multijimbo

This is the third of a series of indeterminate length.  In a fourth meditation on being a teacher, part 1, I set out my basic goal of keep tracking of what work I am doing to rework and redevelop my (mathematics) teaching.  I also spent a bit of time contemplating the talismanic status that students bestow and bequeath on printed notes.  I’m not sure whether my speculation at the end of that post, that students like printed notes because it delineates the boundaries of what might be taught in the class and more importantly, what might be covered in the exam.

In a fourth meditation on being a teacher, part 2, I speculated on the value that I add beyond the printed notes that I’ll be presenting my students with at the beginning of the semester.

So where are things at present?  I’ve been working on the printed notes and I think they’re coming along nicely.  My current plan is to structure the notes (at least approximately) to have 1 chapter of the notes match to 1 lecture.  To some extent, the material in the printed notes will be the standard sorts of things that a student mathematician could reasonably expect: definitions of basic terms, properties, invariants, and constructions; statements of lemmas, propositions, and theorems; proofs of some, perhaps most, of these lemmas, propositions, and theorems; and the explication of these definitions and constructions, lemmas, propositions and theorems for a fixed set of examples that we carry through all of our Chapters.

None of this is particularly revelatory or new.  Rather, this is all very very standard.  But some of what we’ll have in the Chapters is a bit non-standard, in the sense that it’s not the sort of thing I’ve often seen in textbooks.

Take 2 invariants or properties, seemingly at random, ram them together and ask, can we characterize all graphs that satisfy both properties or that satisfy some equation involving the invariants.  Take a seemingly straightforward example, my personal favorite is the co-prime graph, and try to calculate all of the invariants for it, even where these calculations lead us into unknown territory.  Actually, I like it when these calculations lead us into unknown territory, because this is Teaching-Led Research, and I like Teaching-Led Research.

But these are just the printed notes that I’ll be giving the students taking MATH3033 Graph Theory in a few weeks time.  There is still the question, what is the value that I add, that my presence in the class room adds, beyond the structure of the material that I am presenting to the students in the printed notes.    And that, that I am still working on.  One thing that I can do, and that I will do, is to take an example that isn’t in the printed notes, and to work through each definition, property, et cetera, for this new example, in as conversational a way as possible.

But I should be able to do more.

~ by Jim Anderson on 7 August 2016.

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