Drs. Frank Sottile and Sarah Witherspoon, while on sabbatical at U of T, brought their son Sam to the Abelard School. We were very touched to receive this card from them, as the year comes to a close. We will miss Sam, and wish him well as he returns home!
Reflections
Joseph Sproule’s 20th Reunion Speech
At Abelard’s 20th Reunion celebration on May 26, 2017, our alumnus Joseph Sproule gave a touching and eloquent speech — he generously agreed to share it on our blog:
Good evening, everyone. It is with great pleasure that I join you all today to celebrate the twentieth anniversary of the Abelard School.
I had the good fortune to attend Abelard in its first three years, a formative era that may be thought of as a kind of Abelardian Paleozoic, during which the school emerged like some glistening scholastic tetrapod from the steaming jungles and verdant swamps of the late 1990s. Some of you will remember those days well; while others were still young tykes, as yet unaware that you would one day tread the halls of our beloved school. Either way, whether by means of memory or imagination, I ask that you now cast your minds back through the mists of time to the hazy summer of 1997…
Allow me to set the scene: The first Harry Potter novel has just been published; Backstreet’s Back is the number one album in the world; Titanic is pulling in billions at the box office; and, in an old bank building across from an abandoned train station at Yonge and Summerhill, four teachers are in the process of opening a new school.
Who are these intrepid educators? None other, of course, than Abelard’s founders – Michelle Lefolii, Alina Rossinsky, Shai Maharaj, and Brian Blair – a potent pedagogical quadrumvirate brought together by shared vision and a passion for teaching. That vision and passion – as well as a great deal of hard work and dedication over the subsequent two decades – has borne rich fruit: the hundreds of students who have benefitted from Abelard’s unique approach to education; the community that has grown up around the school; and, of course, the Abelard School itself, which continues to go from strength to strength.
But permit me to speak for a moment, not of the Abelard of today – a school coming into its maturity with an established reputation for excellence and a burgeoning legion of alumni – but of those early years at Yonge and Summerhill. It was a time of new beginnings, of infectious imagination, dynamism, and energy. The shape of the school was still being moulded into its now familiar form, as teachers and students came together to participate in a wonderful academic experiment. But, even then, it was already so very Abelardian: brilliant, fun, challenging, and, let’s be honest, at times more than a little bit quirky. Whether reading French literature, learning the functions of the organelles, translating Attic Greek, or playing cards at the picnic table in the school parking lot, I remember there being a vibrant energy in the air. It was more than just the excitement of attending a new institution; it was the sense that we were taking part in the creation of a new community, bearing witness to an idea being transformed by inspired teachers and enthusiastic students into a reality.
Over the years, that idea has taken on a life of its own, and there have been many twists and turns in the Abelard story. Staff and students have come and gone; the school has moved location twice and will soon do so again; new courses have been offered and curricula have changed. But Abelard has remained Abelard, strengthened and sustained by a network of past and present teachers, students, board members, parents, and other friends of the school. The spark that was lit in the summer of 1997 has grown into a sacred flame, lovingly tended for the past two decades by an ever-growing number of people with ties the school. Indeed, one could argue that those people are the school, and the friendship and support that we offer one another is one of Abelard’s most precious legacies. The Abelard School’s gift to its alumni is therefore much more than a rich education and a rigorous intellectual preparation for later life; it is also the circle of friends with whom we continue on our journey long after our high school years are behind us.
Today, seventeen years after I graduated, I still feel as much an Abelardian as ever. I sit on the school’s board, rarely miss an alumni event, and keep in regular touch with my many high school friends. I also feel connected to the school in less tangible but equally important ways. As a doctoral candidate here at the University of Toronto, I’m constantly aware of Abelard’s lingering influence on both my conduct as a student and as a teacher – indeed, on my approach to learning and my attitude to life more broadly. It is a reminder that the Abelardian education not only imparts information but also fosters a truly scholarly ethos – a lifelong commitment to intellectual curiosity – both to seeking knowledge and to sharing it and using it for good. I am certain that in all of your varied and multifaceted lives, you too can identify threads that link you back to Abelard in one way or another.
