Success Stories

Open communication in education is not a given. It takes a long time to build, but it is worth it, says Iva Dřímalová, recipient of the Rector's Award for Outstanding Educators.

Celebrate Teachers' Day with an inspirational interview about how to teach mathematics to future teachers.

RNDr. Iva Dřímalová, Ph.D.

lecturer II
Department of Mathematics and Statistics

Iva Dřímalová graduated from the Faculty of Science at Masaryk University (SCI MUNI) with a degree in Mathematics and Physics focused on teaching. She obtained the degrees RNDr. (Doctor of Natural Sciences) and Ph.D. in the doctoral study programme of Mathematical Analysis. She works as a lecturer II at the Department of Mathematics and Statistics (ÚMS SCI MUNI), where she focuses on mathematics didactics and is preparing for habilitation in this field. She was awarded the Rector's Award for Outstanding Educators at MUNI in 2023, the Dean's Award at MUNI in 2022, the Student Chamber of the Academic Senate of MUNI (SKAS MUNI) Award for student involvement in teaching in 2019, and the Award of the Head of the Department of Mathematics and Statistics (ÚMS SCI MUNI) for both her bachelor's and master's theses. She is a member of the committee of the Society of Mathematics Teachers (SUMA).

Linear algebra is a subject that brings her joy. Photo: Irina Matusevič

In the last three years, the Rector's Award for Outstanding Educators has always been received by teachers of mathematics and statistics associated with the Department of Mathematics and Statistics at SCI MUNI. Last year, I conducted an interview with Jan Böhm, and the year before with Petr Liška. Why do you think you are so popular?

I believe we have kind and appreciative students who value our work. Both Petr Liška and I teach the same people, students of mathematics focused on teaching. They appreciate our work and approach and see the difference in approach in other programmes in their combination.

What do you think students value most about your teaching?

I think they appreciate being seen and accepted by us as individuals first and foremost. They say that their teachers at other faculties sometimes do not even realize they are teaching future educators. We have noticed, and they know it. We address them as future teachers. Personally, I believe they value the fact about me that I primarily teach them as human beings, and only secondarily as mathematics students. I truly pay attention to them and work with them as they should work with their future classes and pupils. What could be called my didactic belief, I put into practice in my teaching.

Students are often surprised when I ask them how they feel, why they might be struggling with problem-solving, and what I can do to help them improve. I am interested in their needs, work with them via dialogue, and actively create a safe environment in the classroom where I can talk to them as to people in the role of students and immediately follow up with a comment directed at them as future teachers: "Look how I did this and that now (for example, reflecting on your needs); why do I do it?" Truly teaching and not just delivering a monotonous lecture. I believe this is essential for teaching future educators. This way, I bring pedagogy, psychology, and didactics into practical teaching. I think students enjoy this approach.

Colleagues Iva Dřímalová and Eduard Fuchs from the Department of Mathematics and Statistics SCI MUNI. Photo: Irina Matusevič

You mentioned that doc. Eduard Fuchs from the Department of Mathematics and Statistics is a great inspiration for you, as he has long been devoted to mathematics education. In what ways?

Eduard Fuchs patiently guides me in didactics and facilitates contacts for me, even outside the university. He inspires me for many reasons. The longer and better I know him, the more reasons there are. Without him, I would be completely lost in mathematics didactics. For example, he introduced me to Associate Professor Helena Koldová from České Budějovice, who is the queen of didactics for me. Eda Fuchs is the person who keeps me going in many ways and gives me the courage to do things that some colleagues might say are total nonsense. He has always been a great figure for me, and I am grateful to have the opportunity to collaborate with him; I highly respect him. He always tells me honestly whether my idea is nonsense or if it is a good one. And if I happen to come up with something absurd and am about to leap in with both feet, he just patiently warns me without condemning me.

Eduard Fuchs also led you, among other things, to the idea of attempting to qualify for habilitation in mathematics didactics. Is habilitation in the field of mathematics focused on teaching common?

No, definitely not at our department. It is quite a difficult idea to accomplish. To become an associate professor in mathematics, one typically needs to publish quality research in impactful journals for years. An article I have been working on for a year will be submitted to a mathematics teacher's journal, which has no impact. Didactics is a much "softer" field than pure mathematics; it is more about opinions, more like social science than expert mathematics. My doctorate is from a different field, so I am still feeling my way around in didactics and gaining my first experiences with research in this area. We do not have a research assistant aspiring in the field of mathematics didactics at the department, and we have not had one for a long time. Over the past year and a half, I have been trying to juggle both teaching and this new direction in research. You can guess how it is going. But I am determined to keep trying for a while longer. And I am grateful to my colleagues for tolerating my efforts and for the support they provide me. I am still optimistic and believe that everything will turn out as it should.

