In 2024, I had the opportunity to return to a course that once defined the beginning of my own journey in science.
As a 19-year-old student, I remember sitting in a large lecture hall, trying to keep up as equations filled the blackboard faster than I could process them. Like many others, I struggled — not because the material wasn’t interesting, but because I never really got the chance to engage with it.
Fifteen years later, I found myself teaching that very same course — a large first-year calculus course with around 180 students.
And I decided to do something differently.
A simple idea: learning requires engagement
Instead of relying on traditional lectures, I redesigned the course around a simple idea:
Students don’t learn by passively receiving information — they learn by actively engaging with it.
This led me to introduce active learning strategies throughout the course:
- pre-class quizzes to encourage preparation
- in-class problem solving and peer discussions
- interactive lectures using digital tools
- and a strong focus on creating a psychologically safe learning environment
Importantly, I did not change the course content, the level of difficulty, or the structure of the final exam. The only thing I changed was how the material was presented and how students interacted with it.
What happened?
The results were striking.
Students performed significantly better on the final exam compared to previous years.
Engagement increased — more students completed the course and participated actively.
Student satisfaction improved dramatically across all evaluated aspects of the course.
But beyond the numbers, something else changed.
The atmosphere in the lecture hall was completely different.
Instead of silence, the room was buzzing with discussion. Students were asking questions, debating ideas, and helping each other understand difficult concepts. As a lecturer, I was often interrupted — in the best possible way — by students who were deeply engaged in the material.
Teaching is communication
This experience reinforced something I have come to believe strongly:
The core principles of good teaching are the same as those of good research — clear thinking and clear communication.
Many of the strategies I implemented were inspired by cognitive science and psychology:
- avoiding the “curse of knowledge” by carefully considering what students do not yet know
- giving context before content, so new ideas have somewhere to attach
- fostering psychological safety to encourage participation
- and using small nudges to support consistent engagement
At its core, teaching is not about delivering information. It is about creating the conditions under which understanding can emerge.
More than just mathematics
One of the most meaningful aspects of the course came at the very end.
Several students reached out with messages reflecting on their experience. Some mentioned that the course had changed how they approached learning. Others said it had influenced how they think about problem solving more broadly — even beyond mathematics.
There were also small, unexpected gestures: handwritten cards, flowers, and kind words of appreciation.
These moments meant more to me than any metric.
A piece of work I am proud of
This experience eventually became a pedagogical manuscript, where I documented both the methods and the outcomes of the course.
It is, without a doubt, the piece of work I am most proud of.
Regardless of the outcome of the review process, that will not change.
Final thoughts
Active learning is not a new idea. But in many areas of higher education — including mathematics — it is still far from standard practice.
My experience suggests that even relatively small changes in how we design and deliver courses can have a profound impact on how students learn, engage, and experience education.
If we want students to succeed, we should not only ask what we teach, but also how we teach it.
Because in the end, learning is not a passive process.
It is something we do together.
Johannes G. Borgqvist, PhD 
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