Divided!

I knew the day of reckoning was coming. As my son’s math homework became more complex and we had to add columns and rows to the multiplication tables we used for finding mnemonic patterns, long division loomed on the horizon. I’m not arithmophobic. I aced second-year Probability and Statistics, got through Calculus 201 (albeit barely), enjoyed Analytical Chemistry, and researched early modern account books and reckoners for part of my dissertation. Even in my career as an English/DH professor, I happily populate spreadsheets, devise complex formulas for norming and analyzing grades, and crunch through encoding whenever I get the chance. But I missed the unit on manual long division in grade 5, and never did master that dark art. Not until yesterday, that is.

I skipped an entire year of the BC elementary school curriculum. My school’s solution to a bored kid in Grade 5 was to move her abruptly to Grade 6 after Christmas. Whether or not the academic benefits outweighed the dire social consequences remains an open question. But one thing is certain: I was hopelessly confused by this process that all my new peers seemed to have mastered, ignorant of its purpose, and too shy to ask for help. Somehow I compensated—first by working out the answer laboriously in my head and then by resorting to a calculator as soon as we were allowed to bring one to school—and got all the way to my late 40s without needing the skill. But now my 10-year-old son is halfway through the very bit of the curriculum I skipped.

When he asked for help with his math homework on Tuesday, I scanned the page and saw the symbol I’d been dreading: that alarming combination of closing parenthesis with a long bar. (Apparently, ⟌ has no name. No wonder I’ve been filled with nameless dread for nearly forty years! It’s some consolation that Unicode thought to include it. Look up U+27CC if you ever need to insert the glyph into a document.)

Geeky asides aside, I had to confront my fear of long division (a phobia that, like U+27CC, lacks a name). My first move, though, was avoidance: “Hey, honey, how about if I cook supper tonight and you help with homework?” I thought my son would be happy with this arrangement, but it transpired that he prefers my partner’s cooking. So I had to confess my true motives.  With my phobia outed and my culinary skills in question, humility was really the only option.

I listened in on the lesson and heard my own confusion and resistance in my son’s voice. “What is this arrow for? Why can’t I just do it my head? The answer is obvious! What’s the point of all these lines and remainders?” The homework coach patiently explained that the learning outcome was mastery of the process, not production of the right answer. We have to learn the process on simple problems so that we can scale it up to less tractable problems, he said. How many times have I said similar things as a professor? So there was no excuse for not mastering the process of manual long division by remainders, despite the ubiquity of devices that calculate a million times faster than I ever could.

The next night we moved the white board into the kitchen and I became the student. Within three minutes, I was wielding the dry-erase marker myself, reckoning quotients from random numerators and denominators. The cleverness of the method—essentially an algorithm that breaks down long division into a series of shorter divisions—is deeply satisfying.

Long_Division

My first thought after performing two or three divisions in rapid succession was “This is genius! Who invented this technique?” And then of course I had to ask the question in a more formal way in the library today. English mathematician Henry Briggs (1561-1631; see ODNB or Wikipedia) usually gets the credit for teaching the long division algorithm in this particular way.

In 1597, Briggs was appointed the first professor of Geometry at Gresham College in London, endowed by Sir Thomas Gresham who built the Royal Exchange in London. In 1616, Briggs wrote the preface to the English translation of John Napier’s Mirifici Logarithmorum Canonis Descriptio (1614). The printer of A description of the admirable table o[f] logarithmes with a declaration of the most plentiful, easy, and speedy use thereof in both kindes of trigonometrie, as also in all mathematicall calculations (STC 18351) was Nicholas Okes, best known to Shakespeareans as the printer of the Pied Bull Quarto of King Lear but best known to MoEML and much admired by me as the printer of most of the mayoral pageant books. Long division has been hovering, unseen, on the periphery of my research life for a long time.