Iva Dřímalová says that teaching seminars is primarily about communication. Photo: Irina Matusevič.

You mainly teach mathematics didactics and these other subjects. Do you build on the pedagogical-psychological foundation that prospective mathematics teachers must master?

I primarily teach seminar sessions for two fundamental subjects focusing on algebra and geometry basics in the first year of study. Students perceive these subjects as demanding. Students have a pedagogical-psychological foundation, but it is not subject-specific. Ensuring subject-specific orientation is our task. For example, in the "Inspiration for Teachers" course, which is an excellent course led by perfect people, students learn about a concept or method. They ask their pedagogy teachers how to apply it in mathematics. Often, the answer does not come. What we should do in subject didactics is take such a specific thing or method pointed out by pedagogy teachers and demonstrate it to them. So, when students theoretically learn about the "discovery method in teaching," I should arrange for them to actually try it on a university material. Ideally, this should be included in mathematics didactics. However, I manage to incorporate it into the first year of study as well. We should demonstrate specific pedagogical methods in real teaching to students. They experience the method; they do not have to know how to apply it in the role of a teacher—I am the teacher. Students then see the concrete impact of the method on themselves. After experiencing it, they form their own opinion. I include real teaching methods wherever possible. I use and comment on the use of formative assessment, work with students' mistakes, approach them individually, work with talented students, and reflect on their needs. The subject I teach allows for this, which brings me great joy. For example, when a student is at the board, I reflect on their performance; mathematics is in the foreground. Then I pause the mathematics, we observe and notice, and thanks to the pedagogical-psychological foundation, I can say " I am formatively assessing you because..." and the student should understand. In pedagogy, they hear that they should examine reasons why students are unsuccessful. In my classes, I can show them how to do it in mathematics. But until we demonstrate it directly to them, they cannot apply those very valuable well-explained insights and methods they learn in pedagogy. I would like us to establish a closer cooperation with teachers of pedagogical subjects; I think it would be a relief for everyone, especially the students.

In Iva's classes, students use a coloured traffic light system, little boats. Green means "I'm successfully sailing through, I understand everything," yellow means "I believe I'll get it in a moment, I'm close," and red means "I'm lost, I'm sinking." Photo: Irina Matusevič.

What is your new subject, Practicum in Teaching Mathematics, about?

It is about support, motivation, safety, and relationships among students. And, of course, about mathematics. I am very grateful that the faculty allowed me to introduce a new subject where I can train students in skills such as building a safe environment in teaching, and this is done through mathematics and real work with mathematical problems, not just in the realm of stories. It is an elective subject for students in the 2nd, 3rd, and 4th semesters, so it is for those most at risk of academic failure. The subject helps students persevere in their studies, get acquainted, learn to collaborate, work with their own and their classmates' mistakes, and figure out how to learn. How to survive in the mathematical world. And then, it is up to them.

Every week, we go through what the students had trouble with or what caught their interest in mathematics. For example: "The definition of a limit appeared, and I don't understand it at all." We work with the topics that students bring. I facilitate discussions, lead activities, set pedagogical goals, and ensure they are achieved. Students do not have to master this; it is enough for them to experience it. Students have the opportunity to "mess up" something completely and share how they feel about it. Talented students have a chance to shine. In a safe environment, they step into the role of a teacher for the first time in their lives. We work on homework problems that nobody can solve alone. I do not tell them how to proceed, but I guide them to help each other and solve the problem. The goal is to solve, not to find the solution. I only correct them when they go completely wrong. They usually arrive at the correct solution, although the path is often not only thorny but also sprinkled with burning gasoline. We function as a guided support group. It is something called a support centre at other faculties, and it is "in" now and will be in the future. Many schools are trying to introduce it but do not have the means. We do. I am grateful for that, and I hope the concept remains functional.

Lingebrosaur and tokens. Tools for motivating students to voluntarily solve challenging problems at the board. Lingebrosaur is the challenge mascot of the class. Tokens provide immunity against forced participation at the board. Photo: Irina Matusevič.

Do you also apply an individual approach to students in your teaching?

