Mathematics and Biology Between Germany and Mexico. Interview with Maite Wilke Berenguer and Adrián González Casanova

Today’s well-known Collaborative Online International Learning (COIL) —a form of virtual exchange effectively expanding around the world— brings together pedagogical practices, remote interaction methods and incresingly accesible technological tools. There are times when collaborative processes among scholars happen without them being aware that similar experiences are taking place elsewhere or even without them knowing that the universe they are exploring go by the acronym of COIL in academic analysis and planning. That is the case of the collaboration experience between Adrián González Casanova from UNAM Institute of Mathematics, located in Cuernavaca, Morelos, and Maite Wilke Berenguer from Humboldt University in Berlin. Both of them will tell us about their work together.

Adrián González Casanova has developed mathematical models used in the study of the biology field of evolutionary adaptation. Maite Wilke, a population genetics expert, applies mathematical models to the understanding of evolutionary dynamics when interacting with other areas; thus, their dialogue on the basis of their backgrounds came “naturally”, as Adrián says.


Carlos Maza: How did you come about with the idea of engaging in a collaborative teaching process?
Adrián González Casanova: Maite and I have studied and worked together for quite some time. Since we were both in Berlin, we developed strong collaboration links and published about ten articles together. When I returned to Mexico, I invited Maite over, so she has met my students and has worked with some of them. We spontaneously thought of taking on another project together.


CM: Tell us more about your trajectory, please, about the award you received for your essay on mathematical models application to the study of living beings evolutionary behavior.
AGC: There is an incredible experiment, the Lenski experiment, by means of which he and his team tried something relatively simple. They put Escherichia coli bacteria in a minimum glucose medium; the simplest medium there is. The bacteria eat all the sugar, they took a sample and put it in a similar medium again; they have been doing this experiment for thirty years. The bacteria get used to the stress, learn the game of living in a “happy world” of sugar, receive food every day at the same time, so it adapted to the experiment. The incredible thing about the experiment is that they are using now “fossil” samples —so to speak— from the thirties because they froze the flasks back then and when they remove samples, the bacteria “revive” and start eating again. So, they can compare the degree of adaptation of the bacteria today with the day-zero sample. They put them to compete and they obtain a figure.

It’s fascinating because what animal has better adapted, a cat or a dog? Those are not the right examples for this question. But in the case of these bacteria, we do assign a number to their degree of adaptation to this particular medium. Then, we tried to understand mathematically the relative fitness curve, to what extend the bacteria learn and adapt. In 2016 we published the article (see chart 1) including a model on how relative fitness should increase. Then we received the Itô award because the work was welcomed by the community, with the exception of some people —including Lenski— who thought we were going too far on our reasoning and had no data to back it up.

We then modified the model to make it more data friendly and we saw that, indeed, our thesis went a little bit far. But there is to say that our model had its pros since we incorporated data and it could be interpreted better. For the second article we wrote, we received the 2022 Feldman award of the Theoretical Population Biology journal.


CM: As for you, Maite, what has been your experience in the scientific field?
Maitw Wilken Berenguer: I did a “math diploma” as it is called in Germany, that is the equivalent to both, the bachelor and the master degrees within the same academic program at the University of Berlin. Then I started a doctorate in probability. It was rather theoretical, and at some point, I got tired of working with only one person. Then, I got lucky that Adrian’s group welcomed me and took me in and we did a research article together. From then on, Adrian and I began to collaborate, and in fact, my career changed a bit because I moved from theoretical probability to population genetics, where I finally stayed.
When Adrian got his job at the UNAM Institute of Mathematics, he invited me over to Mexico and I spent almost three months. It was a very productive time. We also did independent collaborations. Since then, I have been to Mexico in four occasions; the last one was just the week before Germany closed borders due to COVID-19. I returned from Mexico in early March 2020. We had already a fairly intense collaboration work, both visited each other on regular basis. Adrian also came to Berlin and, meanwhile, we communicated by email and develped each other’s projects. During the pandemic, everybody suddenly discovered Zoom and we found a new way to keep working together with its many advantages.


