Like the great artists of history, some of our junior artists have been practicing self-portraiture. It takes a keen eye, steady hand, and creative mind to achieve results like these!
by Anna Nabutovsky
excerpt from final project for EWC4U, The Writer’s Craft
And I wept. The tears fell onto the canvas one by one, creating puddles on the bright display. And I hoped they would wash away the paint, leaving the canvas blank, fresh, clean, and ready to begin anew. And I wept, watching the tears fall onto the canvas not clearing a thing away but rather smudging the paint, leaving it a blurry, murky mess. And I sighed, knowing that tears would do me no good. So I took out my finest brush and my darkest shade of red, and painted over the canvas, covering the shameful blur with a powerful, deep, seeping, all consuming red.
In the iridescent glow of the moonlight
In the outline of a palm on the glass
In the flickering of lights
In the moment of passion
There was beauty
In the fantasies you had
In the dreams that were not realized
In the sleepless nights
In what could have been
There was hope
In the days spent without care
In the sound of your laughter
In the lecherous thoughts
In the treacherous moments
There was desire
But when the flame burns out
When reality collides with vision
When you stand before me as you are
And I stand before you as I am
Nothing left unseen
And nothing left unspoken
There is emptiness.
The moment was red. Thrashing wildly against the restraints of reason, tugging at the chains of social order, and entirely rid of the emotional consciousness which plagues day to day interactions. From tense voices to piercing screams in an instant. The shatter of wedding china, ceramics shredding into fine pieces, impossible to fix, broken apart for good. And then silence, the red fades to white. White hot rage, broken away from passion, fading to indifference.
The beginning of a day
The coy playfulness of a wink
The excitement of risk
The treacherous sound of your heart beating
A moment of desire
A ballet of silhouettes
A soft whisper
A silky strand of hair
The movement of one hand
The cry of pain
The sound of water running
The ending of a story which never began.
Four borders, fading at the edges. I look down. She sits alone on a rocking chair draped with a wool blanket. The room is small, poorly lit, with only a faint glow which casts menacing shadows. She is old, but more frail than befits her age, so frail in fact, that she blends seamlessly into her surroundings, becoming one with the battered, dusty furniture. A Persian rug is strewn across the floor, not exactly carelessly, just haphazardly. She looks up suddenly from her trembling hands, and we see her eyes. Vividly expressive. Now watery, but once a bright blue, filled with a zest for life. The room grows darker, as the wax drips from the lone candle in the corner. She looks down, with a half defeated sorrowful glance, and begins to rock in the chair. The candle in the corner drips again, creating a stain on the rustic wooden table, which shakes slightly. She looks up again, her thin lips twist into a half scowl which evokes more pity than fear. Her bony fingers reach for her cane, she trembles slightly, unable to grasp it, and gives up with a defeated sigh. Her eyes fall onto a photograph which hangs above the torn sofa. It is a mustard yellow colour from age, but that gives it a quaint sort of charm. It depicts a smiling young woman. Bright blue eyes. Her hair waves in the wind in an elaborate adage. There is much innocence in her gaze, a smirk plays on her lips, which shows that she has not yet shed all the layers of youthful conceit. Yet, she is a worldly sort of beauty. A becoming young man stands in a wool coat by her side. His blonde hair is covered with snow. He looks at her, not at the camera. She lowers her gaze from the photo. A single tear slides down her face. Not just nostalgia: regret. She shifts her gaze again, and looks out the lone window. It is already April, yet winter refuses to leave. There is something beautiful about the plush white carpet and black still night. They call forth memories of laugher, and fireplaces. It is too late for that now. It is springtime. Yet the snow persists, refusing to leave the past and make room for the future. The moonlight gives the still landscape an ethereal glow. She sees two men pass by, both wearing large spectacles and wool coats. They pass with a sense of impending purpose, yet simultaneously a cavalier air follows them. They don’t seem to notice the stars or the moonlight. She is glad when they pass, their briefcases sully the beauty of the night. I hold her gaze for a second longer. She is fading away at the edges. The picture crumples, and falls to the ground.
I dip my brush into the paint, watching each stroke find a home nestled amongst the others. The paint dries quickly in the blazing heat. I wipe my brow to stop the sweat from dripping into my eye. Alongside me the others work chirping away in a flurry of merriment. The giddiness twirls around me, engulfing me into its welcoming embrace, begging me to join if only for a second. Yet, for some reason I resist the temptation preferring sulky isolation to the surrounding joy. I frown, immersing my paint brush into the can and stroking the walls of the decaying tunnel with the familiar rhythm. Sounds of laughter echo around me again. Talk about pathetic fallacy, I think to myself bitterly. The high pitched squeals of delight go hand in hand with the admittedly glorious weather and vivid colours. I shake my hand, everything is almost offensively bright. Like a scene plucked from a children’s book, designed to fool the naive and innocent into believing in the lightness of momentary paradise. Their joy rains onto my parade. It is ironic considering I am the sole dark blemish on the purity and sunniness of our surroundings. Somehow that makes me feel worse. I dip my brush into the darkest colour available, a glaring anime purple, and shudder. I watch the young girl next to me spread the yellow paint generously over the walls. She has a butterfly tattoo on her ankle. I think its shamefully typical, but maybe she has it all figured out. Pink butterflies, ankle tattoos, silky blonde hair, and an infectious smile. I look up at the previously grim tunnel now painted to resemble a rainbow. Glitter, unicorns, butterflies, rainbows, and me, I think to myself. Name the thing the does not belong. I smirk and start to think about rainbows, the irony of sunshine and rain working together. I look to the herd of giggling girls next to me. Sunshine, I think to myself. Suddenly, I stop, feeling a genuine smile creeping onto my lips for the first time today. This rainbow wouldn’t exist without rain. I am grim, dark, and hopelessly past naiveté, yet I can’t help but giggle, and for one moment I feel as though I truly belong.
