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.

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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?

Differential Equations Outline

I have been thinking about my differential equations course all afternoon and evenings. I have lots to do to put it together, but here are my big decisions:

Stuff that Stays the Same:

  • Build around Hirsch, Smale, and Devaney’s Differential Equations, Dynamical Systems and an Introduction to Chaos, 3rd Ed.  This is for the focus on modern dynamical and qualitative techniques (which I like). Basic coverage is chapters 1-10 (core material), 11 (basic biology models like Lotka-Volterra and SIR), 14 (Lorenz System), and then some lighter coverage of chapters 13 and 16 (I wanna tell the story of the 3-body problem and Poincaré’s discovery of homoclinic orbits).
  • Some Lab Explorations: use several of the activities in HSD as assignments. I think 5 of them will do, with one due every three weeks. We’ll use CoCalc as the main tech, augmented with Field Play. Lab assignments are to be peer graded.
  • Week Two is all about using that technology. We spend the week in a computer lab learning the tools and getting the first lab written up.
  • Weekly “homework reports.” Instead of asking for a homework assignment that has to be marked seriously for correctness and returned, I’ll just ask for a report on what kind of work that the student did during the previous week on the assigned reading/exercises/etc. This course is full of more advanced students, so I feel it is appropriate to move this responsibility onto them. (I took this idea from Joshua Bowman.)
  • An extra assignment for the grad student(s) to read and report on the proof of the Fundamental Existence and Uniqueness Theorem.

Stuff that is New:

  • A (nearly) weekly “technique” assignment. The last iteration of this course didn’t have quite enough work on important, well-known techniques for solving systems by hand. So, I’m going to add some. These won’t happen every week, because at some points we will have new linear algebra to learn, etc etc. Anyway, the new topics are: separable equations; homogeneous equations; exact equations; integrating factors; linear equations; numerical methods (Euler and RK45); Picard’s method; power series methods (easy ones); Laplace Transform; Fourier Transform.
  • A weekly “techniques quiz.” This will be a one item, 5-7 minute quiz on each Monday to check up on the techniques in a simple way.
  • Split the Final Exam into an “in-class” and a “take-home” portion. The in-class version is on Monday of finals and will ask big-picture questions. The take-home part will be like one of the lab experiments, aiming for summation of ideas.
  • Maybe I’ll switch to using Jupyter notebooks rather than Sage worksheets? I have to think about it. Maybe that is too much for this iteration.

If I have all of this right, the cycle of work will be something like:

Monday – technique quiz, TJ preview of material
Wednesday – homework report, class discussion
Friday – labs due (sometimes), class discussion

Tomorrow I’ll revise last year’s syllabus to reflect the changes. Then I’ll start writing the assignments and assessments out, update the course web page, and set up CoCalc for the term. (It might take till Monday or Tuesday to get all of that done.)

Simple Progress: web site & geometry

Well, I made some good progress. It took a bit longer than I hoped (what doesn’t?), but I have now made general updates to my UNI web page and I have reset things for my Euclidean Geometry course. [Everything! all the assignments, the syllabus, etc]

There is nothing truly new in my planning for that course, except that I have decided to add a little extra communication with students about their progress via an email every three weeks. I didn’t write this into the syllabus, but I plan to do it. These emails shouldn’t be too big a burden because the class only has 10 students enrolled. (I hope no one drops, because that is the minimum required before the Dean and Provost start making noises.)

Oh, and I reread Tim McNicholl’s The Extreme Moore Method. It is just as a I remember it. Still feels like home. One of my challenges will be making linear algebra and differential equations feel as comfortable.

Now for a little break, and then move on to differential equations. I hope to have that one done by tomorrow afternoon.

Getting Ready for Fall 2018

I have started getting ready for fall term, and I feel like I have some thinking to do. So, I return here to use this as my write-to-think space. Writing to think has always been a good teaching practice for me, and I am thankful for the amount of feedback I get from you, my only reader. (Hi, Mom!)

This term I am teaching three courses:

  • Differential Equations
  • Euclidean Geometry
  • Linear Algebra

Classes start on August 20th, which is less than two weeks away. I hope to have plans made and syllabi constructed by the end of this week. That is unlikely, of course, but I bet I can have two done and make a good start on the third by Friday afternoon.

Since building early successes is important for one’s mindset, I am going to start with easy tasks and work toward the harder one. Here is what I have to do:

  1. Re-read Tim McNicholl’s paper on the Extreme Moore Method, which was an important part of my conversion experience to IBL teaching. I want to get re-energized to make decisions based on my core beliefs. Since I last read the paper about 10 years ago, I might find out that some of my core beliefs have shifted. That’s okay, and it will be important to find out.
  2. Plan Euclidean Geometry and reset it for this term. I am making no major changes, so this should “go fast.” But I should at least think it through again.
  3. Plan Differential Equations. I don’t have time to make big changes in this one, though I would like to. At the moment, I am thinking about adding a “technique of the week” component. Currently the course is focused on numerical & qualitative work, and I want to put in just a little bit more of “this is how you find a solution to an ODE by hand.” I also hope to switch the technological components to using Jupyter notebooks instead of Sage Worksheets. (I am still using CoCalc as a platform.)
  4. Plan Linear Algebra. This is the big one. I have so much to rethink and redo. I’ll say more when it is time.

So, if you get excited about the details of trying to teach college math courses, follow along in the next few days.