For Asaf Hadari’s students, math becomes an ‘experience’
Students in Asaf Hadari’s mathematics classes are urged to work together to solve problems, and being excited and exhausted by mathematical challenges is all part of the experience. The winner of the 2014 Dylan Hixon ’88 Prize for Teaching Excellence in the Natural Sciences and Mathematics, Hadari says that mathematics can really only be learned by doing, and that failing is a natural part of the process.
Course: “Vector Calculus and Linear Algebra”
In his inaugural address, President Peter Salovey described students as one of the “treasures” of Yale. What excites you about teaching Yale undergraduates?
One thing that excites me about teaching Yale undergraduates is their capacity to surprise me, which is something that I see every year. I get answers from them that I wouldn’t have thought of or get a solution to a problem that I wouldn’t have expected to see from an undergraduate student. Or sometimes, I just get a question that’s out of far-left field, but it interests me to hear it from them.
Do you learn anything from your students?
I think one thing that happens in mathematics is that you get this transition from a concept being difficult or obtuse or arcane, to the same concept being obvious. The learning occurs when there’s this sort of transition from one to the other. Teaching students forces you to stay at that transitory level, where arcane things are turning into obvious things. It forces you to re-think them and re-understand them over and over again every year, and it allows you to really connect with those concepts once again.
What drew you to teaching, and what do you find rewarding about it?
Both of my parents are teachers in a teachers’ college; my brother’s a teacher; my sister’s a teacher; one of my grandmothers was a teacher; the other was a superintendent of counselors in the schools. Despite all that, I never had any interest in teaching. I was sort of the black sheep in the family. I was interested in science and math. The others in my family are all involved the arts. I went into mathematics for research reasons, and I think that teaching is something that I discovered was rewarding along the way. I wasn’t expecting to like it, and surprisingly, I enjoy it very much.
It’s the contact with people that I enjoy. My parents and my brother and sister are in the arts and into performing; they teach those kinds of things. Teaching math to some extent is a performance — when you are up at the board, you are performing, and you are interacting with people. That’s what’s fun about it.
Is there a teacher who particularly inspired you?
I’ve had all kinds of teachers who’ve had a lot of qualities that I value very much. I’ve had teachers who are very, very clear, and I’ve teachers who are very rigorous, and I’ve had teachers who have placed a lot of emphasis on intuition. They are all concepts that I value very much. But I had one teacher — his name is John Aronson — and he had sort of a different quality. He had this wicked little cackle, and this gleam in his eye, and he used to give us the most difficult assignments. They were great! I never had more fun than when I was doing his assignments. They were exploratory — you learned a lot of things; you confronted the assignment. He was obviously enjoying himself, giving these assignments, and he was enjoying himself in class. He’s the one who influenced me the most.
If there’s one thing you’d like your students to learn from you, what would that be?
I almost want to say that there’s not one thing that I want my students to learn but there a lot of things that I want my students to experience. I want my students to experience mathematics, to live through it. I want them to feel the almost existential terror that I think they feel when I give an assignment every week. And I want them to feel the sort of heart-wrenching frustration of being stuck on problems and trying them and trying them again and not being able to succeed in doing them, because I think that failure is a teaching experience.
I want them to feel the wild triumph of solving things, and I want them to feel excited at learning new things. I want them to feel the curiosity that they get from new topics. I want them to experience math alone and in groups: I want them to experience it socially. I want them to talk to each other about it. I want them to tell other people about it. I want them to be elated by it and exhausted by it and to live through it, because mathematics is something that you can’t really learn about. It’s something that you really have to do, something that you have to experience. By experiencing it and by doing it, you learn the ideas, and you learn the methods, and you learn how it’s done. That’s almost more important than the actual material itself because the material can be learned later on, and you’ll pick up the material by doing this.
What advice would you give a Yale undergraduate about his or her time here?
One piece of advice I would give to Yale undergraduates is to enjoy their time here. You’re heirs to a great wealth of knowledge. There’s a lot of things you could possibly learn here — a lot of exciting things that you would never have thought about, a lot of exciting things that you would never known existed. This is a great time in your life to take those things in. Take the interesting courses. Take as many as you want. Learn things. Don’t worry too much about grades. Don’t worry too much about all the difficulties inherent in it. Just take the time and inhale as much knowledge as you can.
Is there a memorable classroom experience as a teacher you’d like to share?
One thing I always remember is the first class I ever taught, and I was very nervous. During that class, I did two remarkable things: The first was that I cut myself on a piece of chalk, and the second was that I banged my finger on the board. I had two bleeding fingers, and I remember thinking, “This is a very terrible start to a teaching career. This is not going to go well.”