Inventor of logarithms, Napier recognized the impediment that complex calculation presents to mathematical investigation. “There is nothing,” he wrote, “that is so troublesome to Matheticall practise, nor that doth more molest and hinder Calculators [people performing calculations], then the Multiplications, Divisions, square, and cubical Extractions of great numbers” (STC 18351; Sig. A5r).

Briggs seems to have been a good teacher. At “Gresham house,” he “publickly taught the meaning & use of this [Napier’s] booke.” Given that not everyone could attend his classes, he aimed in his preface to “give some taste of the excellent use” of the book. He wanted to make clear that the techniques described in the book had an application. This particular book wasn’t ultimately about long division, which was merely a technique for performing the calculations necessary to produce logarithmic tables, but the message is pedagogically valuable.

When my son needs help with long division again, I will try to historicize the method and explain that it is simply a way of breaking down and rendering on paper something he understands quite well in the abstract. There are other algorithms that predate Brigg’s long division, and perhaps my son would find one of them more appealing. I will try to explain that the technique is not an end in itself, even though his math textbook presents a culturally and historically specific method as a universal law. And I will happily draw arrows and divide with him.

The Gruffalo and The Gruffalo’s Child

The Gruffalo, Front CoverWe have read this wonderful pair of books by Julia Donaldson countless times. What’s not to love about a tiny mouse who preys upon the fears of his predators with a bit of imagination and consistently catchy couplets? When it turns out that there is such a thing as a Gruffalo, the mouse has to think fast! In the sequel, the “Big Bad Mouse” is the bogeyman conjured up to keep the Gruffalo’s daughter away from the “deep dark Wood.” When the Gruffalo’s Child sneaks out to see for herself, the mouse has to think fast … again! Axel Scheffler’s illustrations offer additional details that my young readers love (cavewall drawings of Snake, Owl, Fox, and Mouse, for example). For the adult reader, the exquisite politeness of Mouse, Fox, Owl, Snake, and Gruffalo point to familiar social menaces and solutions more than to “nature red in tooth and claw” (Tennyson 57.15). What grown-up hasn’t wanted to conjure up a gruffalo of an excuse to escape an unwanted lunch invitation at least once in her or his life?

But I keep coming back to Donaldson for her note-perfect poetic meter, which is an integral part of the storytelling. Good poetry lays down a beat and then varies it in meaningful ways. The Gruffalo is mainly iambic and dactylic, invoking patterns children know well. (An iamb is one unstressed beat followed by a stressed beat: da DA. A dactyl is a stressed beat followed by two unstressed beats: DA da da.) Say these two dialogic couplets out loud to hear the dactyls tripping along decorously:

[Fox] Where are you going to, little brown mouse?
Come and have lunch in my underground house.
[Mouse] It’s terribly kind of you Fox, but no —
I’m going to have lunch with a gruffalo.

All very polite and light, until the mouse brings up his imaginary pre-arranged lunch date. The mouse forces Fox off the social script.

[Fox] A gruffalo? What’s a gruf-fa-lo?

With the two interrogatives (the first one a non-sequitur or non-sentence), the meter abruptly shifts to spondees (two stressed syllables), which I’ve marked in bold. There are many ways to read this line (and I’ve tried them all over the course of reading this book aloud several hundred times), but the words seem to come out best as querulous spondees. To me, the change of meter signals an irruption into the normal flow of social dialogue. The mouse inserts a surprising piece of information. The Fox can’t help but ask — just as Owl and Snake will do in the subsequent pages.

The mouse is in control of the social dialogue from this point on. First, he gets to complete Fox’s incomplete half-line:

A gruffalo! Why, didn’t you know?

In studies of Shakespeare’s verse by theatre practitioners, there’s general consensus that shared half-lines indicate haste, with the second speaker jumping in to finish the line (Rokison). In this case, the mouse feigns exclamatory surprise (“A gruffalo!”) and shames his interlocutor with the implication that Fox is outside a knowledge community (“Why, didn’t you know?”). Without much time to think, the mouse resorts to a repeated adjective rather than specifics of the gruffalo’s appearance:

He has terrible tusks, and terrible claws,
And terrible teeth in his terrible jaws.

