As a matter of fact, Portegies (now 36 years old) already experienced what it was like to be a teacher in his teenage years, as he taught at his swimming club. He has always enjoyed teaching, and as a TU/e student (Applied Mathematics and Applied Physics) he was already working in the classrooms as a student assistant. After obtaining his doctorate at New York University and completing his postdoc at the Max-Planck Institute in Leipzig, he returned to Eindhoven and became an Assistant Professor in Mathematics & Computer Science.
There, he is responsible for the Analysis I and Analysis II courses. These courses are very difficult, mainly because students have to develop a new skill: providing mathematical proofs. These are watertight arguments to show that a mathematical statement is true. It takes time and effort to master this skill and students often run into stumbling blocks along the way, such as fear of failure and motivation problems.
I hope to prevent students who are working on something difficult from getting distracted, for example by social media or thoughts that they ‘are not up to the task at all’
Portegies has made many changes to the courses, not because they were not up to par, “but because it’s beneficial to occasionally renew a course and adapt it to students’ experiences”. He appoints a feedback group for each series of lectures and talks to his students weekly about their experiences.
“I have made it clearer and more explicit to students what exactly is expected of them when they have to provide mathematical proofs. In order to do this, I created step-by-step plans and worked with others to develop the educational software Waterproof, which students can use to practice the process of writing proofs. I also wrote a course reader that replaces the textbook, and I often hear from students that they really appreciate that. But perhaps most importantly, I talk to students explicitly during the lectures about their experiences and struggles.”
Portegies is always willing to talk about how math “and all sorts of things outside of studies” can be equally tricky. “As a young person at university, you may find yourself reaching your limits for the first time. I like to tell students that it’s not a bad thing to spend an hour or two or more struggling with or even getting completely stuck on a mathematical proof; that those hours can even be considered time very well spent. It’s part of the learning process. Allow yourself to get stuck.” But how do you do that? How do you avoid dragging yourself down with the words of your inner critic? “What can be very helpful is to stay kind to yourself throughout all your struggles.” He has a motto that ties in well with this: “Mathematicians don’t need to prove themselves.”
As a teacher, how can he make sure the students keep up? When study associationGEWIS asked Portegies to prepare their members for their resits, he came up with analysis yoga. No, it does not involve doing exercises on a mat in the Student Sports Center; it is a serious meeting in a lecture hall where he attempts to help students develop kindness to themselves and allow themselves to get stuck. The crux is to stay focused while working on something difficult.
I like to tell students that it’s not a bad thing to spend an hour or two or more struggling with or even getting completely stuck on a mathematical proof; that those hours can even be considered time very well spent
“I try to get students to work on problems individually and make sure that their attention is brought back to the task at hand every time. I hope to prevent students who are working on something difficult from getting distracted, for example by social media or thoughts that they ‘are not up to the task at all’.” This way of teaching did not remain limited to GEWIS’ request; Portegies now uses it regularly.
Another thing he finds important is making the lectures, which are attended by hundreds of bachelor’s students at once, personal. “I do my best to learn as many names as possible and enjoy talking to students. I hope they can see that I like to be approached by them.”
Portegies does not have any tips for fellow teachers. “I find it difficult to assume the position that I would know how to do things. There are a lot of teachers who put a tremendous amount of effort into teaching, each with their own style, and that’s a good thing.” But it would be a positive development to include student wellbeing more explicitly in teaching, Portegies believes. “We would do well to talk with colleagues as well as students about to what extent and how we want to do that.”
Many of the topics referred to by Portegies above derive from Eastern philosophy. Ever since a colleague and friend of his in Leipzig gave him a book on Zen Buddhism, he has been thinking a lot about this. Loving kindness to yourself and others is called metta in this philosophy, and Portegies coined the term “Metta Mathematics”. “It’s the staple of what I try to do with the students. Being open, being warm, valuing others, and helping students realize that, regardless of academic achievement, they are just fine the way they are.”