While individual classes might leave the school for an activity that enriches students’ learning, like the recent grade 12 biology excursion to a lab at U of T, we regularly take all of our students to attend live performances. We attend live theatre and opera in part because we hope that our students enjoy the experience, but there is considerably more potential benefit to a night (or afternoon!) at the theatre than just pleasure.
Last week, The Abelard School attended The Magic Flute, presented by the Canadian Opera Company. Mozart’s opera tells the story of Tamino’s quest to rescue Pamina, whose hand he has been promised in marriage by the Queen of the Night. The characters struggle with and against the forces of good and evil as they contemplate what it takes to live an honourable life. The opera features deeply-loved music like the Queen of the Night’s “Der Hölle Rache,” and the charming duet between Papageno and Papagena. True to fairy-tale form, everything ends happily.
The opera gave us all lots to talk about in the following days. Among other things, we discussed metatheatrical staging, the history of opera performance in Austria, the difference between historical production practices and staging today, and the (dated!) representation of women in The Magic Flute. Pedagogically, it is important to see live performances because these are all subjects that aren’t as easily accessed in reading a libretto or score alone. A live performance weaves together layers of meaning, where the languages of the stage–lighting, acting, design, writing, and more–are at free play with one another, collectively either reinforcing or asking us to question our initial responses.
There are less tangible but equally valuable reasons for bringing the entire school to the opera. A 2015 study by researchers at the University of Arkansas demonstrated that attending theatre, “increases student tolerance by providing exposure to a broader, more diverse world; and improves the ability of students to recognize what other people are thinking or feeling” (Greene et al). The report compellingly argues that students become better at navigating the world around them for having attended a live performance. Or, as another study more succinctly puts it, participating in theatre “provides an environment […] which support[s] young people in making positive transitions to adulthood” (Hughes 70).
Attending The Magic Flute, then, reflects one of the core philosophies of an education at Abelard. We are committed to helping students discover their own strengths and to developing their morals and values so that they might help make the world a better place by their contribution to it.
Greene, Jay P., Collin Hitt, Anne Kraybill, and Cari A. Bogulski. “Learning from Live Theater: Students realize gains in knowledge, tolerance, and more.” Education Next, Vol. 15, No. 1, Winter 2015. http://educationnext.org/learning-live-theater/.
Hughes, Jenny, and Karen Wilson. “Playing a Part: The Impact of Youth Theatre on Young People’s Personal and Social Development.” Research in Drama Education: The Journal of Applied Theatre and Performance, Vol. 9, No. 1, 2004, pp. 57-72.
We are incredibly proud of our students and the calibre of the work that they produce. The following essay was written by Sivan Piatigorsky-Roth in her grade 12 English class. It is a phenomenal example of the depth and sophistication of the literary study we undertake at Abelard.
The nature of James Joyce’s Ulysses makes it simultaneously impossible to understand without investigation, and impossible to reach conclusions on. It is a book about our obsession with finding meaning, and it is a book as well about what that investigation and inquiry means in and of itself. The thirteenth chapter in the mammoth novel, “Nausicaa” details the time between 8:00 and 9:00 on the day of June 16, 1904. The main character, Leopold Bloom, sits on Sandymound Strand, observing three young girls and fantasizing about one in particular, Gerty MacDowell, thinking about her life and her consciousness. As Gerty arouses Leopold, who subtly pleasures himself, a Benediction service takes place at a nearby church, reaching its climax (everyone cried O! O! in raptures – pg. 350) along with Bloom as a Roman candle firework explodes overhead. Realizing Gerty has a lame foot, Bloom spends the rest of the chapter pondering sexual attraction and thinking primarily about his wife. The book as a whole is about dualities, and this chapter in particular focuses on them, yet Joyce is careful to collapse and merge the parallel ideas in “Nausicaa” and show that in fact, the twofold depictions in Ulysses are truthfully one and the same.
This chapter is the first in the book to focus on a woman. It is unclear if the female thoughts in the chapter belong to Gerty herself (which is what we are led to believe until the final lines of the chapter) or if they are a product of Bloom’s fantasies. Gerty is depicted as a feminine duality. She is a seductress and an innocent child in one. She is a girl “loveable in the extreme” (pg. 332), with a face “almost spiritual in its ivorylike purity”. She has clear blue eyes, pretty dress and dreams of a strong husband. She thinks in advertising clichés, fairytales, and the sentimental talk of women’s magazines. Yet Gerty, for all her virgin naivety, plays the part of the siren as well as the maiden. She spends her time prettying herself, hunting for the right colors (pg, 335) and smiling at her reflection in the mirror (pg. 335). She wears charming underwear (pg. 335-336) and she shows her ankles flirtatiously to Bloom, knowing well that her purity arouses him, and taking delight in the results of her tease.