The mouse will elaborate these details in his next encounters (with Owl and Snake), when he’s had more time to conjure up the vision of the Gruffalo. But this moment, when the mouse is only beginning to imagine his Gruffalo, always makes me laugh. “Terrible” is the best he can do — four times! Technically, the repetition of “terrible” is an instance of “diacope.” Silva Rhetoricae defines diacope as “Repetition of a word with one or more between, usually to express deep feeling.” The mouse is certainly feeling something deep: fear of being eaten by Fox! And so he is both in control of the exchange and not entirely in control of the image … yet. When he does fully master the idea of a gruffalo, the Gruffalo (now with an uppercase G) materializes in front of him, a new terror to be managed.

The mouse’s bravado and quick thinking are deeply pleasurable precisely because they come from a place of vulnerability. He is vulnerable to things bigger than he is, to veiled threats that seem like kindness (“tea,” “lunch,” “a feast”), and, finally, to his own imagination. To a child trying to parse a world full of bigger people, mysterious requests, and nameless fears, the mouse is an achievable heroic model.

This exchange in The Gruffalo should remind you of another question-and-answer nursery rhyme, also in alternating dactylic lines:

Pussycat, pussycat, where have you been?
I’ve been to London to visit the Queen.
Pussycat, pussycat, what did you there?
I frightened a little mouse under her chair.

I like to think of The Gruffalo as the mouse’s revenge. Ultimately, The Gruffalo is an instance of the “world turned upside down” motif, where normal hierarchies are inverted.

Image from the British Library © The British Library Board.
Image from the British Library © The British Library Board.

In the lower left-hand corner, you can see a crudely drawn mouse or rat chasing a cat — part of a series of inversions (fish swimming in the air, a man’s hands where his feet should be, a horse pushing a cart). Such images, popular in Renaissance Europe long before their appearance on this 1646 title page, often include children instructing their teachers or blessing their parents. The mouse’s triumph over Fox, Owl, Snake, and, ultimately, the most terrible thing he can imagine, is the triumph of the child. And it all plays out in mutually supporting ways at the level of narrative, image, and verse.

References

Burton, Gideon. Silva Rhetoricae. http://rhetoric.byu.edu/.

Donaldson, Julia. The Gruffalo. Ill. Axel Scheffler. London: Macmillan Children’s Books, 1999. ISBN 978-0333710937.

Donaldson, Julia. The Gruffalo’s Child. Ill. Axel Scheffler. London: Macmillan Children’s Books, 2005. ISBN 978-1405020466.

J., T. The World Turn’d upside down: or, A briefe description of the ridiculous Fashions of these distracted Times. London, 1646.

Rokison, Abigail. “Shakespeare’s Dramatic Verse Line.” The Oxford Handbook of Shakespeare’s Poetry. Ed. Jonathan Post. Oxford: Oxford UP, 2013. 285-305. DOI 10.1093/oxfordhb/9780199607747.013.0024. See section 16.2, “Shared Lines.”

Tennyson, Alfred Lord. In Memoriam A. H. H. OBIIT MDCCCXXXIII. 1850. Text from Alfred Lord Tennyson, Poems, ed. Hallam Lord Tennyson and annotated by Alfred Lord Tennyson. London: Macmillan, 1908. Available in digital diplomatic transcription at Representative Poetry Online. Ed. Ian Lancashire. Toronto: University of Toronto Libraries, 1998.

A Day in the Life of One Academic

Time to stop tinkering with fonts and templates and WRITE something.  I was going to launch this blog with an explanation of the multiple meanings of “Occasional Drama” (consider it “forthcoming”) but “The Day of Higher Ed” calls me to a different reckoning.  Lee Bessette has challenged us to “record, in minutia, what we do as professors from the moment we wake up to the minute we fall asleep.  All the work we do that contributes to our job as educators.”  And maybe a blow-by-blow summary of Monday, April 2, is as good an introduction to “Occasional Drama” as any other.

