We need to tell students that they’re great more often, says Petr Liška, holder of the Rector's Award for Outstanding Teachers.
Mgr. Petr Liška, Ph.D.
Department of Mathematics and Statistics
Petr Liška joined the Faculty of Science MU Mathematics and Physics Department in 2004, with a focus on education. However, when he realised that he had not been adequately trained in triple integrals and partial equations in secondary school, he switched to Mathematics and Descriptive Geometry. He successfully completed his studies in 2010 and started his Doctoral studies in Mathematical Analysis, where, under the guidance of Prof. Zuzana Došlá, he devoted himself to the qualitative theory of differential equations. He has been teaching at Masaryk University since 2007, and he has been a lecturer at the Department of Mathematics and Statistics since 2020. In his lectures, students really appreciate his empathy, flexibility and human approach, which helps them understand even the most demanding and less popular mathematical areas.
Photo: Irina Matusevich
Peter, you won the Masaryk Rector’s Award for Outstanding Teachers at the end of 2021 (click here for our report), so congratulations. Tell us, how did you win the prize?
I must say in advance, I’m not sure that I’m that excellent an educator that I really deserve the award! Nevertheless, it was mainly based on student voting, and I think it helped that I taught a great bunch of future teachers for several semesters. And then there were probably more votes from the Faculty of Informatics MU. I also teach there and the students seem to be satisfied with me.
The text of the award states that the students you teach appreciate your empathy, flexibility and human approach, which helps them to understand even the most demanding and less popular mathematical areas. How do you put these personal "skills" into teaching?
Unlike most of my colleagues, I don’t go to class thinking that I want to do perfect mathematics; after all, I’m not a perfect mathematician. I want the students to understand the material and to enjoy the lesson. Of course, the mathematics must be of a high level; however, especially when teaching future teachers, I try to show them what the material I am explaining is for. I don’t use any unique methods or loads of study materials; instead, I try to be accessible, to understand that they don’t understand the substance of the problem, and explain it to them.
When you say "understand that they don't understand", how do you do this? Do you try and put yourself in their position and look at the topic through their eyes? Is that even possible?
It is possible, but it’s getting harder and harder. The older I get and the more I explain the topic, the less I understand what students don’t understand, and I am beginning to lose patience with age. I may be able to explain theories and terms, but I just don’t understand that they are not able to count; that they don’t get enough practice in basic mathematics at secondary school. I have come across this more often lately and it’s almost certainly due to distance learning.
In addition, as soon as I stop talking about mathematical terms, definitions and proofs in the lecture, I feel that the students sometimes ‘switch off’ and fail to notice that it is actually important 😊. But I am still working on my teaching style and I still think about how best to explain things…but it can be a fight.
Usually, I know when students don’t understand the material. Sometimes, I have time to take a bit longer explaining a problem, but sometimes not, unfortunately. It was easier for me when I was just a tutor and the students and we were all in the same boat when we had to take an exam with a lecturer. But now that I’m the lecturer, I can hardly be in the same boat against myself 😊.
Please, tell me why you think students describe you as having a "human approach"?
That’s a good question. I guess it’s because I’m not afraid to make fun of both myself and them. I have my favourite jokes, and we can have fun. Sometimes, it happens that we talk more than we count. And I can still understand that sometimes they can’t do something, I can forgive them for that and I’m sure they will get it next time. I just see them as human; after all, to err is to be human. I’m not unnecessarily "tough", which is sometimes a mistake, but after all, that’s what a human approach involves.
How is this human approach reflected in tests?
I am in a luxurious position, in that I am mostly teaching future teachers. My goal is not to make them first-class mathematical scientists. It is not entirely about accuracy, but about understanding the substance. When it comes to "derivation", the most important thing is that they know what it’s good for, and that they understand it in general. I also try very hard to make our field fun. At the faculty, we try to make them into top experts, but in the end, they they stop liking the subject, which is sad because our faculty is often the first choice for applicants.
Do you mainly teach student teachers?
Yes, I mainly teach future teachers, especially in my Bachelor’s degree in Mathematical Analysis. Then I also teach Differential and integral calculus at the Faculty of Informatics in the Autumn, and then I teach one subject, Dynamic systems, as a specialised mathematics course at our faculty. There is always a bit of mathematics, then I will immediately show a specific model and plenty of evidence of what it is good for. I also lecture at Mendel University, where mathematics is used in the fields of International Territorial Studies and Regional Development. There, the students are "non-mathematicians", and in this case, the main thing is to show them that mathematics is a problem-solving language, and to show them the problems that can be addressed (and solved). In mathematics, if we want to understand something, we must get familiar with it and practice, practice, practice - and sometimes that can be annoying 😊.
Are you in contact with any of your former students?
I am in contact with graduates of our teaching courses. I try to get feedback, both on my subjects and on the study of the field as a whole. I ask them what helped them in practice and what they lacked. They are not always enthusiastic about everything, but fortunately they remember my subjects in a good way. Although I mostly teach vocational subjects, I try to show them some overlap in style. This is not possible to teach in secondary school, but because of this overlap, they understand the topic, or I can at least show them what works in our world. I teach them that the extra information is certainly useful, and that’s something the students appreciate.