I would therefore like to finish with an expression of thanks: to the school’s founders for making their dream a reality that has blessed us all; and to the many teachers, alumni, administrators, and friends whose unwavering dedication has strengthened and enriched the school over the years. As the Abelard School prepares to enter a new era in its expanded Church Street premises, I think there is good reason for confidence; the past twenty years have seen the school’s roots grow deep and its foundations strong; and the ongoing support of the Abelard community will no doubt ensure that the school continues to reach ever greater heights in the years to come.
The Extended Community
If you read the promotional materials for smaller schools, you’ll see things like personalized learning and small class sizes listed among the advantages of attending academies like ours. While these are absolutely important considerations for people looking into a school, we like our small classes because our tight-knit educational environment allows us to foster relationships that form a much larger extended community. We recently spoke with some of our alumni who still frequent Abelard as volunteer tutors to find out why they keep coming back to our school. For them, it seems, it is all about the relationships too.
Noa Magen, a 2015 alumna who now studies Cognitive Science at the University of Toronto, tutors French at Abelard. She says that Mr. Blair’s philosophy class inspired her interest in how we know things, and that he is a big reason that she is in her current field of study. She is tutoring French in part to keep up skills and in part because it feels nice to help the next generation; she knows how rigorous the Abelard program can be–she recounts having already read most of the books assigned in her first-year university literature courses in our grade 10 English class–and is happy to pay forward the support she received while a student here.
Samantha Tristen, another 2015 alumna now studying History at U of T, also tutors French at Abelard. She echoes Noa’s feelings about the kind of support she received at our school. In addition to gaining a lot from Abelard’s advanced curriculum, she says that her teachers knew her well enough to recommend books and extension opportunities that suited her interests specifically. She continues to visit Abelard as a tutor because she likes to help and, like Noa, she wants to keep up her skills. She has also found that investing in interpersonal relationships has resulted in new opportunities: Mr. Young invites Sam back to helm two of his history classes each year.
A 2016 graduate, Maxim Vorobyov visits us regularly as a math tutor. Unlike Sam and Noa who attended Abelard for grades 9-12, Maxim joined us halfway through his highschool journey in grade 11. He likes tutoring math because it keeps him connected with the foundational skills that he still uses in University, and equally because he doesn’t want to lose touch with the school. One of the things that most stands out for him about his Abelard experience is that he, like Sam, felt heard by his teachers. Dissenting opinions, as long as they were well researched and well articulated, were treated with respect.
We love hearing from and working with our alumni. Particularly now, as we celebrate the school’s 20th anniversary, it is extremely valuable to us that we celebrate the the connections that make up the extended Abelard community.
On Computer-Free Classrooms
Computers today are everywhere, and it is understandable that many students and their parents feel with some urgency that technology needs to be part of the classroom. At Abelard, we do believe that technology has a place (in our computer science class, for one), but we continue to resist allowing students to use technology in most classes for several very important reasons.
At a practical level, when students’ use of technology is not being structured by a teacher’s assignment and supervision, it can be distracting. Although we certainly see students preoccupied by phones every once in a while at Abelard, it isn’t only our observation that makes us wary of the free-for-all use of computers. A study published last summer in the journal Labour Economics looked at how unstructured technology use impacted test scores and found that, “highly multipurpose technology, such as mobile phones, can have a negative impact on productivity through distraction” (Beland and Murphy). This distraction, they found, was reflected in poorer results on test scores across all grades. A distracted student is less successful.
Further, and perhaps even more importantly, our focus at Abelard is University preparation. At the core of University studies is the ability to think deeply and critically, and there is evidence that students who take notes by hand develop these skills better than those who use computers for note-taking. In a paper published in Psychological Science, Pam Mueller and Daniel Oppenheimer study whether digital note-takers perform better than their long-handed counterparts and unequivocally land on the side of students who take notes by hand. Their primary observation is that computers facilitate a verbatim transcription of notes, while people who take notes by hand organically synthesize and summarize ideas. This in-situ mental processing develops precisely the critical thinking tools that our students will rely on in University.
