Dana Hliněná: The best way to learn mathematics is through your own mistakes

Although the office of Dana Hliněná is located at the FEEC Department of Mathematics, she currently gives lectures to students of FIT as her department is responsible for teaching mathematics at FIT. The popular teacher is already looking forward to live classes and also to devoting more time to her favourite field of fuzzy logic.

She has decided to become a mathematics teacher when she was in fifth grade at primary school. She found her love for mathematics thanks to mathematic Olympics. "In my opinion, the problems solved at mathematic Olympics are better than those usually solved at schools, they give space to inventiveness and play even to children at lower primary schools. We had a perfect mathematics teacher at grammar school, she was like my maths mom with whom I am still in contact; she basically assured me that mathematics is my true calling," remembered Dana Hliněná.

Back then, she wanted to teach at a grammar school, so she studied mathematics and informatics at the Faculty of Natural Sciences of Matej Bel University in Banská Bystrica and, in 1995, she started working at the Sučiany grammar school. However, she was there only for six weeks. "There was a selection procedure for the position of an assistant at my faculty, so after six weeks, I returned and stayed there until 2002, when my first daughter was born. I believed I would never leave Banská Bystrica, it is a beautiful town with nice surroundings, I was content." But her Czech husband, who was also employed at the faculty, was feeling homesick and when he received an offer to work in Brno, they moved there in 2005 and Hliněná started working at the FEEC BUT Department of Mathematics.

"I have to say that I reconsidered my decision already during my studies and I was sorry that I chose teaching. If I had chosen a scientific study programme, I would have an easier time after graduation, but I hope I managed to close the gap," admitted Hliněná, who selected fuzzy logic as the subject of her research. Fuzzy logic differs from classic logic which only uses two logic values - true and false, usually represented as 1 or 0, in that it can operate with an infinite number of values lying in the interval 0 to 1. "Nothing is strictly black or white in the real life and it is fuzzy logic, which gives us a wider range of possible decisions. It can be said that it does a better job reflecting the real world," explained the mathematician. She had to put science on the back burner a little as she had to take care of her family, but, at the moment, she would like to fully return to the subject of her research.

As far as teaching is concerned, Dana Hliněná is one of the most popular teachers at BUT. In the most recent Best Teacher survey at BUT according to the Students' Evaluation poll, she ranked first at FIT in the Bachelor's studies category; previously, she repeatedly ranked among top ten. "I'm thrilled, but also a bit nervous. I'm afraid students' expectations regarding the subject will be wild, and then there will be me, explaining ordinary mathematics, not performing any miracles. So it is a responsibility." Being able to explain mathematics well and to keep students interested is essential; nobody will find their way to mathematics without that.

"During our university studies, we followed a strict approach: definition - theorem - proof, but this is probably not the best procedure for first encounter with university-level mathematics. For this reason, when teaching first-year students, I focus on explaining using examples and always try explaining the matter at hand from different points of view so that students can understand as best they can. So when I see (which was not possible during distance learning) they do not understand something, I try to approach the issue from a different angle," said Hliněná.

Although her office is located at the Faculty of Electrical Engineering and Communication, she, in her own words, only goes there to visit. That is because she is currently only teaching the students of informatics. "Another reason why I enjoy teaching them is because I studied mathematics-informatics myself, so it is closer to me. Thanks to that, I know in which areas of informatics the students may find practical use for mathematics." The experienced teacher still prepares for lectures, makes new assignments every year and each year starts from scratch.

There is no risk of falling in a stereotype as she no longer teaches some of her former subjects as they were replaced by new ones. What is the most important thing for a teacher during the lecture? "You need to be more interesting than the videos students watch during lectures," laughed Dana Hliněná. She believes that her students were able to cope with the Covid times fairly well. "I teach many first-year students and I also teach some elective courses for students in later years of their studies, but basically, I teach all mandatory mathematics courses for first-year students both during the winter and summer semesters. The first wave did not affect first-year students that much, during the second wave, they had two days of in-class lessons in the winter semester and then the school closed. But in the first year at FIT, there is generally an outflow of students, so it probably didn't really affect the mathematics courses. Distance learning is a much bigger obstacle for example for the Advanced Mathematics course, which is an elective course taught in later years of studies. When a course involves more complex tasks, it also requires a greater degree of interaction and such courses definitely do not benefit from distance learning," said Hliněná, who also stressed that in general, in-class practical seminars are very important in mathematics.

"When I'm showing students how I solve some problems, it is completely different than when they go to the blackboard themselves and for example make a mistake I didn't think of. That's how they'll learn, but during distance learning, they only learn from my mistakes - for example, I make mistakes in addition - but if I warn them that people do such and such mistakes at a certain stage and the students don't make these mistake themselves, it's not as effective. The best way to learn is through your own mistakes."

Dana Hliněná already had a timetable for the winter and summer semesters during the holidays. "I already know my courses start on 21 September and provided it is going to be in-class teaching, I'm looking forward to it. Although, I did tell my husband I probably don't know how to teach in class anymore after that year and a half. I don't know, I have to try. I hope I will not deter students as my goal is to make them like mathematics. Teaching is what I always wanted to do and I still enjoy doing it."