CM: At DGECI in UNAM, we are extremelly interested in the advantages of online collaborative learning in reaching a greater number of students who can benefit from this system.
MWB: Adrián and I talked about the pandemic, the courses available in the population genetics area and how getting grades jointly could be done so that our students could take advantage of our various strengths. In the middle of the pandemic, we increased our working together. All courses, both at UNAM and in Germany, moved to digital mode and Adrián came up with the idea of delivering our subjects simultaneously. In this way we also brought together our students groups.

There are two main advantages when using this format; first, the students have the chance to meet teachers from other places, with different teaching styles and maths-teaching methods. Secondly, it can be done in a way that allows students to get into contact and interact and this is a great advantage.


CM: Is it like having students from two groups in the same room?
MWB: We would have loved to achieve so. One of the questions is actually how to do it. The fact that we are all attending the same Zoom classroom, listening to the same person, doesn’t mean that the students are going to interact. The teachers need to search for mechanisms to be included in the class so that students can also interact.


CM: What mechanisms did you find to motivate students to engage with each other?
AGC: We tried to organise them into groups to do the tasks and exercises we proposed. The groups were made of students from both countries. We may need to improve it and think it over. A couple of students interacted very well, but many others stayed in their own corner, “on their side of the Atlantic” let us say.


CM: Are there other disadvantages in the virtual environment compared to face-to-face traditional way?
MWB: I believe it’s always harder to interact with students online than in a regular classroom. In the classroom, if students work in groups, I can go from group to group, and even if I’m talking to one group, I can see and hear what the others do. This also works on Zoom with a group. I can come in the group room, be with them and they know I’m watching, but I can’t see the rest of them at the same time. So, this is another limitation. But by using this format, we have a way to join classes transatlantically that otherwise we will not be able to do, so we must find solutions for working by this means.


CM: Have you had any institutional support to develop your collaborative project? Have you received any help from your respective academic authorities?
AGC:The honest answer is that they’ve given me all the support I’ve asked for, but I haven’t asked for any support at all [laughs]. It worked for me because I registered the course in the master’s program within the syllabus and, collaboration emerged along through the course, but I did not involve other people.

MWB: We delivered the course during my very first semester of work at Humboldt University
(I had just joined the university), so I still had no contact with the institutional structure. The real help was to have the freedom to choose the schedule, a requirement for this type of courses, as well as in terms of the classes distribution. The amount of class hours varies from country to country during the week or the semester; when the semester starts and ends may also be different. We coincided for most of the academic year, but we were a little bit outdated. So, we had to organize ourselves to give a class at the beginning and make sure the group that started a little later would not miss it.


CM: ​​​​​​​In addition to the schedule and calendar differences, we had to deal with coexistence issues, according to specialists. When students travel to another country, they learn much more than what the regular course or program does offer. Online collaboration works differently. What are those differences? How does your personal experience develop along the online course beyond the syllabus?
AGC: I think there’s still a lot of work to be done creating projects that encourage collaboration beyond the task. We have to think about how we are going to encourage the exchange, but, in our experience, I think this first attempt has had its benefits. The students saw people from the other side of the Atlantic, at the Humboldt University of Berlin, who are not that different from them. There is always a fear of “What am I learning? Am I learning at our level here or theirs?”, or “I’m a very good student here, but would I be very good also there?” Well, these concerns somehow vanished and I think that for some students who later on would want to do a degree or doctorate course in Germany, this experience would be very useful. They already have an idea on how the courses are like overthere, how people are, for example, how the oral exams are since it is a very common way of evaluation in Germany. The first time I submitted myself to an oral, it was terrifying. There is a less traumatic way of finding out; talking to their peers over there, they can realize about their strengths and weaknesses in maths.


CM: ​​​​​​​Evaluations also poses questions to be solved in this type of collaboration, how do we evaluate the two groups? Are they working in coordination with each other or does each of them respond to different criteria and evaluation systems? How did you evaluate them afterwards?
MWB: Everyone evaluates their group in the way they would have done it if the students had taken the course just at their university. Universities have very different requirements or procedures for evaluating careers courses. We didn’t have an issue in this regard because we delivered our classes making sure that students were ready to undergo the final exam. There was no issue at all.

AGC: In my view, it was an asymmetrical situation because on the Mexican side, we basically evaluate student’s written works. Maite corrected many of them, in somes cases her opinion was crucial. In the German side, they had a classic oral exam where I did not participate (although I contributed with some comments).

