Teaching Philosophy of Gábor Lukács

Teaching is not a task, duty, or job, but a mission and a lifestyle. The mission starts at the beginning of the semester, on a beautiful sunny September or snowy January day, when during the first lecture, I introduce myself to a group of new students who become my students; from that first lecture, I am responsible for their academic progress and well-being. During the academic term, my day starts and ends with thinking about my past and upcoming lectures, and with checking my email to see if my students have any questions; I aim to answer emails from my students within a few hours, and often manage to do so within minutes. The mission of a teacher never ends: every semester brings new students.

I have been teaching mathematics since 1998. My teaching experience ranges from first-year introductory service courses where the students are not interested in mathematics at all, to advanced level courses for mathematics honours and graduate students. In spite of the differences between these two ends of the spectrum, there is one overarching principle that I always strive to follow: I want my students to feel that I am "on their side." I view the two Student's Teacher Recognition Awards that I received in 2010 and 2011 as an affirmation of my teaching philosophy.

Due to the (perhaps excessive) emphasis on evaluation, examination, and grades, students may perceive the relationship between the instructor and the class as an adversarial one. Such a perception undermines the trust that is required between the educator and the students in order to transfer knowledge effectively. Therefore, I consider it my primary task to convey to students that I care about them and their concerns, and that their academic success is of great import to me. I find the trust thus gained (which has to be gained every semester, in interaction with each and every class) a far more powerful tool to motivate students than any ex cathedra preaching.

In my experience, teaching and research are naturally interrelated, and I can hardly imagine doing one without the other. I take a great deal of pleasure not only in instructing advanced level courses, but also in the pedagogic challenge that teaching elementary level classes presents.

Introductory service courses

My role as a teacher is to create a rapport with my students that allows for effective communication of knowledge, development of their skills, and building confidence in their own abilities. The most important skill for teaching introductory courses is a sense of empathy and sympathy for students and their problems, and a desire to reach out and help. Each class has its own personality, and each class poses new challenges: learning students' names and earning their trust.

The majority of the students find introductory math uninteresting, because they are forced into these courses without adequate explanation or justification for having to take them. The material tends to be of the "plug the numbers into the formula" type, with few logical explanations, and often bears little relevance to the careers students intend to pursue. I overcome this challenge by relating the material to real life examples taken from a variety of areas, such as music, cartography, or aviation, even if, technically speaking, it is not part of the syllabus.

Students often find math difficult and scary because of their past experiences. My goal is to allay these fears, and associate math with positive experiences, such as funny short films (1-2 minutes), which I sometimes show at the beginning or the end of my lectures, or amusing anecdotes, which I incorporate into my classes. Creating a relaxed, informal, and positive classroom atmosphere helps not only in keeping up attendance, but also in making students more comfortable to ask questions.

For me, teaching is a dialogue, not a monologue. Although I prepare detailed notes for my lectures, I use them only as a guide and backup. Regardless of the size of the class, I solicit and answer questions, and I welcome digressions that help clarify past lectures or fill gaps in students' academic background.

Teaching introductory service courses, such as first-year linear algebra and calculus, can be challenging not only because of the lack of interest in the material on the part of the audience, but also due to the grossly inadequate mathematical background of the students. The latter is a particularly severe problem at post-secondary institutions that admit students without screening their mathematical skills and guiding them to courses that suit their levels based on placement tests. As a result, it is not uncommon to encounter students in introductory courses who have problems with fractions. Such students often have good learning attitudes, but their problems with mathematics date back to their elementary school years. I find it particularly rewarding to help such students achieve academic success, because I feel that I am able to make a difference in their lives.

Mathematics Honours courses

Teaching advanced mathematics courses is my main opportunity to create and shape the next generation of mathematicians. It also allows me to recruit students for summer research projects and the graduate program. My role in relation to such students is to educate them on how to use their talent, how to think correctly, and of course, how to express their mathematical thoughts in a sound and rigorous way. My goal in such courses is not only to teach the material, but also to be a guide to correct mathematical thinking and scientific communication, with an emphasis on clear arguments and logical structure.

I have extremely high expectations for honours students. They are smart—in fact, very smart, and often brilliant—and so I provide ample coursework that creates a real challenge for them. It is important to me that honours students feel that they have earned their mark, and that a good mark, or even verbal praise from me, will be meaningful to them.

The rule of "do not abandon your students" applies equally to honours students. While I encourage them to work on the assigned problems by themselves, I am always available to discuss their—possibly incorrect—ideas about the problems. After each assignment, I hold a problem session that often runs into the weekend, where I discuss most of the questions and their solutions with my class.

Although it takes a month or so for students to get used to this level of expectation, it is almost guaranteed to result in an A+ grade at the end of the academic year, and certainly a superb end product as far as the students' skills are concerned.