There are further reasons for limiting technology use in the classroom that have to do with social development, learning focus and attention, and improved work ethic, but for us these are secondary to the measurable beneficial effects of an old-fashioned classroom on our students’ success both at Abelard and in the future.
Works Cited
Beland, Louis-Philippe and Richard Murphy. “Ill Communication: Technology, Distraction & Student Performance.” Labour Economics, Vol.41, 2016, pp. 61-76.
Mueller, Pam A. and Daniel M. Oppenheimer. “The Pen is Mightier than the Keyboard: Advantages of Longhand over Laptop Note Taking.” Psychological Science, Vol. 25, No. 6, 2014.
The Model UN Trip – A Student’s Perspective
We asked one of our grade 12 students to share her account of the school’s trip to participate in the Model UN. This is Lili Coelho’s story.
*****
Last month, a group of Abelard’s politics students traveled to New York City for a three-day model UN conference. It was a short yet hectic trip; every moment was occupied, and the pace never slowed. It was something that many people never have the opportunity to experience, and as a grade 12 student, I’m infinitely glad that I did.
Our trip began with a bumpy morning flight and a day of sightseeing. While I had been to New York before, I’d never spent much time in the city—full of iconic landmarks and vibrant activity, it was quite spectacular. We walked through Times Square to Strand Bookstore, then to Greenwich village for a cozy Italian dinner. Our group spent the first day together, enjoying each other’s company, before we were launched into the conference proper. It was truly a great way to begin the trip—surrounded by friends, enjoying the sights.
We visited the Natural History Museum on the morning of our second day. I think I speak on behalf of everyone when I say that the dinosaur skeletons and the habitat displays made us feel like kids again, fascinated by the natural world. It was a snowy day on the Upper West Side, but after the museum we leisurely strolled back to the Hilton, discovering shopping centers and incredible cafés along the way. Back at the hotel, it was finally time to prepare for the opening ceremonies at the United Nations Headquarters itself—we put on our best clothes and made our way out.
I wasn’t anticipating a wait of over an hour in below-zero temperatures, but that’s what we got. Airport-level security slowed the line down to a crawl, and we ended up huddled together for warmth beneath the unforgiving wind by the time it was our turn to enter. No matter how painful the wait was, though, it was worth it. As I walked through the halls of the UN to the General Assembly, all I was wondering was “whose footsteps am I following?”
The General Assembly itself was more grandiose than the pictures had made it seem. While we all wished that we could have had the closing ceremonies there so we could actually vote on resolutions, I think being there really got us all into the Model UN mindset. The keynote speaker was polarizing, so I won’t elaborate on that—but it was incredible just to be there.
That night, the conference finally began. The first committee session was a haze of networking, note-writing, and figuring out how everything worked. I think a lot of us felt out of place—many of the American schools in attendance had been to multiple other conferences in the past few months, and we had to pick up a lot of knowledge as we went along. However, over the course of the session I became not only more comfortable, but confident enough in my position on the issue being discussed to go up and speak in front of approximately three hundred people—as someone who has always been extremely anxious in public speaking situations, that was huge for me. The session lasted until midnight, and my partner and I left feeling satisfied and excited for the next day.
I think that, over the course of four more sessions, we all surprised ourselves. Unfortunately, I wasn’t able to hear any of my classmates (apart from Randa, my committee partner) speak in their respective committees, and the next few days were so hectic that there was barely time to talk to each other. I went up to speak a
few more times, and we ended up writing an entire clause in the working paper that eventually became a resolution. Randa and I made friends and we made enemies as we became more involved in the process than we ever thought we would be. At the end of committee sessions, when our resolution passed, we were exhausted, but happy and satisfied with what we had accomplished.
On our final night, most of us ended up leaving the Delegate Dance (which was far from an Abelard-style party) to spend some quality time together in one of the hotel rooms. We shared our experiences from the conference and reflected on them. While we all accomplished different things in our committees, all of us enjoyed the experience.
