**Author**: Bénédicte Leduc

**One eTwinning project**: Young Scientists Working Together

**Three partner countries**: France, Italy, Spain

**Four international teams**: Germain, Hypatia, Lamarr, Mirzakhani

With the outbreak of the pandemic in the world we often hear about “exponential growth”, “Rt factor”, “peak of contagions”. All these concepts, used in Medicine, are typical of Mathematics, which has become one of the most fashionable disciplines in recent times.

Actually, mathematical concepts are often used. Sometimes in informal contexts, speakers are not fully aware of the meaning of the terms they use and of the theories underlying them.

Therefore, it is important for students to learn in a critical and scientifically correct way which mathematical theories underlie the choices of governments, which are often not understood by the population that therefore, may not follow the indications adequately.

**Our methodology**

After several online meetings, we (the three teachers-partners involved in the eTwinning project) agreed to use Problem Based Learning Method for this challenging project.

Those who don’t know this teaching approach and its benefits, can have a look at

this article on Edutopia, where the methodology is introduced and the importance (and the difficulty!) of a good choice of the project’s driving question is clearly pointed out.

The goals were plural, let’s quote:

– make the students discover through the activities, their own researches, how mathematics are involved, used in different ways to apprehend and tackle the Covid situation we all experience.

– make the students work as four international teams, as they would do in an international research team.

– improve the students’ skills both in mathematics and English, the common language of the project.

We finally identified four issues to be treated by the students, which led us to propose them four driving questions.

**The four driving questions**

Here they are:

- What does “flatten the curve” mean? And how Math is helping?

- When must be taken measures to contain the spread of a virus? The importance of contact tracing and how to identify reliable indicators.

- Can we learn from the past? Can models of old pandemics be useful to avoid making errors and saving lives?

- How can we model the spread of the virus within a group?

Once the students were aware of the four driving questions, according to their interests and own sensibility, they naturally split into four international teams.

We were then ready to meet, teachers and students all together thanks to an online ice breaking meeting.

Note: at that time, the French students were at school, while their Italian and Spanish mates were at home, with online lessons.

**The ice- breaking meeting**

The ice-breaking meeting was organized in order to encourage all the 37 students to get to know each other, and begin to react as an international team thanks to different activities, that is to collaborate and communicate via a forum available on the Twinspace and created for each team.

After the introduction of the partner schools, the students were firstly invited to participate in a Mentimeter survey, in order to create a temporary but already collaborative logo for the etwinning project.

Here is the dedicated page on our Twinspace fort the Mentimeter survey results: Survey results

In a second phase, came the moment to choose a name for each international team, among a selection of female mathematician names were provided. After debating, each team came up with the name they chose for their group. My students worked the year before on a history and mathematics activity, centered on mathematicians, it was so easier for them to explain the name’s choice.

*All the visuals belong to the Author – Attribute CC-BY *

Here are the couples team/driving questions:

- the team that answered the Driving Question “
**What does “flatten the curve” mean? And how math is helping?**“, chose**Sophie Germain**, the French mathematician who contributed notably to the study of acoustics, elasticity, and the theory of numbers. She had to hide her identity as female, using a male pseudonym, Antoine-August Le Blanc, as women were still excluded from academic circles at the time.

- the team that answered the Driving Question “
**When must be taken measures to contain the spread of a virus? The importance of contact tracing and how to identify reliable indicators**“, chose**Hypatia**, because she’s been one of the earliest mathematician women in the world’s history. Also she was a philosopher and she studied astronomy and the members of the team want to give her the acknowledgement that she deserves.

- the team that answered the Driving Question “
**Can we learn from the past? Can models of old pandemics be useful to avoid making errors and saving lives?**“, chose**Hedy Lamarr**, who was an Austrian-American actress and inventor who pioneered the technology that is the basis for WiFi, GPS, and Bluetooth communication system.

- the team that answered the Driving Question “
**How can we model the spread of the virus within a group?**” chose**Maryam Mirzakhani****,**the mathematician dead in 2017 who became the first woman and the first Iranian to be awarded a Fields Medal.

In a third phase “an International teams competition” took place, prepared upstream (by another international team…the teachers’ team).

The members of each international group tried to correctly answer questions about the towns and regions of the partner schools. For those who live in the town to which the image refers, the answer was obvious, but it was not so for partners who live elsewhere. For this reason, the members of each group had to try to help each other by interacting on the forum, suggesting the correct answers to the partners. At the end, the international team whose members had obtained the highest average of correct answers would win.

Finally, some instructions were given to the students to prepare the first steps of their work:

- They had to upload photos on the Twinspace which altogether, will be a piece of the definitive logo.
- Each team had also to prepare a video according to predefined themes: “my surroundings”, “my region or my city”, “famous local people”, “cuisine and specialties”.

**Tools**

Intentionally, each team had to deal with a different approach to their knowledge of the curriculum, in order to create kind of a jigsaw.

However, each one had to use ICT* and web resources in a more conscious and active way, they were able to verify how the medical concepts we often hear about are supported by mathematics.

