Benjamin Meco recognised for his teaching – sees mathematics as a social discipline

UTN’s Pedagogical Prize is awarded to a teacher who has shown exceptional pedagogical skill, commitment and innovation in teaching. That the prize this year goes to a PhD student is unusual and has occurred only three times since the prize was first awarded in 2002.

Nevertheless, says Director of Studies Inger Sigstam, it is not surprising that this year’s prize goes to Benjamin Meco. While PhD students usually teach primarily as tutorial leaders, Benjamin was already given the opportunity during his third year to take on full lecturing responsibility for a course – an assignment he carried out with great success and has continued to develop.

“Benjamin has truly distinguished himself through his strong interest in teaching and through the very positive feedback he has received from students,” says Inger Sigstam.

Benjamin himself was both surprised and pleased when he received the news.

“I was surprised, the prize was not something that I expected nor had thought about. Then I was very happy, it is always great to see your work appreciated, especially when it is something that you have invested a lot of time an energy into.”

Was there anything in the citation that particularly touched you?

"I think what touched me most is that the students see me as thoughtful and that they feel that the classroom is open and welcoming. To me, mathematics is a social discipline and I have experienced my most memorable moments with the subject together with others. I hope that I contribute to others having similar experiences."

In the citation, you are described as a teacher who creates an open and welcoming atmosphere where all questions are encouraged. Is that something you work on actively?

"I would say that I work actively with this. Of course I hope that my personality contributes, but we all have better and worse days, sometimes I am tired or my mood is down and the same can be said for the students. I don't think that there is anything specific that can be done to achieve this, rather that many small things contribute to such an atmosphere."

"For example, I look for things in the course material that I myself find interesting, then my feelings for the subject become more genuine and I think that they can then rub off. I try to take the students' questions seriously and show appreciation for their questions. I look for interesting things in the course related to their questions and in general I try to engage the students with the material and the lectures. I believe that if one does not view teaching as a collection of material to cover, but as something one wishes the students experience, then one does many such things automatically."

Which courses have you taught over the past year?

"I have been a teaching assistant for Algebra 1 and I have been fortunate to lecture in the course Real analysis. Analysis is a subject I enjoy a lot, so I am very happy to have had this opportunity."

What does a course in real analysis offer – and which students benefit most from it?

"I guess if you are a student of mathematics the answer is mostly that so much other mathematics builds on this course. Most likely I am a bit biased, but to a student of mathematics I would say that not taking a course in real analysis is to inhibit oneself mathematically."

"However there are also some engineers and bachelor students in physics for example that are interested in this course. To them, I think a course in real analysis can be extremely beneficial, because it is a course where one is trained to argue. Very roughly speaking, Real analysis is a course in calculus but with a lot more rigor. However the point of this course is not just to put calculus on a rigorous foundation, but also to introduce rigorous mathematical thinking to the students."

"Common objections I hear are "as engineers we use calculus to calculate, not to prove something mathematically, there is no point for us to suffer through this", and "in real life nothing is as clear cut as in pure mathematics courses, they do not apply because reality is much messier". I empathize with this, but I think that this makes it even more important to study a course like Real analysis, precisely because it traines one to argue rigorously in a situation where things are clear cut and there are no real world distractions."

"I think an analogy with swimming conveys this feeling well: if you cannot swim in the calm waters that is Real analysis, how do you think you will fare in the open sea that is real life?"

What would you like to say to students who feel that they are struggling at a disadvantage in mathematics?

"I think it is difficult to say something that applies to everyone. First and foremost I think one needs to ask what the reason for being at a disadvantage is. Sometimes we compare ourselves unfairly with others, sometimes we forget how far we have already come. Often, I think we should be kinder to ourselves."

"That being said, sometimes we are unhappy with our performance and I do not think there is anything wrong with that, as long as we do not become displeased with ourselves. When feeling that we have not reached our expectations I think it is important to ask ourselves what we need in order to grow. Sometimes the material one is working with is too difficult, then maybe one should take a step back and study the foundations. Sometimes there is no time, then maybe mathematics or something else should be put on hold, sometimes one does not have energy, then maybe one should rest. Sometimes the expectations are unreasonable and then maybe one should change them."

"All of this is individual, to give yourself what you need, self-knowledge is paramount."

Students emphasise that you are responsive to feedback and adapt your teaching in the moment. How do you view the relationship between teacher and students in the learning process?

"This could have to do with how I lecture. In advance of every lecture, I have a rough plan for what I would like to explain, what ideas I would like to display and then how all of this is related. The details are not always completely worked out. I think this works well because students usually have questions that encourage you to go on a tangent, sometimes you notice that you need to slow down and add details and sometimes you notice that fewer details would be better. In this way, I think the lectures naturally form into something that is closer to what the students need."

"By not being completely prepared for all the details during the lectures, I think the students see how ideas can emerge in an organic way, instead of just seeing a polished final product. They get to see that even people that know the subject well make mistakes, are wrong and have mental lapses here and there, without any of this having to be dramatic. I don't think the lecturer should be a person that flawlessly dictates the course material to the students, for this they have the learning materials. I view the teacher as a person from which the students can draw inspiration when they search for their own way to navigate the subject."

What do you hope students take with them from your courses, even if they do not continue working with mathematics?

"To have an intuitive sense of something, and then to put it into words and explain it to somebody else is a skill that can be trained. Studying mathematics, I think that at some point this becomes what one invests the majority of ones time into. Real analysis, the course that I have been teaching, is to many students the first course where this much weight is placed on translating ones gut feeling to something concrete. Throughout the course, I try to have plenty of slightly vague discussions that we later flesh out with rigorous mathematical language and I try to show that intuition can often be embodied, and in different ways for different purposes. I hope that the students eventually feel that their rational side and their intuition are not two separate tools with different areas of application, but that these can and should to be applied together to enhance their thinking in different ways."

Is there anything from your role as a researcher that has helped you in your teaching – or vice versa?

"I think that preparing presentations about my research has helped me a lot. My advisor has been very helpful in this regard and I have learned a lot about how to effectively communicate an idea from her. I also believe that when specializing in a subject we often forget how difficult it was in the beginning. Like many others, I often struggle to remind myself of what is difficult and not for the students."

Is there a particular moment in your teaching that has stayed with you?

"The first time I was going to be responsible for a course all on my own I was very nervous. It was unclear to me exactly what I had to keep in mind administratively speaking, how I should behave towards the students and so on. Then after a couple of lectures I started to realize that I mostly enjoyed the time I spent on teaching. I don't find it boring to prepare and teach lectures, or to put together exams, or to interact with students, or to organize the course's Studium page. At some point I realized that teaching was what I looked forward to the most in my work."