A reset

It’s the middle of August, so it’s that time again… Fall semester is hurtling towards us!

I have a lot to do to finish getting ready (more on that another time), but my organizational situation at work has degraded pretty severely the last two years and that has to change so I can be productive again. So I am sending the rest of this week getting reset.

Today is “digital files” day. I’m going to go through all of my digital inboxes and storage. It’s time to get things in order. I’ve thought hard about how I want the results to look, so now it’s time to sort, make back-ups, and clean up. If all goes well, this is the goal for today, and tomorrow I will repeat with the physical files in my office.

This had been a personal accountability post, and only a personal accountability post. If this had been an actual post…

Thinking about Land Acknowledgements

I have seen several talks in the last few years that start with formal land acknowledgement. If this is a new concept to you, each has gone something like the quote below. (I am paraphrasing, so please forgive me for the resulting lack of nuance, and all the resulting misrepresentations.)

Before we begin, let me first note that we are currently located on unceded land which was the home to the {names here} peoples.

It’s a paraphrase. I don’t want to burden anyone with my rendering.

The {names here} part should be filled in with the name of the relevant people, in their own language, who are known to have lost the land when white settlers showed up. Often, this acknowledgement comes with a slide showing a map of the current political divisions imposed on the land and rough approximations to the political divisions of the people who were displaced or marginalized. I can clearly recall Deborah Ball and Belin Tsinnajinnie doing this at the national IBL conferences the last two years, and Rochelle Gutiérrez did it for both of the talks I saw her give at MathFest this past week.

I am thinking about the choices one makes when doing this. Okay, I am thinking about some of the choices one makes when doing this. I’ll take as given that the speaker has already decided this is important and that they are willing to wade into the politics of making such a statement before saying anything else. Right now, I am thinking about the technical choice: How does one decide who to acknowledge?

I ask this because the history is complicated. I read Black Hawk by Prof. Kerry Trask earlier this summer, partly because I live in Black Hawk county Iowa. That book focuses mostly on the Black Hawk War of the early 1830’s, but tries to put it in a larger cultural and historical context. The deeper history of the Sauk and the Fox peoples (or, better, the oθaakiiwaki and the Meskwaki, — I am not confident I have those correct…) discussed just in this text indicates that in the early 1600’s they lived in eastern Michigan. So, this group of people got pushed west several times.

Anyway, I am trying to get better educated about these things, and I’m going to start at Native-Land.ca, where they have maps and relevant discussions and links to websites for some nations.

Thank you, MathFest

I’m gonna ramble a bit. Be warned.

I was pretty cranky a week ago. Work has not gone as well as it could, in basically every aspect, for at least a year. I am way behind on major important projects. And those things I did manage to do, I did less well than I am capable of doing. UNI has been challenging me in unpleasant ways. For some reason I thought a good hobby was one where everyone yells at me (hello fellow referees!) This list could go on a long time. I started letting myself down, and then letting other people down… Anyway, I wasn’t quite at the stage of calling my department head to declare I need a mental health break this coming semester, but it crossed my mind.

I arrived at MathFest really out of sorts and unhappy.

But I have spent the last four days talking with friends old and new. I met people in person I only know from the internet. I saw people I have ice cream with at almost every meeting. I got to talk to people I like that I only see once every few years. I met plenty of new people, and got to introduce people I was sure must know each other.

And here is the thing: through the MAA, I have met so many impressive people. I walk into a room, and I am inspired by all the cool things they do: fantastic teaching and mentoring, amazing mathematics, important research on education, wonderful art, Herculean service to the profession, and so many other things. Old folks with storied careers, young ones with boundless energy and enthusiasm–Everyone is so damn clever and caring!

And an important thing happened this week: These people treat me like I belong.

Earlier this week, I saw MAA President Michael Dorff tear up talking about how the MAA is important to him because it is all about people. He is right.