This imagined duality is likely a result of Bloom’s own preconceptions. As an advertising agent, Bloom is likely to be well versed in the clichés of advertisement, as well as their audience (young women, largely). The thoughts in Gerty’s head reflect what he imagines a young woman’s thoughts to be consumed by, and are strikingly different to the interior monologue we get later from his wife in chapter eighteen, a genuine female consciousness. Gerty’s language takes directly from women’s magazines of the day and only alludes to unpleasant ideas such as her foot or masturbation rather than directly addressing them as Molly does in chapter 18, actually thinking for herself. The final lines suggest that Gerty sees Bloom sitting on the rocks and thinks he’s “cuckoo”. Bloom throughout the novel is always many things at once. He is a born Jew who converted in marriage and is not circumcised (the foreskin is not back. Better detach.- pg. 356), and here his fantasies take the form of a feminine consciousness along with the masculine. It could be that the recurring theme of metempsychosis has reappeared, and Gerty’s femininity has settled into Bloom for a few pages, supported perhaps by the repetition of sight, eyes, and painting as motifs while Gerty thinks, shifting towards scent when she leaves, a sense that has previously been associated with Bloom’s consciousness. It could be as well that Bloom is simply aroused by such elaborate fantasies, as he spends a great deal of time thinking on sexual attraction and its nature.
Another duality presents itself in the form of desire. The desire for a connection, both spiritual and physical, runs throughout the book, but in particular throughout this chapter. The coinciding mass and masturbation are two parallel ways of alleviating the parallel desires in both the mind and the body. While Bloom is a man rooted in the physical, who spends his time bathing, defecating, masturbating, and eating, his search for intimacy manifests itself in the spiritual as well, as he meditates on his relationship with his wife, his son’s death, and his book-long search for a son figure, culminating in his meeting with Stephen.
The religious desire and devotion, however, is rarely seen as equal to the physical desire, but is rather thought to be of a higher morality than the more depraved bodily urges, and Bloom is not oblivious to this, thinking himself a “brute”, and then letting his mind turn towards, interestingly, religion (pg. 361). Bloom is not a Christian. He doesn’t go to church and holds atheistic views. Why, then, do his thoughts turn towards Judaism? He is bombarded with anti-Semitism, and certainly is a Jew in the ethnic sense of the word, but as a converted atheist, the religious aspect of Judaism is fairly far removed. After an act seen as depraved or shameful, however, it is no accident that his mind returns to the purity of devotion and desire rather than the ‘lesser’ or more base manifestations that desire and devotion can take. Although he is not well versed in Jewish practices and customs, confusing tephilim, prayer wraps worn by Jewish men, and mezzuzahs, small prayers hung on the dorrframe (p. 361), Bloom still thinks of religious worship after his sexual worship of Gerty.
Gerty herself is paralleled with the Virgin Mary who is being supplicated in the nearby church. Indeed, the symbol associated with this chapter is that of the virgin. Although the aforementioned duality certainly does exist, and Gerty assumes a seductive role as well as an innocent one, Bloom’s infatuation with Gerty’s youth and chastity is mirrored in the prayers to the young and chaste Mary. Gerty MacDowell is described as having a “waxen pallor of her face” that is “almost spiritual” (pg. 333), and the Virgin Mary’s banners are described on page 332 as being blue, a color associated repeatedly with Gerty. We can look again towards metempsychosis and wonder if Gerty contains some part of Mary’s soul, or we could look to the equally recurring question of consubstantiality and wonder if Gerty and the Virgin Mary are somehow two parts of a greater whole- a chaste product of a culture that values and even fetishizes youth and innocence.
Bloom’s presence at Sandymound Strands, and his day long stroll through Dublin have left his wife Molly at home all afternoon, where Leopold is certain she is having an inevitable affair with a man named ‘Blazes’ Boylan. Following his masturbatory episode, upon realizing that Gerty has a lame foot, Bloom ruminates on previous sexual encounters, prostitutes and what arouses them, and the various men who have been attracted to Molly, realizing that his watch, which has stopped at half past four, has probably stopped at the time that Molly and Boylan slept together. thinks on his wife and his daughter, who cannot be much younger than Gerty is. His thoughts, which are consumed by sex and magnetism, keep tracing back to Molly, maybe through guilt or maybe through genuine desire and love. June 16, 1904, the date that Ulysses is set, is (according to the Wikipedia article for Nora Barnacle, Joyce’s wife), the day of Joyce’s first date with his wife. It is clear from the date and from the final chapter of Ulysses, which envisions a sample of Molly Bloom’s consciousness, that Joyce is thinking (at least on some level) about Nora while he writes, literally putting himself in a woman’s mind for large sections of the book and relatively candidly addressing female sexuality and consciousness.
The associated organ, color, and art (eye, blue, painting) all coincide in Gerty’s consciousness. Her clear blue eyes are emphasized. Bloom can feel them watching him (“Leopold Bloom (for it is he) stands silent, with bowed head before those young guileless eyes”) and Gerty likes to wear blue for luck and to flatter her eyes, putting emphasis on the straw hat with an eggblue chenille underbrim (pg. 335) and the blue underwear she wears. Gerty’s blue is for luck, and it is fitting that her eyes match. As luck would have it, Gerty is present on the beach just after eight o’clock on June 16, just as Nausicaa, by some divine involvement or simply by luck, appears to Odysseus as he needs her, and despite his frightening appearance and nakedness, helps him. The other associated color, grey, is the color most commonly associated with Athena, who protected Odysseus throughout his journey.