Yes, as much as my strength allows. As a teacher, I do not see any other option if I do not want to do my job poorly. Discussion naturally arises around individual work with students about justice, which is extensive and managed by didactics. In some situations, for example, I relieve students by telling them they do not have to go to the board to solve problems during seminars while most students have to. I assume they will take away from this experience that someone did something for them when they needed it in their specific (often difficult) situation. After a good and meaningful experience, they can allow themselves to do the same in their future practice as teachers. They can then discuss justice and individual work with pupils in pedagogical subjects; it is easier for them when someone actually applies this approach to them. They can get upset and set boundaries. They have something to react to.

I teach students empathy. I try to approach them personally, learn their names, I consider it important. Names are not my strong suit; I have been calling one Jakub "Michal" for the second year now, but I do what I can. And I also try to challenge everyone appropriately, so they do not get bored. I work with talented students as they should be worked with. I neither ignore them nor use them to degrade others. It took me years to learn this.

Why is empathy so important for you in teaching? How do you, as a mathematics didactics teacher, empathize with students focused on teaching to help them learn as much as possible?

I am sensitive to people's behaviour; empathy is the key to interpersonal understanding for me. The key to empathy is attentiveness and dialogue. In my teaching, mathematical content is completely in the background for me. Mathematics happens as it should, but for me, the people in the classroom come first. I observe how the class behaves, whether they communicate with me, who is active, who is not; and I focus on how to convey the material to them. It is not most important to arrive at the correct result but to reach it in a way that people notice what is happening. I make sure students are active because they learn primarily through their own activities. Teaching and demonstrating that I can solve something are two completely different things. We constantly communicate in dialogue; I am always asking them questions, carefully and purposefully choosing them, and creating a demanding and performance-oriented working climate for them. Students probably enjoy suffering because they are satisfied with it. They are fully attentive because they know I can ask anyone anything at any time. I teach them not to be afraid to answer: "I don't know." And despite the pressure, they like to come to class, at least a large portion of them. Functional communication and information that a student does not know the answer help me target the teaching where it is needed.

Why do you think teachers should share more of their feelings with the class­?

It does me a good service. In lessons with students focusing on teaching, we also discuss whether it is okay for the teacher to share their mood (in Practicum). As a teacher, I come and say, "I feel irritated, I don't know why. Today, I would need your help in teaching because otherwise, it will be worthless." And students usually forgive and help. We are teachers, humans. We are not machines. That is why I think it is important to be able to share to some extent our mood with students. Once I share that I bring a problem from somewhere else, students know that something happened somewhere else, and my strange mood is not their fault. When we learn to explain the reasons for our moods, students will better know where they stand. Sometimes I come to class completely "hyped up," enthusiastic and full of energy. I bring an amazing idea from my very limited perspective. I come and say, "I have an idea, it seems great to me, but you may not think so." But then they understand why I am so "hyped up." They laugh, "grill" the idea, learn empathy, openness, and vulnerability. Sharing my probably unjustified enthusiasm helps me not to leave the class disappointed in case of lukewarm reception. It helps me connect more with students, empathize with them.

What do you think teachers at Masaryk University should develop­?

I think that as educators, we need to advance in accepting diversity and be aware that simply following established procedures because “it has always been done this way” is not the only way. It is a question of how prepared and being prepared teachers are for diversity, for the arrival of transgender students, people with mental illnesses or special needs. Are we as educators prepared for the arrival of a new generation that has grown up with a smartphone in hand and a podcast in their ears? I do not think so. There is room for further development here. As a teacher, I want to set an example of how to accept diversity and how to communicate about this acceptance. It is often a struggle for me. There is not enough attention paid to the emotional and general needs of students. There are CERPEK workshops on various interesting topics, and teachers should learn to take advantage of these opportunities.

Why is open and non-violent communication important to you in teaching?

I perceive that many students are rather closed off. When they come to the first year, they are not willing to express their opinion, they are afraid of making mistakes, and they are nervous when they have to count at the board. There is a barrier of fear of non-acceptance. This fear prevents students from working and developing in mathematics. The absence of open communication does not lead to good results – never and nowhere. In open communication, I trust that my counterpart is interested in my opinion or performance and is trying to understand me without wanting to harm me. For me, this is indispensable in teaching. Open communication in teaching is not created overnight, it is a long-term process. It is hard but worth it. Non-violent communication teaches us to listen and respect each other. As a teacher, I also learn to observe and think more and to get less upset and cry over spilt milk. Students want to be heard and respected, just like us, their teachers. And appropriate communication enables that.