Tonight, I feel better. I am reenergized. I am smiling while thinking about work for the first time in a long time.

So, thank you, MAA. Thank you, colleagues I know. Thank you, colleagues I don’t know.

Thank you, MathFest.

Why am I so miserable at my job this week?

I have not felt successful in the classroom this week. Let’s leave aside the incident where I made a student cry in one class, because that I can sort out. That is, I have already started sorting that out and, though it was no fun, it is fixable. I guess it helped set a bad tone for the rest of the week.

No. The real problem is in my other course. I just have been incompetent. There are some possible explanations I thought about this afternoon:

• I have a bad head cold
• I have forgotten how to give a coherent lecture (it’s been a long time since I gave a lecture-heavy course)
• Lectures are a bad fit for how I like to communicate with my students.
• Differential geometry is kinda hard

All of those are true, to greater or lesser extent. But after calming down, I realize the real problem is this.

It is the end of week five.

Really, that’s it. It always takes me 5-6 weeks to become dissatisfied with my work on a new prep.

I think this is about how long it takes for me to see the ways in which my idealism and big-plans-are-the-only-plans-attitude fails to meet the needs of my students.

I don’t get to teach this course often enough to actually learn “the typical student” and figure out how to help them.

This teaching business is hard.

Choose-your-own-adventure Assessment via *Points Accumulation* (gasp!)

I’m planning for Spring 2019, which is MONDAY, and I have a lot of work to do still on Math 3630/5630: Differential Geometry. I am behaving like a professional and trying to plan things the way one should, start with (1) figuring out your context, then (2) write student learning outcomes (SLO), then (3) plan assessment of those, finally (4) settle on teaching and learning activities to prepare students, and when all that is all done write the syllabus. (Thanks to Dee Fink for showing my how to organize this correctly.)

I’m gonna ramble a bit before I get to the big thing. Just hang on. I wanna write one blog post today, not seven.

Step One: Context

Now I got off to a better than average start by sending my students a questionnaire at the end of last term. It was a simple google form asking students about their backgrounds, what they are comfortable with from the list of prerequisites, and why they are taking the class. This turned out to be really useful. I learned these things:

• These are fairly advanced students: one junior, two seniors and five graduate students in our MA program. All have concentrations in mathematics, though one calls it their “second major, after computer science.”
• They are 50/50 split on why they are taking this course: for some it is required (the grad students), but some are there because it sounds interesting.
• Most of them are through our undergraduate analysis course, though a few are halfway through (its a year-long sequence), and one has not, yet. So I can almost-but-not-quite assume they know stuff about epsilons and deltas.
• About half of these students report wanting to continue their education as a next step (PhD programs in math), and the rest want to talk about getting involved in higher ed in some way (tutoring, community college teaching)
• They have widely differing comfort levels with using technology to do mathematics. This talked me down from some rather ambitious plans that would have made a mess.
• Despite having all passed the prerequisites, they report big gaps in their comfort level with some of the material that would be considered important before enrolling. I’ll have to manage this carefully. I think I’ll just drop “5 minute reminders” all the time.

I have a class that meets three days a week for 50 minutes each, in a room built for group discussion more than anything else. There is a chalkboard and presentation equipment, but it is all mashed together at the front of the room. If I want to present a lot, chalk is going to be awkward, but using the computer would be easier. There are lots of tables set with students chairs facing small groups of 4-6 people.

Step Two: SLO

I have the university level learning goals, and the department level learning goals. Those are about as broad and vague as you would (should?) expect. Stuff about making arguments, solving problems, writing, speaking, and thinking critically, etc etc.

