Recorded maths lectures on video — now she's lecturer of the year

It was a rainy morning. Elisenda Feliu — bike helmet perched on her head, soaked trousers — stepped into an office on North Campus. She had been summoned to a meeting. But instead of being greeted by filter coffee and the day’s agenda, colleagues and managers surrounded her with cameras and congratulations. She had been awarded this year’s ‘Harald’, the University of Copenhagen’s teaching award.

Elisenda Feliu was bewildered. »I didn’t even know I’d been nominated,« she said.

The Harald is given to teaching staff who have made an extraordinary contribution. Any student can submit a nomination.

Elisenda Feliu is a professor of mathematics, a head of research at the Department of Mathematical Sciences, and teaches several courses at the University of Copenhagen (UCPH). One of these is the introductory course Mathematics/Statistics — a first-year course in mathematics and statistics for biology students. Feliu teaches the mathematics part, introducing future biologists to mathematical models and methods. It was this course that earned her the prize.

»I was in shock. I thought it must be a mistake. I know the students are happy, but I hadn’t invented anything special. I’m just doing regular teaching,« she said when the University Post turned up to meet this year’s teaching award winner in her office on the fourth floor of a grey concrete North Campus building.

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Box of Japanese chalk

The office is unremarkable: height-adjustable desk, a collage of pictures from a ride on an old roller coaster, and a bookshelf.

I know the students are happy, but I hadn’t invented anything special.

Elisenda Feliu, mathematics professor

On the wall, however, is a four-metre-long black chalkboard — the preferred tool of mathematicians. They hate whiteboards, she explains, and are picky about their chalk. On a shelf is an almost empty box of extra-thick Japanese chalk.

»It’s the chalk of mathematicians. I don’t even have any of the bad stuff. It has to be good quality,« says Elisenda Feliu, adding that nothing beats the feeling of walking out of a classroom covered in chalk dust.

The nomination that earned her the prize states that the professor excels at connecting with students on their own terms.

The students point to Feliu’s deep commitment, her cheerful disposition, and her ability to empathise with them:

»Feliu is always up to date on the students’ other concurrent courses,« the nomination reads, »so she always knows how far along they are in their studies overall, and what it is that is the most important thing to focus on.«

Elisenda Feliu has flipped the traditional lecture-based teaching model on its head. She records theoretical lessons as short videos for students to watch at home. Then, when they meet for class, she uses the time to do blackboard exercises in a shared classroom setting. After that, the students work on exercises and discussions in smaller groups. In her experience, this approach makes the material stick better than just standing at the board explaining theory.

Back row in Barcelona

Elisenda Feliu grew up in Catalonia and studied mathematics at the University of Barcelona, where she also completed her PhD.

It seemed unlikely at first that mathematics would be her career path, she says:

»Maths wasn’t even a consideration when I was thinking about what to study at university. I looked at biology, chemistry, physics and other natural science programmes. At the time, I thought mathematicians lived in a world of numbers disconnected from society — and I didn’t want to be part of that. It was out of the question.«

A philosophy class in secondary school changed everything:

»It was like something clicked inside me. The idea of getting to the core of something, of learning things simply because they’re fun to learn — I liked that,« she says.

Shortly after, she showed up for her first mathematics lecture at university — quite different from the ones she delivers today.

»Completely traditional,« she says of the teaching, where a professor wrote on a blackboard in front of 200 students. It suited Elisenda Feliu fine. You could stay anonymous, hide away in the back row if that’s what your mood called for, and participate in the lesson when you felt like it.

There was a great sense of freedom in that kind of teaching, she says.

»If you wanted to go to class, you did. If you wanted to stroll down the Rambla instead, you did that.«

She has carried that sense of freedom and trust into her own teaching. The biology students get the solutions to all the exercises from day one.

»They should show up if they get something out of it.«

Back then, it was unusual for students to finish their degree on time, according to Elisenda Feliu, but she still managed it. And when she graduated, she didn’t want to leave the university or her friends, so she stayed on to do a PhD.

»There wasn’t some deep inner force driving me. I just wanted to stay in the community — and I wasn’t done with mathematics.«

Do Danes really talk like that?

In 2010, hopes of securing a research position in Spain were slim. The country had been hit hard by the European debt crisis. Elisenda Feliu was offered a six-month research stay abroad — she chose Denmark and Aarhus University.

She gave up her flat, packed her stuff, and left. When the six months were up, she got two postdoc grants that allowed her to stay in Denmark — first in Aarhus, then in Copenhagen.