*ICT: mentimeter; video software; spreadsheet software; eTwinning Twinspace environment; Python; info graphic software…

The problem based learning approach helped them learn cooperatively:

- by helping to expand the classroom ;
- making it, therefore a great European class.

**Let’s work hands-on the analysis**

Each group had, as explained above, its own challenge. To help them collaborate within their international team, a devoted sub-page with the driving questions and a forum was created.

### The students were aware then that the final outcome would be an infographic poster, with requirement specification.

We gave some advices to help them “how to work”:

- Read carefully the
**driving questions**for their group-challenge. - Look for some relevant
**bibliographic material**. Don’t worry, we propose some interesting web, videos and documents for you. - Distribute the tasks within your team and share ideas using your
**team forum** - Use some collaborative tool to prepare the
**infographic poster**, - Keep asking their teachers if they had doubts or were stuck.

In order to monitor the status of their project, we asked them to keep a diary up to date. That means:

- Chose periodically the leader of their team (it had to be a rotatory role)
- That person was in charge of writing the task’s distribution, the achievements and the issues they were facing. It was their opportunity to explain how the members of their team were performing and if any changes were required.
- The teachers would read their progress there and would provide them with the required guidance to overcome those issues.

**Work Programme**

So that each driving question was easier to deal with, we suggested a work programme, divided in four or five tasks, with an expected achievement stept by step.

The French students worked mostly during their CLIL lesson.

I will share here the example of **Team Germain Page**

I created a site giving access to the four codes to fill in, using Trinket, in order to avoid the issues linked to the different versions of python that students could use.

Etwin_Science-project_YosWot_Coding

**Driving question:What does “flatten the curve” mean? And how Math is helping?**

**TASK 1 – Understand the different modelling strategies.**Read carefully the referent document: Etwin_YosWot_Python-modelling where the students could find an explanation of different models and how to implement them using Python.

Some videos to help them understanding the curves:

**TASK 2 – Summarize the referent document**Prepare a summary with the main ideas of the referent document.This material strongly helped them to deeply understand the document and to prepare TASK 4.

**TASK 3 – Code the 4 Models**Use the link at the end of the referent document to get the 4 unfinished Python codes. Fill the gaps and check that you obtain the proper results.

**TASK 4 – Prepare a video**Build a video (in English) explaining the main ideas behind the reference document and their modelling results.

**TASK 5 – Prepare the infographic poster**Use any collaborative tool.

**Four international teams, one single big class: experts’ videoconferences**

Students benefited from two very interesting and rich online lectures

These two visio conferences provided a new perspective with outside views, coming from two different worlds of expertise.

Firstly: Dr. Marinella Lavelli, pediatrician and expert in immunology, gave a lecture on “**Covid19: clinical and epidemic profile**“.

So that the lecture was easier to follow, Dr M. Lavelli:

- prepared a glossary for students, so they can better understand the concepts explained during her lecture:
- provided a pre-test for the attendees just before the conference.

During this webinar, Doctor Marinella Lavelli explained some particular features of COVID and the relationship of these peculiarities with the trend of pandemic.

SARS CoV2 is an emerging virus and nobody was immune. The high population density in some areas, like big cities, and the high travel frequency made rapide the spread of this virus all over the world.

Dr A. Cabaña’s lecture was organised around three points:

- the SIR model for epidemics (which was a key concept in Mirzakhani’s work for instance)
- What is the volume of the particles of SARS-COV2 in the world today? (a funny mathematical calculation)
- The incubation period.

This lecture allowed students to get in touch with Mathematics of higher level, through adapted explanations though. Let’s quote for instance, systems of “differential equations” ; lognormal distribution.

It highlighted the importance of modelling, thanks to mathematics, and the role of a model that, even if it’s not perfect, helps to understand and forecast tendencies and thus is an indispensable tool to make adequate decisions.

This conference was an opportunity to open students’ minds to new horizons. They have been able to understand how fields that apparently had no links were in fact intimately connected.

**Infographics**

In order to share their discoveries, students produced collaborative infographics, which are eventually to be accessible to teachers and parents, via for example, our school website in France, and visible in our three schools.

**Final step: Online meeting**

To happily conclude the project, an online meeting at which the four teams present and share their works and conclusions was scheduled.

**Partner teachers**

This eTwinning European scientific project was a great common work led by three enthusiast teachers, who gave a lot of energy into this common adventure:

Enrica Maragliano, Liceo Classico e Linguistico Statale “G. Mazzini”, Italy.

Elisabet Mas De Les Valls , Centre d’estudis Prat, Spain.

Bénédicte Leduc , Lycée Brocéliande, France.

*All the visuals, photos and screenshots belong to the Author – Attribution CC-BY*

A very comprehensive, informative, creative project! Congratulations!

Thanks a lot for your comment!

VERY GOOD JOB.

Thank you very much for your comment!

Very good job, Benedicte!

Thank you Enrica! It has been such a pleasure to work with you on this project.