I will now return to our first meeting in 2010, when the faculty won a large project, thanks especially to Prof. Zuzana Došlá, then vice-dean for external relations. Thanks to this, many innovations were introduced into our faculty’s teaching programs. You were a project manager and I did public relations for the project. What did this project mean for you and how do you perceive the changes that were introduced into teaching future teachers at the faculty?
I was a fresh graduate, a man full of ideals, young and irreconcilable. I proposed several things for the project that I thought would be good to introduce or change; however, not everything went as well as I’d hoped. Ensuring disciplinary interconnection, for example, which is just difficult in practice. Nevertheless, the project instigated a lot of good things. It established the first step to increasing the number of hours set aside for teaching experience, and optional subjects were added. New subjects were also established that are still on the curriculum today, such as what the students now call "subjects from classroom J". These are subjects that develop "soft skills", such as working with group dynamics, communication training and “brain storming” sessions for teachers. Some of these subjects are very popular.
You can read more about the project here, on the Learn to Learn website, a project that was designed to provide inspiration for future teachers, and that still provides information and inspiration today.
What do you think would be good to do for future teachers at the faculty? What do you think is missing?
In my opinion, we don’t spend enough time telling students how great they are. It’s not encouraged here. When a person comes to the MU Faculty of Law, for example, they tell them that they have entered a prestigious school and that they are great. But teaching students are even better, and no one tells them this. They have chosen a difficult field with two professional subjects, and on top of that they take a pedagogy/psychology course, a state degree and a difficult graduation exam involving two professional subjects, two didactic subjects and pedagogy/psychology. And now I don’t know how to say this right, but we don’t seem to show them enough respect. In many courses, people don't really know that the student teachers are there. For some, they are "less clever" than students of classic vocational studies. But they are experts in two subjects, and we don’t tell them how great they are. My students were completely blown away when I told them. They should hear it more often, and be prouder of themselves, because graduating from a teacher training degree course is a challenge.
I think we discourage many students by putting too much pressure on their expertise. Some leave part way through their studies, and some complete their studies, but they all say “they won’t go on to teach at a secondary school because they have the impression that they aren’t up to it professionally. So, we reduce their self-confidence to the point that they prefer to do something else or teach at a primary school because they feel bad about themselves.
And how do you think teaching students are helped by subject didactics, i.e. lessons where they learn how to teach specific subjects?
Here, too, I think the same applies, i.e. not to try and make teaching students into super experts. We should understand that it is a future teacher in front of us, and we should concentrate more on didactics. And we can do it; we can improve how we teach specific fields and topics, how to do it differently, more interestingly and how to connect subjects. Then again, there are some legal that we can’t change, such as completely change the subjects, introduce six-months of teaching practice, etc. But what we can do is value the fact that someone wants to study didactics. This is in line with the new concepts introduced this year for the education of future teachers. So, we shall see what happens.
As part of this project, the pedagogy/psychology course also began to change in 2010. How do you think this will develop?
Some changes have already been made. The problem I see is that it’s not very well thought out; for example, the faculty employs lecturers for certain subjects from other faculties, such as the Faculty of Arts and Faculty of Education MU, and sometimes the topics overlap. They are taught the same things on different courses. On the other hand, this is gradually improving as teachers communicate with each other more. In addition, they study “general didactics”, which means there are many things that cannot be used in mathematics at all. And we are coming back to the fact that there is a lack of support for the subject-specific didactics, and that it is not well connected with the pedagogy/psychology course. In our case, the didactics of mathematics means ‘this is how you do it”. But how to teach it? How to make the interpretation more interesting? What methods to use on this and that topic? What should the motivation be? But this is not dealt with enough. Students that then go on to teach may be less prepared in this regard than students from the Faculty of Education MU. They may not be experts in mathematics, but they know how to teach better. We offer few model procedures for teaching something, and graduate teachers must then discover everything as they teach. We spend a lot of time trying to turn out experts in the field, while in other countries, the focus is on teaching skills. I think it should be somewhere in the middle. I perceive this from the reactions of our students.
How do you find ways to explain complex and often very abstract topics?
I think about each lesson in advance, and then after each lesson I think about whether it worked out. I try to work on myself. This year, I also signed up for several workshops organized by CERPEK; I became a member of the Community of Future Teachers; I learnt to think about things I haven’t thought about before, and I deepened my pedagogy/psychology skills. But early on, I was most inspired by an online course at MIT called “How to teach college level science?”. On the course, they emphasised that teaching should be a "story"; the interpretation should go somewhere, it must be interesting. For example, in dynamic systems, there is a "predator-prey" model that arose when a marine biologist noted there were fewer fish after the war, which was strange as there had been no fishing during the war. At least that’s what he thought. He was dating a mathematician’s daughter at the time and the three of them talked about this over dinner, and the mathematician came up with the model. So, in a similar way, I try to include a story at the beginning of the topic. When we make a model, I don’t start with an example; instead I say, “this is a model of love”, and everyone starts thinking about it because suddenly they’re interested.
Do you work with student feedback?
Yes, I’m trying. Recently, I prepared my own questionnaire, which asked about things other than the survey subject. Probably the strongest thing I learned from this was when a student wrote that she understood that teaching students were not the sharpest pencils in the box. We all know this metaphor, but she developed it and wrote that it would probably be better if we tried to sharpen them, rather than break them. Well, I like to be the kind of teacher who sharpens pencils rather than breaks them, so maybe I’m not doing so bad after all.
Peter, thank you for the interview and I wish you well.