But what should I try to teach in my course? As an advanced course, I have the luxury of aiming more at content and a bit less at foundational skills. The course catalog is not as helpful as I would like:

MATH 3630/5630 (800:155g). Differential Geometry — 3 hrs.
Analytic study of curves and surfaces in three-dimensional Euclidean space. Prerequisite(s): MATH 2422 (800:062); MATH 2500 (800:076); junior standing. (Odd Springs)

https://catalog.uni.edu/collegeofhumanitiesartsandsciences/mathematics/#courseinventory

Right… I read that as, “Do whatever and have fun.” So… I had to come up with my own. I won’t pretend I am completely finished with this, but I DO have a good start, because I stole the idea of “Big Questions” from Kate Owens. My Big Questions are these:

1. How can we use smooth functions to describe {curves, surfaces} in Euclidean 3-space?
2. What is the difference between intrinsic geometry and extrinsic geometry?
3. How do we understand the internal geometry of a {curve, surface}?
4. How do we understand the external geometry of a {curve, surface}?
5. What are some of the concepts of curvature and how are they interpreted?
6. What is the difference between the geometry of a {curve, surface} and the topology of that object? How is the geometry of an object related to its topology? Can knowing something about curvature tell us something about topology?

We might not get to that last one, but I really hope to explore some interesting theorems in each of these regions for both curves and surfaces. Anyway, later today I hope to sketch out a calendar of study topics and see what I can reasonably pack into a term with 42 class meetings.

Step Three: Assessment Plan

So, I started thinking about this: How do I assess student learning on those things? (yeah, they are a bit vague, but still.) Which are more important than others if I have to make hard choices?

The trouble is that I don’t really care. I mean, I want the students to do some math and learn some stuff. But I don’t particularly care exactly how they choose to do the math and I don’t care exactly which bits they learn.

That sounds terrible. But I mean it. I want to give the students some flexibility and autonomy. As long as they are doing work that involves the ideas of the course somehow, I will be happy.

So my stupid idea is this: a choose-your-own-adventure points collection assessment system. I am going to offer the following types of assessment options:

• Exams/Quizzes: sit-down exams with no references aimed at small bundles of material coded to the big questions above. About 100 points each.
• Weekly Homework: regular assignments. But I’ll only collect reports (which I stole from Joshua Bowman) that are small, and students may turn in their “best two problems of the week” for real comment, credit and revision. About 25 points each, 5 for the basic report, 10 each for good written solutions.
• Projects: Independent Projects on related material or topics just off the main thread of ideas in the course. delivery of these to be negotiated, but I will definitely accept short papers and oral reports. point values will vary, depending on the project, but from 20 to 100 points each. I have a list of about 10 ideas for this. I’ll need to think up some more. I will also invite students to suggest project ideas.

Then I will assign grades based on some sort of stupid table I write up. Collecting X points will mean a grade of Y. Each particular thing will be assessed as pass or fail. (for exams, that will be question-by-question. Also, I’ll have to write some rubrics and make them public.) If you pass you add the points to your total. If not, you have the chance to revise your work, or try a different assessment. I will have to make two columns to this table, because the undergraduates and graduates have to have different expectations. I am going to try to set things so that a student can expect to pass the course in a variety of ways. In particular, an undergraduate should be able to get an A in the course if they `do well’ on three exams and weekly homework. In particular, if a senior who plans to go to industry just wants a C so they can graduate, they can pick their level of commitment, learn some stuff, and call it a day.

So, oddly enough, my adventures with alternative grading systems has led me here. I am inspired by standards based grading and mastery grading and specifications grading, but I have no strong feeling about exactly which standards are important. And NONE need be. I just want students to learn some (relevant) stuff and show me that they did it.

Questions for Readers

Now is the part where you help me, assuming you read so far. (Hi, Mom! — I’m kidding. My mom would not have read this after seeing the title.)

• Why is this a bad idea?
• What would you want to know about this after it is done? Say I wanted to write a PRIMUS paper about it, what would you want that paper to address?

IBL can still surprise you

Today I had a really interesting conversation with my Euclidean Geometry students. It was a new wrinkle on a thing I had planned for, and it shows how you can still be surprised by an IBL class even when you have run the same notes more than a dozen times.