04h00.  Today, my occasional pre-dawn research and writing time was wholly given over to the creation of the final examination for English 147:  Literary Traditions and Transformations.   The exam has to be done today so that I can head off to the Shakespeare Association of America conference in Boston at 5:45 a.m. on Wednesday with a clear conscience.  I remind myself of the course objectives and learning outcomes, look through my own notes and slides, pick passages, write essay topics, and finally try to imagine being a student writing this exam.  Student assessment is a tricky business; after fifteen years of setting exams, I still worry and second-guess throughout the process.

06h30.  The Bookworms awake early, cranky and incapable of effective communication.  The next two hours are a blur:  make nutritious breakfasts, negotiate the complexities of dressing rituals and the morning melodrama of favourite shirts being mired in the laundry system, admire Lego structures, rescue aforesaid Lego structures from dinosaur attacks, resolve several disputes, and look for Waldo with a magnifying glass while teaching the G-Worm about alliteration (Waldo, Wenda, Wizard, Wag).  While drinking tea, I brush up on Jungian Psychology 101 in preparation for my lecture later in the day.  I owe my morning shower to Miss Frizzle and The Magic School Bus.  Gathering boots, coats, hats, knapsacks, security blankets, and raingear makes me grateful that I teach adults and doubly appreciative of childcare providers and elementary school teachers.  Every venture outside our door is a variation on Thomas’ Snowsuit.  Once in the car, we listen to stories on CD or deal with the usual questions about the Big Bang, where babies come from, how electricity stays inside the wires, or why the digger/truck/car/bike/machine/tree/dog/stoplight/pedestrian is doing whatever it’s doing.  True inter-disciplinarity happens in the preschool years.  I’m grateful for all those courses in Physics, Chemistry, and Math in my B.Sc. days.  By the time I drop the Bookworms at daycare, I’ve already done a day’s worth of problem-solving.

09h00. Daycare drop-off accomplished, I can turn my thoughts to my work.    On Friday afternoon, I mapped out the month of April in yellow flags stuck to the  portrait of Elizabeth I on my office wall.  Like me, Elizabeth is up to her ears in tasks.  I begin Monday by gazing at Elizabeth and contemplating the tasks she has for me.

09h30.  Weekly check-in with my research and writing buddy.  These meetings get shorter and shorter as the term progresses.  Come summer, we’ll start reading and discussing each other’s work again.  Meanwhile, we remind each other that research really is 40% of our job, even if 100% of today is devoted to Service and Teaching.

09h45.  I take my laptop over to Special Collections Reading Room in the Library.  I’m co-curating an exhibit of rare books donated to the McPherson Library by the late Dr. Patricia Koster (more about this in a later post) and we (doctoral candidate Sandra Friesen, a team of students, and I) are at the stage of placing books in the display cases and writing up the bibliographical descriptions for the 180 books we’ve selected.  It’s a peaceful place to work, even though we’re rushing to finish up the analytical work.  Handling the tooled leather bindings, turning old linen-rag pages, looking for watermarks, reading the marginal inscriptions of past readers, transcribing the title pages:  these activities have a meditative quality for the bibliographer.  I even get to do an exciting bit of bibliographical forensic work:  a signature collation to determine that we do indeed have first editions of Dryden’s Fables (1700) and Pope’s Works (1717).  I’ve been typing so much lately that I have shooting pains in my right hand, wrist, and forearm.  When the pain gets unbearable, I stop to read some of these wonderful old books.  The lack of critical apparatus and editorial footnotes lets me read guiltlessly.  I soak up rhyming couplets, Restoration playtexts, gossipy prose, hilarious dedications “To the best judge of this book, Myself.”  It’s a rare reminder of what first excited me about literary study.