The visual nature of the associated art, painting, keeps with the emphasis on Gerty’s eyes. Bloom thinks “the very soul is in her eyes” (pg. 336) and when Gerty looks at the sea (blue like her eyes, or maybe grey like Athena’s), she thinks of the “paintings that man used to do on the pavement” (pg. 341). Bloom as well thinks of painters in Lombard street later, on page 357, although this time he is reminded of the turpentine smell coming from the paint rather than the visual aspect of the painting. To Gerty, the art of painting is visual, as is everything else. She uses her eyes as her main tool, fabricating her life around her image, using the art of painting even on her own face, painting (as Hamlet would say) herself another. To Bloom however, the art is olfactory, as is most of his sense perception. When Bloom thinks of painting, his mind returns to the scent of turpentine, before drifting to thoughts of Molly’s scents and the lemon soap in his coat. The associated art of painting also manifests in the phrase that is repeated, “Tableau”, a game where players pose in frozen images when the phrase “Tableau!” is shouted, making a scene. This frozen scene is reminiscent of a painting, where the figures or images are frozen in time.
The complex winding of Ulysses follows the complex winding of Odysseus himself as he travels from Troy home to Ithaca. It is not a novel that exists to be read, but one that exists to be studied, one with as many turns and whirlpools as Odysseus himself encounters on his journey home. The book exists in dualities. It traces Stephen and Leopold, their day and when it diverges and unifies. It follows the spiritual and the physical, the masculine and feminine, birth and death, father and son. This chapter in particular blends dual themes into one. Bloom is Bloom and yet he is also Gerty, Gerty is a child and yet she is a temptress, she is Gerty and yet she is the Virgin Mary, the visual nature of painting is not so far removed from the olfactory nature of it, and Molly and Gerty and Milly and even Bloom himself are not so different from each other after all. Beyond the dualities, however, it is unified. The theme of consubstantiality runs through the heart of the book, and the dualities are all part of the same whole- a mammoth mess of a book, a convergence of themes and allusions, and an essential cornerstone of Modernist literature.
by Michelle Lefolii
Principal (and English teacher)
We study literature first because it brings us joy. As John Steinbeck writes, there is nothing comparable to the pleasure of reading a good book, tunnelling like a mole among the thoughts and coming up with it all over our face and hands (280). There are easier forms of pleasure, certainly, but what we seem to forget too often in our search for immediate gratification is that real pleasure, lasting pleasure, is the product of effort as well as chance. We enjoy natural beauty, but we love our own accomplishments with a unique intensity, a gratification which derives from the satisfaction of mastery. Literature is not easy, nor is it simple. It requires great effort, but it also rewards that effort greatly.
The human mind craves complexity. It is designed to recognize patterns, to make associations, to solve puzzles, so much so that it invents them even when they don’t exist (every good conspiracy theorist knows that!). Computer games channel this drive, and the manner in which they reward it is addictive. Young people exchange tips as to how to navigate these games, how to progress from level to level: they teach one another the laws of the game; it is wonderful to watch this passionate exchange of information, and to see the satisfaction they derive as they advance from level to level.
This is the type of teaching I aspire to when I teach literature: my role is to instruct my students in the rules of navigation for the world of fiction, to show them where the hidden charms and magic spells and secret weapons lie that will allow them to move to deeper and deeper (rather than higher and higher) levels. I pass on tips to them, and then let them experiment on their own. Like games, works of literature share certain design features, certain conventions, and once these are understood the groundwork is laid for an understanding of the unique variations posed by each text, the unique challenges it presents. Above all, I teach my students to search for patterns. And when they discover these patterns they take great delight.
But the pleasure of literature doesn’t lie in its complexity alone, or in the mastery of that complexity. The greatest pleasure it bestows is that of recognition. Literature captivates us by presenting us not with the unknown but with the known. It brings us face to face with ourselves. And this is true whether we are reading Hamlet or Ulysses or To the Lighthouse: literature need not be of our time to hold the mirror up to nature. We need not be of the same culture or the same sex as the protagonist to see ourselves. The world around us changes, is constantly in flux. Human nature, however, doesn’t change. Human emotions don’t change. The questions we ask ourselves about the nature and purpose of our existence don’t change. And these are the province of literature.
In the United States, declining literacy rates and test scores have prompted the development of a new common core curriculum. Politicians and educators are correct to be concerned about a decline in the level of student reading skills. But to address this problem by creating a curriculum in which the focus is on informational texts rather than on literature is ham-fisted. A student who is taught how to read a repair manual is learning a useful skill, certainly. But a student who is taught how to read literature learns how to be human.1
Teaching literature is not easy. It is not as straightforward as teaching students how to read informational texts. It takes time and care. Sometimes it’s a struggle. The question of relevancy arises. But surely our role as teachers is not solely to give our students the skills to enter the job market. In any case, that market is in continual flux: what is relevant to it today is obsolete tomorrow. Shakespeare’s language is not the language of the corporate or professional worlds, or the world of trade. Familiarity with the classics will not help students to get a job. Othello’s Venice is not our home. But when we discuss Othello, we suddenly find ourselves talking about racism and sexism, about misplaced trust, about healthy and unhealthy love, about envy, about the roles both professional and personal of men and women, about fear and insecurity, about manipulation and revenge. These are not merely relevant to the lives of my students, they are of intense personal interest. Young people need to acquire skills, certainly, but they also need to learn how to navigate the world of human relationships.
When we study literature we study ourselves. We see what we hold in common with all human beings. We become more human. We become ourselves.
