Meeting a New Teacher: Gerbert of Aurillac

The other day, I met a woman who’s doing her shadowing today.  She was visiting my school, and observing classes, as preparation for becoming one of our regular substitute teachers.  I was reasonably impressed with her; she seemed competent, earnest and genuinely interested in advancing learning.

We talked about Vi Hart, and it turned out this new teacher had done some of her mathematics study on knot topology, and so I pulled out some books about Celtic knot work, and her eyes lit up.  Then I pulled out The Abacus and the Cross by Nancy Marie Brown, and it became clear that the education of this person in math had maybe not learned much about the history of math.  It was a little startling. Maybe a little dismaying.

As Stephen Downes knows, I’m not particularly good at math, but I like to think I do have a bit of a handle on the history of mathematics.  Is that actually taught as part of the discipline of mathematics any more?  Is there any effort to keep alive the stories of the mathematicians who invent various crazy solutions to the way that various problems work?  Is there any general love given to Gerbert of Aurillac, who introduced the concept of Arabic numerals to the western world?

No, he’s not a(n official) saint.  In fact, Gerbert later became Pope Sylvester II, who is still widely regarded as the magician-pope and possibly in league with the devil.  I don’t know if he has a feast day or not, but it seems to me that it’s worth celebrating, since he was almost certainly one of the great teachers of all time; how many can lay claim to the concept, “well, I simplified addition and subtraction for Westerns to the point where they could invent division and multiplication.”?  THAT’S impressive.

Hail, thoughtful Gerbert, later Sylvester,
who wandered from Aurillac down to Spain:
of maths, and the Church, you’re double Father.
your abacus brought end to Roman pain,
and calculi rolling on chequered banc.
If one writes 2  0 when “twenty”‘s meant,
It’s fairly certain ’tis you we should thank,
even if others thought you demon-sent.
You taught geometry through doodles wise;
and learned the astrolabe among the Moors.
It’s claimed that gears and cogs you could devise,
and your counsel opened knowledge’s doors.
Help me, Gerbert, to learn by insights sweet,
numeric arts that God laid at your feat.

There you are… a kind of mathemagician’s prayer.  Enjoy!

Reading and Writing

Today I gave my students an in-class writing assignment. They handled it well, at their small desks and tables.  I watched them managing their textbooks and their notebooks at the same time, reading a little and writing a little, switching back and forth between one task and the other.

Then it struck me.  They all read and write at the same time.

By which I mean, all of my students don’t read a writing assignment first, and then write about it.  They do both tasks simultaneously.  I’ve been teaching for fifteen years, since 1996, and I don’t think I’d ever seen more than a few kids doing this simultaneously before.  I’d always seen kids reading, and then writing, never trying to do both at the same time.

I think at some point, I shifted away from this as my homework strategy.  I did the reading first, and then I did the writing.  I never did both at the same time. Reading was one activity, and writing another.  I don’t recall — admittedly now 28 or 29 years later —  how I learned to separate the two activities for maximum effectiveness.

I declare myself absolutely gobsmacked.  Why hadn’t I ever noticed this before?  And what effect does it have on learning? How does one separate the tasks of reading and writing, and is it beneficial to do so?  Is it beneficial for the development of their minds to do this?  Or is it an obstacle to be overcome?

I confess I don’t know the answer.  At all.

Web Comics and Artistry

As I’ve mentioned here before, I’m a Druid (Candidate) in AODA, and as I’ve suggested in person, but never before here online, that a Druid practices druidry in the same way that a carpenter practices carpentry — that is, it’s a practitioner engaged in using a traditional set of tools and techniques that result in skillful actions that produce practiced results — results that become more beautiful with more careful practice.  What the results of druidry are, I’m not really in a position to say, for a variety of reasons, but it definitely is a series of actions and techniques that can be applied with results that gradually become more beautiful and elegant with greater practice.

But, it’s after midnight on a school night, and I’m still working on school stuff.  It’s my custom, when this happens, to check out the web-comics I read regularly, and see if a new set of images and words have been posted (it’s getting to be amazing to see the range of artwork available online, updating so rapidly).

I swear this is related to druidry.  And artistry — another one of those -ry words where intentional, deliberate practice makes results more beautiful.  It’s an elegant suffix in English.  Think of all the -ry words you can: ironmongery, armory, perfumery, forgery, carpentry, calligraphy (that one is a bit of a stretch), joinery, falconry, pottery, and so on…

Which brings me to PvP.  PvP is a cartoon about a bunch of crazy online gaming misfits that work at a magazine.  There’s Brent Sienna, who gets attacked by a panda about every hundredth strip, and Francis the misfit kid who’s done a lot of growing up, and a whole host of other characters that I’ve seen develop and change in the time I’ve been reading the web-comic.  The creator, Scott Kurtz, runs a blog alongside his comic, which has detailed an occasional ongoing challenge in dealing with the National Cartoonists Society.

And that brings me to his entry from a couple of days ago, Layers Upon Layers.  See, I have a number of computer programs that give me the power to draw whatever I’m doing in layers… Brushes happens to be one of my favorites at this, but not because I have layers.  No, just because I like producing quick drawings on my iPhone or iPad).

But until I read Scott Kurtz’s post, I didn’t have any idea how to USE layers in a digital drawing program!  I mean, most of the art I make is actually on small index cards or artists’ collector cards, where if you mis-place the pen on the paper, you start over.  Mistakes are an accepted part of sketch art, and the only layers I have are the pencil marks that gradually become layered over with ink… But that’s not digital layering.  It’s not separating out line art from coloring from text from shading; or background from foreground…

It’s an insight into what my friend C(T)P calls “leveling up,” and what Rufus Opus calls “the initiatory work of the traditional grimoires.” Just by reading Scott Kurtz’s article, I have a new insight into how to use my digital tools to better effect as an artist, just as Scott had the insight himself by looking at someone else’s art.

But the thing that brings it back to druidry, and to artistry in general, is that you have to make the commitment to see the world through an artist’s eyes, or through a druid’s eyes, to get into the correct mindset where Scott’s little bit of color commentary about looking at other artists work flow makes sense.  The vast majority of people just don’t care how the art they look at was made.  It’s funny stories and funny pictures, and that’s enough.  The vistas of potential, and of potency, which underlie these bits of silliness, these fripperies, though… there’s genuine skill in their creation, and the only way to grow in these skills is to a) practice them, and b) seek out others who practice them, and learn from their process as best you can.

Underlying BOTH of those, though, is the even more important quality of longing.  You have to actually want to be an artist, or a carpenter, or a druid, to improve in artistry or carpentry or druidry.   That can’t really be imposed from outside, though.  Either you have to be taught how to turn it on (difficult), or you have to have it spontaneously turn on in the kind of miniature moment of glory we used to call gnosis, or mysterium, or sacrament.  

That hidden quality, that quality of gnosis or curiosity, call it what you will, comes to me more easily with the practices of meditation and ceremony, and I can find my way to them more easily now that I have a more regular, habitual communication with my Muse.  But how to turn it on in others?  How to help others learn to engage?

More than any other quality that one must know to be a learner in the 21st century, I think it’s the ability to turn that key, and be in that state of curiosity and wonder, whenever you want or need to be in that state.