Students vote on the beauty of the completed example on a scale of green-yellow-red in the sense of 'I liked it very much' – 'I didn't like it very much' – 'I never want to see this again.' Photo: Irina Matusevič

How do you create a safe and respectful environment in your lessons?

Persistently, tirelessly, intensively, and thoughtfully:-D I am not able to describe it briefly. It matters to me that students do not fear making mistakes. When we aim to discover something in mathematics, making mistakes is an inevitable step in this process. When I am afraid of making mistakes, I do nothing; I sit and wait for someone to tell me the result. Then I quickly write it down and pretend like I knew it all along. Meanwhile, I am afraid and do not feel safe. I am tense, I do not feel good. And that applies to me as a teacher and to the students. I do not want that in the classroom.

Through various methods, I clearly communicate to students that it is important to me that they feel safe. I never insult anyone. Or at least I try not to, but sometimes even mathematics can be insulting, although you might not expect it. I work with mistakes the way mathematics didactics teaches us. We use a colour-coded traffic light system typically used in primary schools, but it works great in higher education too. Students vote on a three-point scale, for example, on whether they understand the solution to the problem on the board (scale: completely-a little-not at all, for example). I make it clear that I support mutual cooperation among students, often facilitating it directly. And I often do fun nonsense; that breaks the ice perfectly. Absurd experiences bring students together. The algebra itself, which I teach, seems absurd to students. It is not that difficult to take it to entertaining extremes. Shared suffering brings people together, and being closer helps them feel safe. Mathematics is an excellent tool for causing suffering. Just use it, and the climate builds up like a dream.

You share your enthusiasm for mathematics didactics with high school teachers. How?

My closest connection is with my husband, who teaches mathematics at a high school. Otherwise, I do not have much of a connection to high schools yet. I am slowly building it up because I will be leading some workshops for high school teachers, so I hope to get honest feedback on my ideas there. I created a webinar for elementary school teachers, but that was a one-way road. I have a frequent contact with teachers at conferences, where I try to come up with didactic contributions to build relationships with teachers. Conversations with teachers at conferences are a big benefit for me.

How do you relax after work?

I have a bit of a bad counterbalance to demanding teaching – my performance hobby. Sports. During my short career at MUNI, I did CrossFit, then weightlifting, but I had to quit because I kept getting injured. Lately, I have been learning not to destroy myself through my hobby; it is a long process, and I occasionally stray from the path. I enjoy walking in the woods with a podcast in my ears and my dog running around in the swamp; I just have time for myself. I consider it a success that I finally learned to notice when I am tired and take care of myself. I am learning to relax. I started my lecturing position with a fresh doctorate and two young children. A doctorate in mathematical analysis with two little boys spaced a year and a half apart was like a walk in a rose garden, rainbows everywhere, of course. It is like a steep run downhill. Slowing down is hard work; I still relax with effort. I feel like I am still running. The university psychologist helped me slow down.

How does your visit to the psychologist at MUNI relate to your agenda as a preventive specialist for academic failure?

This agenda led me to my first visit to a psychologist in my life. And it was a good experience. The agenda is mentally demanding, especially if the preventive specialist is truly in contact with students who are struggling. Students confide in me about their plans for suicide, discontinuing their studies due to depression, anxiety, and similar issues. And with many other study-related problems. I do not know if they are lying to me or telling the truth. But I have to react, advise, and refer them to a specialist. That is a burden I have to bear, and it is easier not to do it alone. It is also a consequence of my communication style with students. I know how to react; we have a manual. I listen to the initial story even if it is not my job to solve it. It is quite a burden on a non-psychologist. Some questions are not answered by the manual, not taken care of. That is why I sought supervision. I would appreciate a more comprehensive care for preventive specialists, for example, more funded sessions (currently there are 3 per career, or at least that is my impression). A workshop from CERPEK would be nice. But I believe the university is still learning to deal with this agenda, and time will bring what is needed. It is good that the agenda was created.

This interview is published on Teachers' Day. What would you wish for all teachers?

That they find a career path where both they and their students feel good, that they enjoy going to work and sleep peacefully at night. Everyone.

What would you wish for future teachers whom you teach?

That they find joy in their studies, that they do not just “mess around”. That their studies make sense to them. And that they enjoy going to future work and leave as functioning human beings, not as exhausted wrecks, because it is easy to devote everything, all your time and energy, to the teaching profession. I wish my students to find balance as soon as possible after starting their careers. And if they are running downhill, I hope they can slow down without getting hurt.

Thank you for the interview.
Zuzana Jayasundera

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