1 Harold Bloom, of course, in Shakespeare, The Invention of the Human, carries this idea even further. My point is not exactly his, but I am indebted to him for the concept of the crucial role literature plays in shaping our understanding of ourselves.
Steinbeck, John. East of Eden. Penguin, 1980.
2017 promises to be an exciting year for Abelard. In addition to the incredible projects we’ll tackle in our classes, we are thrilled to be marking our twentieth anniversary this year. To kick off the celebration, we thought we would share some of our proudest recent accomplishments. We have spent the past two decades consolidating our unique curriculum and believe that we are the best high school in the city for academic excellence, breadth, and depth.
The majority of our current teachers either teach or have taught at university level, including all of our science teachers, who work concurrently at U of T, and our math teacher, who has taught at Brown. All of our teachers are passionate about working with high school level students to assist them in developing the intellectual skills and maturity which will help them to thrive once they graduate.
Abelard has become a school of choice amongst university professors: in the past 5 years, 27 university professors have sent their children to Abelard, realizing that we have a remarkable track record in preparing our students to succeed in university.
University professors (and admissions officers at Ivy League colleges) tell us that our graduates are far better prepared than most first year students.
Our graduates are all accepted to university, and they have won hundreds of thousands of dollars in scholarships from schools such as Cambridge, the Sorbonne, St. Andrews, Columbia, NYU, Berkeley, Brown, Johns Hopkins, UCLA, Dartmouth, Wesleyan, U of Pennsylvania, U of T, McGill, McMaster, Waterloo, Queen’s, Western, King’s, UBC, and Dalhousie.
Abelard alumni have won 2 Thiel Fellowships: Chris Olah (2012) and Vitalik Buterin (2014) — this is remarkable! Only 20 of these internationally competitive $100,000 fellowships are awarded each year to students under 20 and since its inception in 2011 two of them have been Abelard alumni! Chris is now working for Google in San Francisco. His specialties are machine intelligence and neural networking. Vitalik has been named one of Fortune Magazine’s 40 under 40 for 2016!
Vitalik Buterin also won the World Technology Award for IT software (over Mark Zuckerberg!) in 2014 (only 2 years after he graduated from Abelard). He and the crypto-currency company he founded, Ethereum, have been profiled in Fortune, The Wall Street Journal and Time Magazine.
Blyth-Cambridge Trust Scholarship winner: in 2015 Abelard student Malcolm Kennedy was one of only 22 Canadian recipients of this $150,000 scholarship. Malcolm is studying linguistics at Cambridge.
And just look at the track record of our graduating class from last June:
1 $65,000 Kluge Scholarship winner: an admission scholarship to Columbia, to study astrophysics and creative writing.
1 Schulich Leadership winner: out of only 25 $80,000 scholarships awarded to study in a STEM programme. He has enrolled at York to study Biomedical Science.
1 entered Wesleyan University’s liberal arts programme.
3 were accepted into U of T’s prestigious Vic One programme to study Political Science, French and History respectively. 2 of the 3 won the University of Toronto Scholars Program, awarded to the University’s most outstanding students on admission.
1 entered Waterloo’s Nanotechnology Engineering programme.
1 entered Waterloo’s Biotechnology programme.
1 entered Waterloo’s Chemical Engineering programme.
1 entered University of Toronto SC’s highly competitive Financial Management and accounting co-op (only ~180 students accepted).
1 entered McGill’s Faculty of Science on an entrance scholarship.
1 entered Queen’s Faculty of Science on an entrance scholarship.
1 entered U of T’s extremely competitive Honours and Conservatory programme in Theatre and Drama.
We can’t wait to see where our current students will go!
by Michelle Lefolii
We often hear two questions about the way that we teach math:
- why is it important for students to show their work?
- why are students sometimes given test questions requiring them to apply their skills to unfamiliar situations?
As you know, at Abelard we have our own philosophy of education. We have carefully developed our own pedagogical techniques over the years; these are based on what we have learned works best to prepare our students for the demands of university and life beyond.
What we are attempting to do is to train our students to think, and to be able to apply the knowledge and skills they acquire in creative and productive ways.
To know something is not necessarily evidence that you have thought about it, or even that you understand it. We can know things through memorization, and through intuition or instinct, and these are valid and important first steps. However, when we have come to terms with understanding the underlying structure of a concept, this knowledge becomes deeper, more useful and more reliable.
If we both know something and understand it, this helps us to communicate our knowledge to others, and to apply it in many different contexts. And these skills are invaluable both within the classroom and in the world at large.
It is also important for our students to be prepared for university, and how better can we prepare them than by training them to perform the same types of tasks in the same fashion as the universities will require? This is the aim of our curriculum in general, and of course is true of our mathematics courses.
Allow me to reinforce what I’ve just said by quoting from two texts written by university professors as guides to their first year students: the advice they give is equally pertinent to our own.
The following passages are extracted from “A Guide to Writing Mathematics”1 by Dr. Kevin P. Lee, which is given to first year students at UC Davis.
“The Greek word mathemas, from which we derive the word mathematics, embodies the notions of knowledge, cognition, understanding and perception. In the end, mathematics is about ideas. In math classes at the university level, the ideas and concepts encountered are more complex and sophisticated… (and) will include concepts which cannot be expressed using just equations and formulas.”
“If a mathematician wants to contribute to the greater body of mathematical knowledge, she must be able to communicate her ideas in a way which is comprehensible to others… When you use your mathematical knowledge in the future, you may be required to explain your thinking process to another person (like your boss, a co-worker, or an elected official), and it will be quite likely that this other person will know less math than you do. Learning how to communicate mathematical ideas clearly can help you advance in your career.”