She later began taking Danish classes, where she learned polite phrases for expressing disagreement. »I understand what you mean.«

This sounded a bit artificial, she thought — surely no one actually spoke like that in real life.

At a meeting with two departments present, she realised that Danes actually do speak like that.

»I was really surprised at how a dispute was resolved. A situation like that in Spain would have led to people talking over one another, getting angry, and lashing out.«

For the first time, she heard sentences like »I understand you« and »I can see what you mean« — things you rarely hear in Spanish lecture halls.

Danish culture suits her well:

»I like it when things work, and when things are communicated clearly,« she says, adding that she has always been a mathematically minded and highly structured person.

Students with maths baggage

The course that Elisenda Feliu is getting the teaching award for is what’s known as a service course: mathematics for biologists. For many of them, it’s their first encounter with equations since secondary school — sometimes even fractions need brushing up after a few gap years.

Many of the students have had bad experiences with maths and struggle to embrace the topic. They’re studying to become biologists — not mathematicians.

Elisenda Feliu knew, for this reason, that she had to approach the biology students differently from her maths students.

»With maths students, you build everything from the ground up. Everything has to be proven, and there are no black boxes. But for biologists, mathematics is a tool,« she says.

When Elisenda Feliu took over the course in 2014, she reached out to the Biology lecturers to find out what the students were struggling with. She completely redesigned the course so that it aligned with the students’ concurrent course in population biology, and made sure the connection was clear to them. They needed to see how they could apply the mathematics.

»I ask them to trust me«

Elisenda Feliu knows that many of the students struggle with bad experiences:

»I tell them it’s completely normal for your brain to freeze. It doesn’t mean you’re incapable of understanding.«

I ask the students to trust me. It will all make sense in the end.

Elisenda Feliu, mathematics professor

There are no cheat codes to understanding maths, she says. Unfortunately. The only way through is through — and mathematics is about repetition. Repetition, repetition, repetition.

She tells her students that there will be weeks when they don’t understand what’s going on. That’s completely normal, and they shouldn’t give up.

»I ask the students to trust me. It will all make sense in the end.«

Suddenly, it clicks — and that’s the best feeling of all, she says. When it happens, she can see it immediately.

»Their faces suddenly light up,« she says with a smile. »It’s wonderful to see. It’s heart-warming.«

One of her professors in Barcelona once described the experience as painting a black wall white — you apply layer after layer, and then suddenly it covers.

»In many subjects, learning is linear. But that’s not the case with mathematics. You have to accept that you’re working with something you don’t yet understand — and that’s hard. It takes something to keep going regardless.«

The upside of the pandemic

The major transformation in Elisenda Feliu’s teaching came during the COVID-19 pandemic in 2020, when she introduced a so-called flipped classroom — a mix of physical and digital teaching.

Before the pandemic, she often noticed students’ eyes glaze over during theoretical explanations. She had taken online courses herself and found them effective.

But as a self-declared introverted perfectionist, taking the plunge was daunting — and it wasn’t until the threat of a new lockdown loomed that she took the step.

»The idea of recording myself and speaking Danish in a video felt really uncomfortable,« she says.

»But when people started talking about possibly being sent home again in autumn 2020, I felt I had to do it — so the students could still learn the material, even if they weren’t allowed to come in.«

Even though the videos weren’t perfect, they worked so well that Elisenda Feliu kept them when society reopened. She noticed that interaction with students improved. There were more questions and fewer blank stares.

The pass rate also rose significantly:

»In recent years, it’s been around 93 per cent for the maths part alone — it used to be around 80,« she says.

Now she holds one lecture a week where she works through exercises on the board. The rest of the time, students attend exercise sessions and watch the videos at home.

»Most students are happy they can decide for themselves when and how they watch the videos.«

»We just want to do a good job«

One reason Elisenda Feliu has been named Lecturer of the Year 2025 is her passion and enthusiasm for teaching. But she’s keen to emphasise that she is far from the only one.

»I want to highlight the entire teaching culture here at the Department of Mathematical Sciences. We talk to each other a lot and inspire one another.«

She doesn’t recognise the stereotype that researchers would rather avoid teaching:

»We want to do a good job. We think a lot about how the students are doing, and how we can improve the teaching.«

Even after 15 years in Denmark and 11 years teaching the same course, she still finds teaching challenging.

»It’s hard to reach 180 students at once. That’s why it’s so important to be in a setting where teaching is valued.«

This article was first written in Danish and published on 14 November. It has been translated into English and post-edited by Mike Young.