MWB: In their case it was rather a matter of the Humboldt University rules. I have to be the one who makes the exam but another person from the institution, a neutral character, takes notes; so Adrián would have never had the possibility to attend the exam. Those are just the rules in order to complete the task.


CM: Did you previously discuss the contents of each course in relation with the syllabus?
AGC: Yes, we develop them in coordination with each other. There were differences in terms of the school calendar. In Mexico we resume classes a month earlier than in Germany, so we gave a much more extensive introduction to Mexican students. The German students went almost inmediately into the research part.

MWB: Our groups were not homogeneous, that was a challenge. The courses the students in either country had taken before were different, so we had to adapt. I think we were flexible during the course, paying attention to the missing information so we provided it on the go. The fact that courses were outdated or calendars mismatched also helped because we delivered part of the content at the beginning. The course in Germany lasted a little longer so we were able to complete it at the end by combining them.


CM: What language did you use in class? how did you cope with this obstacle?
AGC: We did it in English but Maite speaks Spanish perfectly and we established that they could make questions in Spanish and German. Fortunately, no one asked in German.

MWB: Adrian is not saying that he is fluent in German.

AGC: In general, we used English, except for some Mexican students who spoke with Maite in Spanish out of class. Whenever we were all gathered, we all used English.


CM: ​​​​​​​Did it last the whole semester? Could you address the semester’s subjects as a whole?
MWB: Yes, of course.


CM: ​​​​​​​Have you thought about organising a real-life meeting? We at DGECI are proposing that teachers develop COIL courses and then, organise one course or a summer program where students from the participating universities meet in person (a hybrid model that combines the virtual amp; the face-to-face). Have you given some thought about it? or do you think it could be feasible and interesting?
MWB: We believe this is a simple and accessible way to develop the international area. Getting to have the two groups meet would be great, but funding is the problem. We cannot ask students to finance such a trip. They may think we are demanding a rather difficult condition for them to be in. In fact, we wanted to include as many people as possible. If funds were made available to finance this kind of meeting, I would think it would be great. I think it would add value to the course.


CM: Maite has mentioned an important issue related to academic and student mobility. Most students face those limitations and the virtual exchange offers an inclusive way of exchange. As teachers who have developed this collaborative working experience, what would you think that the university to which you belong should do to foster it?
AGC: I believe that calendar differences pose a challenge. We were able to overcome the gap because of the very conditions that existed then. In math postgraduate studies, you cannot start a course whenever it fits you. There is no way to “change the semester a little bit” and look for the possibility of doing intensive and shorter courses and try to synchronize both countries timing. That kind of support should come from the Graduate Studies Division; we could not just start whenever it was convinient for us.

Furthermore, we can dream of the idea of bringing students together which may become the top of going international, experiencing the adrenaline of being in a foreign country, listening to the language, trying the food, in short, that kind of things that is so important and does not happen online. Being flexible is also important. I don’t believe that the way Maite and I work together is how Germany and Mexico should develop it. Challenges are different in this scenario and teachers should be allowed to make choices in unexpected and unknown situations.

MWB: It worked for us probably because due to the pandemic everyone was forced to take online courses. There were pros and cons. Students are required to have the technical infrastructure to attend the course, devices and a stable internet connection. I believe that online international courses can also be fostered by providing the technical infrastructure within the university.


CM: Appart from Zoom, what other tools did you use or what other means did you work with?
MWB: We used Moodle, which is the German universities system, Google Classroom and Zoom. Students could send written papers via email and we also used Overleaf, the Latex collaborative platform, a math protocol. If students had a tablet, they exchanged views and worked together in writing. One of the aspects we would like to improve next time is to provide more time for the students’ work together and we will have to look for the right tools.


CM: What would you suggest to teachers like you who would like to take on this kind of online collabaration?
AGC: I would advise them to try on. It is a different experience with unforeseen challenges. I think that we are going to refine the course by delivering it over and over. In my view, the first experience was not perfect, but it was a first step to go on building a strategy. It is not the same as giving a class in the room over and over. If you think you are in control, you are not. It is different.

MWB: I believe that the work relation Adrián and I had previously contributed to the kind of course we did. We knew each other and had done other projects before. I have attended some of his classes and viceversa. So, I think it was easier to prepare a course together having this background.

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