“Putting an idea on paper requires careful thought and attention. Hence, mathematics which is written clearly and carefully is more likely to be correct. The process of writing will help you learn and retain the concepts which you will be exploring in your math class.”
“As you learn more math, being able to express mathematical ideas will become more important. It will no longer be sufficient just to be able to write down some final “answer”. There is a good reason why Herman Melville wrote Moby Dick as a novel and not as the single sentence:
The whale wins.
For this same reason, just writing down your final conclusions in an assignment will not be enough for a university math class… You will not be writing papers to demonstrate that you have done your homework. Rather, you will be writing to demonstrate how well you understand mathematical ideas and concepts. A list of calculations without any context or explanation demonstrates that you’ve spent some time doing computations; however, a list of calculations without any explanations omits ideas. The ideas are the mathematics. So a page without any writing or explanation contains no math.”
In a document titled “Math Survival Skills for First Year Students”2 compiled and edited by Geanina Tudose for the University of Toronto at Scarborough Math and Stats Help Centre, we find the following advice regarding problem solving for homework and tests:
“The higher the math class, the more types of problems… increasingly, you will tackle problems which require several steps to solve them. Break these problems down into smaller pieces and solve each piece.
- Problems testing memorization (drill)
- Problems testing skills (drill)
- Problems requiring application of skills to familiar situations (“template” problems)
- Problems requiring application of skills to unfamiliar situations (you develop a strategy for a new problem type)
- Problems requiring that you extend the skills or theory you know before applying them to an unfamiliar situation.
When you work problems on homework, write out complete solutions, as if you were taking a test. Don’t just scratch out a few lines and check the answer in the back of the book. If your answer is not right, rework the problem; don’t just do some mental gymnastics to convince yourself that you could get the correct answer. If you can’t get the answer, get help.
The practice you get doing homework and reviewing will make test problems easier to tackle.”
At Abelard, we do ask our students to work hard. We do expect them to get high marks. But these are not the end goals. We will consider our job well done only if we have encouraged our students to learn, to think, and to apply the fruits of their learning and thinking to a greater context.
Lee, Kevin P. “A Guide to Writing Mathematics.” Nina Amenta Homepage, http://web.cs.ucdavis.edu/~amenta/w10/writingman.pdf.
Tudose, Geanina. “Math Survival Skills for First Year Students.” Teaching and Learning Services, Math & Stats Help Centre, University of Scarborough, 2004, https://www.utsc.utoronto.ca/mslc/sites/utsc.utoronto.ca.mslc/files/resource-files/survival_guide.doc.
by Josiah Cohen
“Hey soul sister, I don’t really wanna miss a single thing you do-oo—tonight” I hummed as I opened the door to my apartment, hot pizza box in hand. Humming some more, I proceeded into the kitchen, cheeks rosy with the cold of winter; January had just turned into February, and I wasn’t sure my coat would make it through the rest of the snowy season.
“Mmm, pizza” said my roommate Brian. He cast his puppy-dog eyes look, but knowing that he’d already scarfed a pizza down, I merely shook my head and started to unpack my stuff.
“Aww, c’mon,” he whined. “I’d sell my soul for a piece of pizza!”
“Take it up with Lucifer, bud,” I replied. “I bought this fair and square, not gonna give some of it up, even if you somehow manage to sell your soul. Surprised you even have one to sell,” I added on in that roommate-banter manner, immediately dodging the friendly punch that I knew would be on its way. Yet the punch never came. I cracked open an eye. Brian was standing there, hands on his hips, clearly deep in thought. Thinking being such a strange occurrence for him, I opened my mouth in concern, only to close it at a disarming gesture. Subtlety and diplomacy were not his strong suits. He frowned in concentration. Then he shrugged, and grabbed for the pizza. Normal Brian was back. Unfortunately for him and his stomach, so were my excellent reflexes. Crowing in triumph, I returned to my room.
That night, I couldn’t sleep. My dreams—nightmares, really—kept me awake: rollercoaster rides that ended “poorly,” if poorly means the track becoming a river of fire; hikes where my feet seemed attracted to crevasses; and, most of all, Brian actually getting that slice of pizza.
* * *
“Yes, my lord Lucifer?”
“There is a soul to be claimed, the goal is the mastication, consumption, digestion, and eventually excretion of a slice of Domino’s pizza.”
“My, have standards fallen from the days of Faust. What man once desired was knowledge, now it is a slice of pizza. I believe menfolk be closer to hell than we, lord.”
“Mephistopheles, I don’t pay you to be a philosopher, I pay you to get stuff done, come hell or high water. Go!”
* * *
I awoke the next morning still tired, my tongue lolling, my legs splayed with feet hanging over the side of the bed. I crawled out of bed and toward the kitchen, hoping Brian might have spared some bacon (this was highly unlikely) or even a piece of cheese (this was also highly unlikely, though slightly likelier than the first possibility). I heard—was it conversation? Weird. Neither Brian nor I liked having guests over before noon, assuming we were even up by then. Who could he be conversing with?
I entered the kitchen and saw a terrible sight. Brian was sitting there, cool, composed, and collected… and eating a very familiar slice of pizza. My jaw dropped. A man, sitting on the far side of the table, rose, dressed in a dapper grey suit.
“Mephistopheles, MDP, at your service.”
