Maths modelling and pandemic understanding
Mathematics has become a “trendy” science in this pandemic period because people finally realised how mathematical models are useful for understanding reality and helping to prevent difficult situations. By now, we are all used to hearing expressions like “exponential growth”, “Rt factor”, “peak of infections”: all these concepts used in Medicine are typical of Maths. Sometimes, however, in informal settings, people are not fully aware of the meaning of the terms they use and the theories that underlie them.
Some European teachers, therefore, decided to ask their students to collaborate remotely to study what lies behind the concepts they see on TV and read in the newspapers. Also, to learn in a critical and scientifically correct way which mathematical theories are at the basis of the choices of governments: often these decisions are not understood by the population, which probably also, for this reason, does not adequately comply with the indications.
The schools that worked on the project were Liceo Classico e Linguistico G. Mazzini (Genoa, Italy), Cité Scolaire Brocéliande (Guer, France) and Prat Educació (Barcelona, Spain), which collaborated in the project “Young Scientists Working Together”, involving students aged between 16 and 18.
The Maths curricula in the three partner schools are quite different and students’ backgrounds were diverse. However, all curricula include exponential functions and this concept was defined as the axis of YoSWoT’s mathematical analysis. For all the involved classes, the project was part of their Content and Language Integrated Learning (CLIL), and for the Italian students, it was also important for the PCTO path (Percorsi per le Competenze Trasversali e l’Orientamento).
Before setting up the project, the teachers, who had never worked together before, met online several times to plan the activities and agree on times and activities to be carried out.
The Project Based Learning (PBL) approach was used in the project and the students, organised in four international teams, were asked to tackle a driving question each on which they worked from January to April, supported by the teachers who helped them socialise and start collaborating.
The teachers, after brainstorming, identified these driving questions for the international teams:
- What does “flatten the curve” mean? And how Maths is helping?
- When must measures be taken 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?
As a first step, teachers organised a start off video-conference to put the students in contact: the international teams had to interact in various activities (Mentimeter brainstorming linked to the PBL driving questions end choice of logo, discussions aimed to the choice of team name among some famous female scientists and collaboration to solve a quiz with non-googleable questions about partner schools’ towns). In this way, all the students were actively involved in their learning process from the very beginning: for instance, the logo was created using the background image set up as a mosaic with pictures posted by students about their school, town, hobbies or linked to the project’s topic.
Each team had to deal with a different approach to their knowledge of the curriculum, in order to create a kind of a jigsaw: in this way, they learned to work cooperatively and, at the end of the project, they became one great European class.
To scaffold students to interact and come up with a common answer to their driving question, teachers prepared for each team steps aimed at improving scientific awareness on one hand but also at encouraging interaction and mutual aid on the other. Some teams worked very well from the beginning, while some others had to warm up and be more supported in their work: they had to produce as a final outcome an infographic poster, with the specification of the acquired knowledge and the reasoned answer to the initial driving question.
Teachers gave some advice to help students about “how to work” such as:
- Read carefully the driving questions for their group challenge.
- Look for some relevant bibliographic material: teachers proposed some interesting websites, videos and documents, but the international teams could find something interesting and suitable to their purpose by themselves too.
- Distribute the tasks within the team and share ideas using the team forum
- Use some collaborative tools to prepare the infographic poster,
- Keep asking their teachers if they had doubts or were stuck
Students benefited from two very interesting and rich online lectures, aimed to provide them with a new perspective with outside views, coming from two different fields of expertise:
- Dr Marinella Lavelli, paediatrician and expert in immunology, gave a lecture on “Covid19: clinical and epidemic profile”.
- Dr Alejandra Cabaña, Professor of Mathematics at the Universitat Autònoma de Barcelona, Coordinator of the Bachelor’s Degree in Applied Statistics gave a lecture “An elementary tour through the mathematical modelling of Covid-19”.
These conferences were an opportunity to open students’ minds to new horizons: they could really understand how fields that apparently had no links are in fact intimately connected.
In order to share the results of their job, students produced collaborative infographics, which are accessible to teachers and parents and the outside community. On each page of the TwinSpace, students also provided a summary of what they wrote in the Google.Doc files, which, together with the TwinSpace forum, were the places where they exchanged the information and made decisions.
To conclude the project, a final online meeting was held: the four teams presented their results discussing successful aspects and pending works. Not involved teachers and stakeholders attended the meeting, asking questions to the teams about their work. As the last part of the learning process, all the pupils challenged themselves in a Kahoot! game, useful to the teachers to informally test students’ knowledge.
One of the objectives of the project was empowering women: gender aspects were considered in the decision of team names, in the lectures given by experts and by showing the many girls involved they could undertake STEM careers in their future.
For the students, it was very important to understand how mathematical models are useful in everyday life, as evidenced by this pandemic situation. At the same time, their participation in the project allowed them to become more responsible and informed citizens, get used to checking the sources of information and not believing fideistically in what is often published on social networks.
Furthermore, students developed and consolidated transversal skills, such as the ability to work remotely in a foreign language with peers they have never met, the conscious use of ICT and the awareness of other educational realities. They also managed to mitigate the negative feelings due to the confinement caused by the health measures implemented by governments to fight the pandemic. All the information about the project can be found on the project’s TwinSpace at this link: https://twinspace.etwinning.net/139113/home
About the authors:
Enrica Maragliano is a Maths and Physics teacher and a passionate eTwinning and Scientix ambassador. She likes trying new teaching approaches for her students so that they are challenged and learn many soft skills, not only in her subjects’ but also in cross-curricular topics.
Benedicte Leduc is a Maths and CLIL (mathematics and sciences in English) teacher, also intervening in continuing education. She appreciates working collaboratively, trying new teaching approaches at any scale, from her school to the stimulating eTwinning environment.
Elisabet Mas de les Valls is a STEM teacher in Barcelona, Spain. She is interested in showing the human side of STEM and thus engaging students. She loves creating experiences that emphasize the contributions of science and technology to our society. Her challenge is to combine these cooperative experiences with the deep work of helping students to feel comfortable when solving individually a calculation in front of a white piece of paper.
Great article Enrica!