12h45.  Lunch.  The line-up is too long at the upscale Bibliocafe, so I walk across the heart of campus to the University Centre for a sandwich, where I bump into a colleague in History whom I haven’t seen all year.  We talk for five minutes on our way back to our offices, the only collegial interaction I’ll have this afternoon.  We talk campus politics, which revolve around workload and pay at the moment.

12h55.  I eat at my desk while reading the 37 emails delivered to my inbox while I was shielded from the internet down in Special Collections.  Only two can be dispatched with a simple “thank you.”  The rest require more thought, but I have to turn my attention to the last lecture of the term.

13h05.  My classes never go well if I reuse an old set of notes.  I have to reread the primary text, rework my notes, and tinker with my powerpoint slides every single time.  Reworking the notes is how I think through an argument and figure out how I want to approach the text or problem.  Once made, the notes have served their purpose; I often don’t need to look at them at all while teaching.  I’m teaching the final lecture on Ann-Marie MacDonald’s Goodnight Desdemona (Good Morning Juliet) — and the final lecture of the course — at 3:30.  I copy part of an old set of notes into a new file, rework them, and then add a new section on how MacDonald traces a Jungian path of individuation for the main character, Constance Ledbelly.  I plan a 5-minute introduction to Jung’s conception of the Self, Shadow, Archeyptes, and Individuation, just enough to make sense of MacDonald’s use of these concepts and maybe to whet the students’ appetite for more information.

15h15.  Off to the classroom, a cavernous room with no windows.  Set up laptop, Clicker base station, slide show, video data projectors, wireless microphone.  There’s good energy in the room today, students are taking notes, and, when I thank them at the end of the lecture for their attention over the term, they are generous enough to applaud.  For a huge course (two lecture sections of 180 students each, with twenty tutorials and twenty TAs), it’s gone remarkably well.   I’ll repeat the same lecture tomorrow to the other section … but I’ll probably tweak it again before I do.

16h20.  Field a couple of questions from exiting students, unhook all the cables, shut down computer, and pack up.  Meet briefly with the TA Coordinator and discuss strategies for managing any problems that might arise while I’m away in Boston.

17h00.  I’ve gone home early today.  The Bookworms will be picked up by their dad while I put some time into the family finances.  All UVic employees had their banking information compromised by a break-in.  Many of us are still sorting out new accounts, transfers of automatic debits, and credit monitoring.  Somehow I feel I ought to be able to do this business on my employer’s time, but then I’d just end up prepping a lecture or marking in the evening on “my time.”  The concept of “my time” and “the employer’s time” is nearly absurd in academia.

17h40.  The Bookworms return, chattering of beach adventures, books read, plans for the evening.  In the blur of hand-washing, table-setting, discussing the importance of vegetables, bathing, and tooth-brushing, reading stories is always a highlight.  Like every English professor who is also a parent, I’m fascinated by the structure and style of children’s books, but even more fascinated by the opportunity to study reader response, or at least the responses of two small readers who are learning the narrative ropes, so to speak.  In an hour, we range across old favourites that we own, new library books, fiction, science books,  picture books, and chapter books.  Our new book for tonight is Henry and the Kite Dragon (Bruce Edward Hall; illustrated by William Low).  There’s a dark moment right in the middle of the book where the Chinese-American children and the Italian-American children are “ready to start swinging” at each other.  The Bookworms are on the edge of the couch, absolutely still (for once), waiting for violence to erupt.  Then the story shifts abruptly, and the two warring neighbourhood groups unite in a shared bid to protect a pet pigeon from the frightening titular dragon kite.  “Ah,” I think, “That was the augenblick.”  Only a few hours earlier, I was talking about the augenblick in Othello and Romeo and Juliet.  And in this moment, the two halves of my life click neatly together.  I’m a better teacher because I’m a parent, and a better parent because I’m a teacher.

23h00.  The Bookworms are asleep, their dad is out in the garage building sections of a new fence, and I have just put the finishing touches on the final exam.  I’ve worked a normal workday (9-4:45), spent a good five hours with my children, and given an extra 3 1/2 hours to my job at the beginning and end of the day.