“MDP for Master of Disappearing Pizzas or MD as in doctor person?”
“I am merely contracted to make sure Mr. Brian Evergreen here masticates, consumes, digests, and excretes one piece of your pizza.”
I checked the calendar again. Yep, still winter, not April Fools.
“This sucks. It was my pizza, after all.”
“Think’st thou that I, who saw the face of God and tasted the eternal joys of heaven, care for your claim of possession of the pizza?”
“That’s ironic, your selfishness, considering how you just dismissed my selfishness.”
The man grinned. With a twinkle in his eye, he said: “A philosopher, eh? Nice to meet another one. Pity you waste your time squabbling over pizza.”
“You never tried Domino’s?” Out of the corner of my eye, I saw Brian narrow his eyes in disbelief. Domino’s was a lifestyle to him—it was inconceivable that someone would never have tried it. “It’s fantastic. I need that slice back, Meph. Can I call you Meph? Thanks.”
He sneered. “Call me what you want, just don’t call me late for dinner, I believe is your saying. I, who have dined from the plates of Popes and courted Helen of Troy, I need no sampling of your pizza. Hell needs no cheese-tomato-bread combo.”
“You don’t get out much, eh Meph.”
“Of course not; Hell hath no limits, nor is circumscrib’d in one place; but where we are is hell, and where hell is, there must—”
“Yeah, yeah. Can you just get me back my pizza?”
His perfect smile widened even further. “Without a doubt. For a price.”
“What does my soul do for you?”
“I can trade it in for a baseball glove. No, you fool, it enlarges my kingdom.”
There was an Earth-shattering roar, and the floor beneath us cracked in half. Meph, Brian, and I were all sent heads over heels. When we finally crawled to our feet, we saw another man in a grey suit, looking very much like Mephistopheles, standing there.
“Oh, come on, Lucifer,” said Meph irritably. “Saying ‘my kingdom’ as opposed to ‘your kingdom’ only enhances the legend.”
“Who cares? But a baseball glove? Really? What use do we have for baseball down in hell? It’s freezing there! Go for a basketball or something, dear God, er, not-so-dear God.”
“Basketball is much better than baseball,” offered Brian, voicing one of his few opinions.
The new suit cast him an appreciative, appraising glance. “Agreed.” Turning back to Meph, his ire increased. “How about hockey equipment? That’s so damn expensive. And there’s even an NHL team named after us, whereas the baseball team that sorta kinda had our name removed it!”
“Hockey equipment is very expensive,” Brian added. I looked at him, amazed. This breadth of purchasing experience was quite unlike my roommate, even more so considering the fact that he had no soul.
“See, I like this guy!” Luke—was that his name? —was speaking to Meph. “Doing a better job than you, even without his MDP.”
“Master of Disappearing Pizzas is very fitting for Meph (Luke let out a snort of laughter). He took mine!”
“Not quite. MDP stands for Most Devilish Person. It’s the equivalent of a PhD in hell, or just getting any degree from Ohio State. Mephistopheles, er, Meph took your pizza?” Luke looked at me inquisitively. I hesitated, unsure whether to remind him that Brian had sold his soul. Meph just glared.
“Well… um, actually, Brian sold his soul for a piece of my pizza. Sorry bud.” Brian shrugged, stoic as ever. He reached for a chocolate bar.
“For a piece of pizza? Brilliant. Now that’s a fair trade, let me tell you. Much better than the old days, when stuffy theologians would sell their soul for knowledge and beauty. Ha!”
“Wow, foolish thing to do!” said Brian. If looks could kill, Meph would have chopped him up by now. I got the feeling that Meph was involved in that particular “stuffy theologian” case.
“I like this guy! But, you have sold your soul. Can’t get that back, I’m afraid. Or you could give me a slice, I’ll trade your soul back.”
Before Brian could leap to accept, I said quickly: “Nope, sorry man, pizza is pizza.” Brian shrugged, stoic as ever. He reached for a second chocolate bar.
“Fair enough. I respect a man’s right to eat pizza. I’ll make a compromise then. You get your pizza back. But Brian here comes with me down to hell and I’ll put him in the advanced MDP classes. Take it or—” here he was overcome by a fit of giggles—“I’ll take it! Ha! Get it? You take the deal or I’ll take his soul! Hahaha!”
I chuckled, if only to placate Luke. It was clear that he was in charge. I glanced over at Brian, only to be amazed yet again as I saw him laughing hysterically. He usually only laughed at toilet jokes.
“We’ll take it,” he said through his chortles. I looked at him in amazement. MDP classes? The thing was ludicrous! He shrugged, stoic as ever. He reached for a third chocolate bar.
Luke said, still giggling: “I’ll send up a man later to finalize the details. But now, Brian let’s go.” The two of them disappeared in a puff of smoke, leaving Mephistopheles and me alone in the kitchen.
I sighed. He looked at his shoed. I checked my watch. He adjusted the cuffs of his suit.
“Well…” he said, seeming a bit sad that the whole episode was ever. I got the feeling that he didn’t really mind the Earth so much. I felt bad for him, which I guess explains what I did next.
“Hey Meph,” I said. “Want to go get some pizza?”
By: Samantha Tristen
Politics. It’s all around us, in the media, in literature, in language, in everything we do. In fact, with the accessibility of information, it seems impossible to escape from it.