Our final day was much like our first. After the closing ceremonies, we visited the Metropolitan Museum of Art, then walked around the city for the final hour before driving back to the airport. And that was the end of the trip.
Overall, I’m incredibly glad to have participated in NHSMUN. Those of us who went are, of course, extremely grateful to Mr. Blair and Mme. Rossinsky, without whom the trip wouldn’t have been possible. It’s strange to think that in just a couple months, I’ll have graduated—the end of an era is approaching. It’s experiences like this that’ll make me remember my last year of high school fondly years down the road. Thank you to everyone who made it possible.
Athletics at Abelard
We wrapped up February with a school trip to Mount St. Louis Moonstone, a ski resort just North of Barrie. Many of our students are accomplished skiers, but even novices were confidently completing runs by the time we left the slopes. While athletics are not a major focus at Abelard, we do value and applaud students’ sporting efforts. Health Canada recommends that high school students get 60 minutes of daily physical activity, but reports that only one in eight actually get the exercise they need (Picard).
We recently sat down with some of the school’s more ambitious athletes to get a sense of why they dedicate so much of their ‘down’ time to exercise, and how they balance the rigours of an Abelard education with hours of extra-curricular training. Lavan Balendran is an avid runner and keen swimmer, while Carmina Cornacchia is a competitive swimmer who is up and training most mornings before many of her classmates are even awake. Elias Zaarour, now in his last year at Abelard, has recently transitioned from being a nationally-ranked speed skater to a crossfit athlete. Emma Adamson-DeLuca and Milena Loginova are both avid ballet dancers who train several evenings a week and most Saturdays. Roberta Vakruchev pursues several sports, and Jackson Levine is into competitive Olympic weight lifting.
When asked why they do what they do, the overwhelming consensus was that time spent exercising helped relieve stress and achieve a sense of personal balance. Carmina, Lavan, and Roberta, in particular, reported feeling focused and in-the-moment when pursuing their sport of choice; while training, their everyday worries were put aside because the physical activity demanded their full attention. Our athletes also reflected on the sense of accomplishment they feel when they achieve a goal, whether that ambition is beating a personal best or getting through the next class or training session. Milena noted that even though she only started dancing a few years ago, every newly acquired skill pushes her to keep going. Although it might seem counterintuitive, our athletes all also agreed that the time they dedicated to training ultimately helped their academic performance. Emma explained that with a limited number of hours to accomplish school work, she is less inclined to procrastinate and so is readily able to complete her assignments. Elias and Jackson spoke at length about how competitive sport taught them how to set goals and how to productively deal with failure.
There is considerable research that backs up what our students report – in addition to gains in physical health, regular exercise helps reduce stress and improve mental health as well (“Physical Activity”). As the weather turns and we return to warmer and longer days, we should all be looking for ways to get a little more exercise.
Works Cited:
“Physical Activity.” Health Canada. http://www.hc-sc.gc.ca/hl-vs/physactiv/index-eng.php
Picard, Andrew. “Only 1 in 8 Canadian kids get enough exercise, report says.” The Globe and Mail. 23 August 2012. http://www.theglobeandmail.com/life/health-and-fitness/only-1-in-8-canadian-kids-get-enough-exercise-report-says/article4189297/
A Night at the Opera
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.
Lauren Segal as the Third Lady, Emily D’Angelo as the Second Lady, Aviva Fortunata as the First Lady and Andrew Haji as Tamino in the Canadian Opera Company’s production of The Magic Flute, 2017, photo: Michael Cooper
Andrew Haji as Tamino in the Canadian Opera Company’s production of The Magic Flute, 2017, photo Michael Cooper
Ambur Braid as the Queen of the Night in the Canadian Opera Company’s production of The Magic Flute, 2017, photo: Gary Beechey
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.
Works Cited
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.
Why We Study 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.
Works Cited
Steinbeck, John. East of Eden. Penguin, 1980.
Looking Forward by Looking Back
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!
Learning by showing your work
by Michelle Lefolii
Principal
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.
Problem types:
- 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.
Works Cited
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.
The Abelard School 