When the Mat1A course coordinators at DTU Compute received the students’ evaluation of the autumn semester in December, they were delighted: the students were highly enthusiastic about the course. Whereas motivation previously hovered around 3.7 on a five‑point scale, it has now risen to 4.0, and the students gave the course 4.6 out of 5 for their learning.
At the same time, the lecturers have observed that the physical lecture halls are once again full, and that students are engaging more actively with the material.
We believe this development is linked to a deliberate return to mathematics as a conceptual discipline, with hand calculation using pencil and paper as a didactical tool. In this way, students develop a more conceptual understanding, while computer‑based tools take on a less dominant role. This appears to have significantly improved both motivation and learning outcomes,” say the course coordinators, Head of Section for Mathematics Peter Beelen and Teaching Associate Professor Ulrik Engelund Pedersen, who, incidentally, was voted Teacher of the Year at DTU in 2025 for his teaching in Mat1A.
First hand calculation, then the machine
Previously, Mat1 was highly machine‑oriented. In 2023, DTU transitioned from the mathematical software package Maple to Python, triggered by the new principles laid out in DTU’s Polytechnical Foundation.
Since then, computer‑based problem‑solving has gradually been adjusted both in teaching and in examinations. The new teaching design means that students first work with hand calculation on new mathematical concepts, and only afterwards employ Python and other digital tools, which still play a substantial role throughout the semester.
“As an example, only a few years ago we could give them a quadratic equation and when they would find three different solutions they would conclude: ‘Well, there are probably three.’ Today, we work at the level of explaining how many roots a polynomial actually has and why. This kind of conceptual insight has been moved to the center, and we have succeeded in teaching them this better – something many believed was no longer possible. It is a while ago, since students could master such things. This is the mathematical understanding we have tried to bring back into the course,” says Ulrik Engelund Pedersen.
Pen and paper also solve the challenges posed by AI
Solving exercises and sitting exams using pencil and paper also has the advantage of addressing the challenge posed by artificial intelligence.
“We could see that students had begun to use AI, but in an unhelpful way: they solved the problem with it and did not really care whether they understood anything. And I must say: if you do not know what the problem is really about, it is much more difficult to assess an AI‑generated answer,” says Ulrik Engelund Pedersen.
“If, however, you understand the concepts, you can more readily see whether something is wrong. That is why we emphasize that students must know the fundamental concepts, because they will use AI for everything once they finish here.”
Students are flocking to the auditoriums
Peter Beelen and Ulrik Engelund Pedersen highlight that motivation has risen from an average of 3.7 to 4.0, which is very high compared with previous years.
When they speak to colleagues, all lecturers mention three persistent challenges: getting students to attend teaching, read the course material, and remain motivated.
“I would say that with the new concept there is substantial improvement on all three fronts. I do not have figures for how many read the book, but I receive many questions about it. And there are now quite a few students attending lectures – so many that we need three auditoriums (42, 41 and 43 in 303A), all of which are full most of the semester,” says Peter Beelen. “In earlier years, after three to four weeks we could easily gather everyone in a single auditorium because fewer turned up,” says Ulrik Engelund Pedersen.
“We believe this is linked to the problem‑solving sessions, where teaching assistants help them with pen-and-paper‑based exercises. And they know they need to master this for the exam. Moreover, no student has complained about using pen and paper. In fact, they quite like it.”
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