Borgersen's Rude Awakening
He describes taking math courses in university as a rude awakening. “In my experience, most things taught through primary and secondary school is something to the effect of ‘learn this now, because you’ll need it later.’ But later never seems to come, so students understandably lose interest. “Arriving in university, students are first asked to do more math for the sake of math, and then are asked to solve more applied problems. But these are generally the dreaded ‘word problems’ which they find very difficult. It seems to be a contradiction: students hate the ‘theoreticalness’ of math, but dread the complexity of word problems that apply math to the real world.”
Using Engaging Course Websites, a Blog and Social Media to Help Students
Borgersen uses all the resources at his disposal to enable students in their coursework, including online practice tests, blogs and even social media. His online syllabus is a many-faceted stepping stone to mathematics resources around the world. There are links to online worksheets, answers to old exams and bonus assignments. He’s set up a web page for each class he teaches that gives the course outline, assignment due dates, problem solving hints, special announcements, office hours and a special departmental “Honesty Declaration Form” that must be printed off and handed in with each assignment. There is also a link to a wiki for one course (developed by mathematics Prof. Michael Doob): an internal web-based encyclopedic guide to material covered, such as definitions, equations and visual representations.
Using Skype to Help Students
Still need more help? Borgersen has posted regular office hours and invites students to phone or email him if they have any questions. He even invites students to use Skype if they need some personal assistance. Despite his truly “open door” policy (virtual and otherwise), Borgersen notes: “I only get maybe half a dozen [Skype] calls per term, and that’s in a term teaching nearly 500 students; although the students that use it like it. In the end, it gives me reassurance knowing that students have little excuse for not getting help with the content, since I am making myself so available.”
Borgersen is convinced that accessibility and availability are the keys to effective learning and instruction. “At the beginning of every term, I do a quick survey asking how many of the students have a laptop or netbook with a built-in camera, and how many of them use Skype already. Both questions receive an affirmative from a very large percentage of the class, so I know they are able to reach out for help if they need to do so.”
He notes that future teaching will look very different from traditional instruction: “I’m looking for a way to make it much easier for students to learn, using technology and resources that were not available previously. For example, I could have a video chat where they don’t need to login and don’t need a program, but just do it in their browser: click a button and they’re talking to me. I’m hoping this may produce great results.”
A true educational pioneer, Borgersen continues to test the waters of educational technology. He says: “I just experiment and try things out, not afraid to fail, but rather, through failure I learn something more about the way the world works and the way my students think.”
Borgersen’s Philosophy in Helping Students Learn
As if multiple web pages and classroom teaching wasn’t enough, there are Borgersen’s blogs themselves. They include his ruminations of all things mathematical and also introspective posts on educational technology and best practices of teaching. His posts allow him to speculate on the nature of reality, current issues in the news and the philosophy of learning. As an example, in response to a question posed to him on Facebook, Borgersen posted the exchange in his personal blog. The original query was whether professors should: “cater to the needs and learning styles of their students, or if students just need to suck it up and learn no matter how the professor teaches.” He replied at length, and summarized his viewpoint: “When students work hard and show a desire and interest in the content, the professor is under a moral obligation to give them the good that is due them.”
He added: “A teacher’s job is to teach. A student (a.k.a. learner)’s job is to learn. That’s why it makes sense to fire a teacher who doesn’t teach, and fail a student who doesn’t learn—rather than fail a student whose teacher doesn’t teach, or fire a teacher when his or her students don’t learn. However, good teachers will strive to help their students in any way they can, whether it be out of empathy, out of an ethical imperative, out of a moral imperative or something else.”
Use of Humour to Entertain Students
Borgersen has tried to help students overcome a fear or aversion to math by trying to be more approachable, more accessible and yes, even more entertaining than many other instructors.
When asked the secret to teaching students in a way that makes them more interested in math, he replies: “I wish I knew. Many people smarter than I have tried to answer that question. For me, I find that a certain amount of ‘entertainment’ is necessary to hold students’ attention. I recognize that I am ‘putting on a show.’”
When he first started teaching, getting through to students was a challenge, because Borgersen says he is “a quiet guy; very much an introvert.” But over the years he learned to get “outside himself” and now is “more like the teacher they need me to be.” He explains: “I have a collection of jokes that I pull from and reuse on a yearly sometimes even weekly basis. Many are lame intentionally and some not intentionally but the point is to entertain, and they do their job.”
What kind of jokes does one use in a math class?
“A gag I use often is a reference to my horrible memory. I’ll tell them, ‘I have a horrible memory. Have I told you that before? I can’t remember...’ I say it often enough about eight or nine times per term that it gets a laugh from them whenever I do.”
There’s also the ancient one-liner: “There are three kinds of people in the world: those who can count, and those who can’t.” Borgersen uses a version of that one, adapted for advanced math: “There are 10 types of people: those who understand binary and those who don’t.” (If you don’t get that one, don’t worry about it. It’s a geek thing.)
He continues: “One joke that is specific to calculus classes is when I reference the boy in the movie 28 Weeks Later who has two different eye colours. I note that his being in the room would make ‘the function that maps everyone in the room to their eye colour’ no longer a function!”
Pah-DUM-pum! Maybe you had to be there. Maybe it was his growing up in the south part of Winnipeg.
Borgersen’s Educational Journey
Borgersen graduated from College St. Norbert Collegiate in 2000, then did a joint undergraduate degree at the University of Manitoba in the joint math and computer science program, with the co-op option. Graduating in 2004, he started his masters program and completed it in 2008. He’s been teaching ever since, and has a typical course load today of six lecture sections each calendar year.
Passion for Mathematics
With his frenetic use of resources and passionate view of his field, it’s obvious Borgersen sincerely enjoys math.
“For me, math is all about truth,” he explains. “I love how there’s no in-between in math; everything is true or false. If 1000 people think one way, but the truth is the other way, the truth is the truth. It’s very powerful."
“I love communicating truth to people. I hope that in every interaction I have with people, I guide them towards a more correct understanding of how the universe works. I constantly strive to move myself more in line with how the universe truly works, and with the truths in the universe.”
So, rather than the truth being “out there,” as one TV show would insist, Borgersen finds truth in the preciseness and elegance of mathematics. He explains: “I want to be like the Bereans described in the Bible, in Acts 17, who were said to have ‘noble character’ because they didn’t just take what they were told at face value, but rather searched out to determine if what they were taught was true.”
With such a strong desire to educate students in the universal truths and elegant solutions demonstrated through mathematics, Borgersen may be one of the last truly noble lecturer/philosophers. At least, one of the few ones on Skype. And again, what’s the secret to learning math?
Borgersen says it’s like the old joke about the tourist who gets on a bus in New York and asks the driver: “How do I get to Carnegie Hall?” The bus driver replies: “Practice!”