multijimbo

My apologies, o patient reader, and I do realize that my backblog is large at this point, and what I’d like to spend some time doing is to tie up a few loose ends.

One of the things I started over the summer was to keep some record of my thoughts around the teaching I was doing over the fall.  If you’re interested, these can be found in a fourth meditation on being a teacher, part 1 and a fourth meditation on being a teacher, part 2 and a fourth meditation on being a teacher, part 3  Looking back, I should have kept a more detailed record of my thoughts as I went along, as I’d planned to do, but I didn’t.

So what did we do.  We had the printed notes and I had the notes dated by the day they were to be delivered.  I asked the students to read the day’s notes before each lecture, and I also recorded each of my lectures, mostly audio but a few video recordings as well.  But polls of hands indicated that not all of the students were reading the notes before the lectures.  And the data shows that about half of the recordings of the lectures were never viewed, but some were viewed moderately extensively.

We started to work through an example that wasn’t covered in the printed notes, but I had to recognize fairly early on in the semester that I’d chosen an overly ambitious example, and we fairly soon defaulted to working through the examples provided in the notes.  This ambitiousness I think might trace back to other things I’ve talked about, particularly the discussion in the language of mastery versus the understanding of the student about what happens when we as teachers think about things deeply but then don’t pay as much attention to the distance that this develops between us and our students as would be most helpful for them.

And so now, the students have taken the examination and I’ll start the marking soon, but I’m also thinking about how things went and what I might want to do differently next year, when I teach this class again.  I will keep with the basic structure of providing the notes at the beginning and setting a reading schedule, but I will also need to remember that if I am the only one asking students to read to such a schedule, then I will need to take more care to explain to my students about why we’re doing things this way.

One of the things that I thought worked well was the idea of taking 2 graph invariants and to bring them together.  One that we started working through was to describe all of the graphs whose chromatic number and chromatic index are equal.  (Don’t worry about the specifics – this isn’t examinable.)  I like this question because it allows us to make use of a number of different results that we considered and worked with through the semester.  But it does require some care, because we didn’t work through to a final answer.  And I’m not sure whether such a characterization has ever been written down.  If you know of where I can find one, I would be most appreciative.

I think this sort of open ended question is something that can work remarkably well, but it does require some care.  At undergraduate level, we don’t often start working on questions for which we don’t know the answer, but perhaps we should do so more often.  Among other things, it reminds our students that even for the mathematics we consider at undergraduate level, we don’t know everything.  I like the mystery of the unknown, of this game of starting from things  we know and understand, and seeing how quickly we can pass beyond the bounds of what we know.

I’ll try and be better at working through here some of my plans and schemes for my teaching next year, and we’ll see what we get.

~ by Jim Anderson on 28 January 2017.

Posted in education and university life, mathematics