And yet, as a child, there is little opportunity to engage in politics. You are too young to vote, study law or global relations, and working in politics seems intangible. Abelard remedies this with its Model United Nations club, providing its grade 11 and 12 students with the unique opportunity to attend the National High School Model United Nations (NHSMUN) every second March.
In Autumn, Mr. Blair – Abelard’s classics, politics, English, and philosophy teacher, and devoted organizer of the Model UN club – announced that we would be representing Liechtenstein at NHSMUN in March. After doing our studies, we learned that Liechtenstein is a small, yet extraordinarily interesting country; it is a mere 160 square kilometres, yet is ranked second in terms of GDP per capita in the world. Furthermore, despite its petiteness, it is an active member within both the UN and Europe (although ineligible to join the European Union, due to its size). We became extremely well-acquainted with this European principality, even learning small yet riveting facts. For example, we learned that Liechtenstein and Uzbekistan are the only two doubly landlocked countries in the world.
Next, Mr. Blair helped us write our position papers, comprehensive research projects that discuss Liechtenstein’s stance on our topic, the history and current status of the issue, and the initiatives Liechtenstein has taken to resolve the topic. The topics covered many types of issues–social, health, environmental, and economic. Mr. Blair especially wanted us to be well-acquainted with the proposed actions and solutions for our topics, so we could be active participants and accurately represent Liechtenstein in New York.
After half a year of our weekly club meeting, we were off to midtown Manhattan for the conference. When we arrived at the Hilton, our small group felt even smaller amongst the 3,800 students participating in the conference, the largest attendance number in all 41 years of NSHMUN.
That evening came the opening ceremony. We managed to find splendid seats in the large, crowded ballroom, and were welcomed to the 41st NHSMUN conference. A few hours later, our committee sessions commenced.
Speaking on behalf on all Abelardians who attended the conference, the sessions were a fantastic experience. Much like Liechtenstein in the real UN, Abelard was a small, but active participant in the Model UN. Many of us were sponsor of resolutions (many of which were passed!), signatories for amendments, speakers during moderated caucuses, and professional and well-behaved delegates. We even got a special mention for our efficiency as pages.
On the other hand, it was frustrating to work with certain delegations. We all found an unfortunate commonality within the conference: many delegations failed to realistically represent their countries, but rather voiced opinions of developed countries, just using the names of their delegation. It was especially disheartening to notice how inactive the Canadian delegation was throughout the conference. However, everyone shared stories of working with the most responsible and professional participants, and being active and assiduous delegates themselves.
The conference concluded in the United Nations General Assembly itself. The waiting period was brutal; the weather was brumal, the ground, sodden. However, this was rendered insignificant upon entering the UN General Assembly. We were struck with a small stroke of misfortune when the school immediately in front of us filled up the last seats on the ground floor of the General Assembly. This, however, meant we would be in the balcony seats, and we obtained a coveted spot in the centre of the first-row balcony. The closing ceremony featured summaries of the activity in each committee, and speeches by various speakers. The one part that moved many of us was the letter Ban Ki-moon, the UN Secretary-General, wrote to the participants of NHSMUN 2015. Although he undoubtedly writes a nearly identical letter each year, we Abelardians were profoundly moved when he spoke that many future great world leaders were listening to his speech right now. Shortly after, the motion to close NHSMUN 2015 was passed, concluding our six-month journey to prepare for this moment.
Ms. Rossinsky, who accompanied us on the trip, ensured that we had a good experience in New York, both inside and outside the conference. She organized excursions to celebrated attractions in the Big Apple, such as the Museum of Modern Art, the American Museum of Natural History, the Met, as well as a walk all the way from our midtown hotel along Broadway to our restaurant in Greenwich Village, stopping by such distinguished chapters of New York’s attraction, including the Strand bookstore and the M&M store.
To those of you reading this who have not participated in the Model UN club, you may be under the impression that it is a great opportunity for people aspiring careers in law, international relations, or politics. This is an absolute truth, but is, by no means, the limit. The conference is also an opportune time to exercise one’s leadership and co-operation skills, practice public speaking and negotiation, gain first-hand insight into the mechanics of one of the most important political entities in today’s world, and meet new people. To junior or future Abelardians who are reading this, I strongly encourage you to take up this fantastic opportunity (and I wasn’t even instructed to write that!). To all those who participated this year, you should be immensely proud of yourselves for making us such a laudable delegation. I like to think that the prince of Liechtenstein, if he had seen us represent his country, would be tremendously proud of us.
In the French programme at Abelard, in addition to learning the language, students at all levels are encouraged to use their knowledge to compose short stories, poems and songs in French. Here is one sample, a “love letter” composed by Anna Nabutovsky, a grade-11 student in our core-French programme:
Mes très chères chaussures de pointe !
Je vous aime avec tout mon cœur. Je vous aime passionnément. Vous êtes mon monde, ma vie, et tout mon existence dépend de vous. Votre beauté est sans pareil, à l’intérieur aussi bien qu’à l’extérieur. Je sais que je ne suis pas toujours gentille avec vous, je vous blesse, je vous casse, et pour vous venger vous faites saigner mes orteils; mais quand je vous quitte vous êtes déchirées. Je ne veux pas vous jeter de la poudre aux yeux et je veux être tout à fait sincère avec vous: Je ne peux pas me changer, mais je veux que vous sachiez que malgré tout, je chérirai toujours notre amitié et le temps que nous avons passé ensemble. Je ne vous oublierai jamais. Vous serez toujours tout près de moi: dans mon cœur et dans mon placard.
Je vous aimerai toujours.