projects I am doing in Calculus II is (1) use calculus to predict how many Covid cases there will be on June 30th, and (2) how much money would it take to pump all of the water out of the favorite lake on campus. These are messy problems, but many students have volunteered that they are the best part of the course.

My school is going back to semester-long programming next year, which is the right move. We only moved to the block schedule due to the pandemic, and now we are not in the same emergency. I want to considering moving to a block schedule permanently (and doing it right) at some point when faculty are ready to consider it. In addition to the benefits listed above, I think it would be smart to move to a block schedule for the following reasons that are unique (or nearly unique) to my school.

  • We have two campuses that are about 6 miles from each other. This means that we have to bus students between every class, which is environmentally not great and expensive for a liberal arts school. The block schedule would cut down on busing, since classes are longer (they would just have to take a bus trip once for a 3-hour class on the block schedule, versus three bus trips for three one-hour classes on the semester schedule).
  • One of our campuses is rural, and the other is in small town of 6000 people. We are keeping with schools in the Twin Cities, which is an awesome metro area, and a lot of students think we are on the boonies (I did, when I was a high school student in the Twin Cities). This would give them a reason to think twice—it would be novel.
  • We have a 2500 acre arboretum on campus and an awesome Environmental Studies program. It seems like we should be leveraging this to take a lot of field trips (Biology, too).

Unfortunately, I think that this year has mostly killed any chance of doing the block schedule at my school. I think that people are going to conflate the block schedule with the hybrid model/pandemic/imperfectly implemented block schedule and be scared off by it. We will see. But I am going to enjoy my last 1.5 classes on the block schedule while I can.

One Win from 2020: Goal-less problems

February 24, 2021

Here is one thing that I have been happy with this year. I decided to give the students goal-less problems for quizzes this year. Here how the process would go in a simplified Calculus I class with the following three learning outcomes.

  1. I can take derivatives of polynomials.
  2. I can determine antiderivatives of polynomials.
  3. I can solve definite integrals using u-substitution.

A quiz would then look something like this: “A car is traveling with velocity t^2 kilometers per second.”

Note that there is no question here. With a goal-less problem, the students need to supply both the question an the solution. So a student might do the following:

“Question: What is the acceleration of the car at time t=1? Answer: Acceleration is the derivative of velocity, so we can compute the derivative to get 2t, which evaluates to 2(1)=2 kilometers per seconds-squared when t=1.”

The student would then submit this to a Canvas assignment that corresponds to the first learning outcome (“derivatives of polynomials”).

But the student could write a second question/answer combination as follows:

“Question: How far does the car travel from t=0 to t=1? Answer: We can find the displacement by determining \int_0^1 t^2 \, dt = \frac{1}{3}t^3 \mid_0^1 =\frac{1}{3} kilometers.”

The student could then submit this to a Canvas assignment that corresponds to the second learning outcome (“antiderivatives of polynomials”). Since this situation doesn’t lend itself to u-substitution, the student could submit question/answer combinations to up to two of the three learning outcomes.

Here is why I am happy I am doing this: one of my unspoken goals (unspoken to myself, even, even though it makes total sense) is that students should not only know how to use calculus, but they should also know when to use calculus. The fact that my students really struggle (in fact, I had to add an entry into my FAQ page about this) suggests that I shouldn’t assume that they automatically learn this without being asked to do something like this. The fact that students don’t struggle with this after the first week tells me that this is useful.

Note that students don’t struggle coming up with questions for material that we learn in the third week of class. This suggests to me that the reason why they are able to develop questions after the first week is the fact that they are being told that knowing when to use calculus is important—it isn’t just that they understand the material from the first week better. They really seem to be telling themselves that part of learning material is learning when to apply it.

I am going to add this to my tool belt. I could see this being done in a bunch of courses. I could imagine giving the students a group in abstract algebra. The students could write questions like “What is the order?” or “Is this abelian?” My colleague has done similar things in linear algebra: he will give them a linear transformation. The students might then determine the kernel, the image, the eigenvalues/vectors, whether it is one-to-one/onto, etc.

I think that I ultimately like this because it breaks the input-output response cycle. The students have to think more—just a bit more—for themselves, but in a way that is not too burdensome.