SPECIAL NUMBERS

Among the necessary mathematical knowledge and skills in daily life, natural numbers, their properties and the relationships between these numbers, the operations performed with these numbers, the properties of the operations mentally skills have an important place.  Considering that mathematics education starts with counting and that I have numbers at every stage of mathematics education, exploration studies and projects can be made in this way for students in mathematics education.  Transferring number relationships to real situations is the basis for starting to make sense of the world in a mathematical way.  The world of mathematics offers a wide variety of number types, all of which have their own characteristics.  Mathematicians formulate theories about the relationships between numbers and number groups.  The most well-known special numbers among numbers are as follows,

  1. If there is a more interesting number than Pi, it is two Pi.  In other words, it is twice the Pi.  This number, known as the Tau number, has a value of approximately 6.28.  While pi relates the circumference of a circle to its diameter, tau relates the circumference of a circle to its radius, and many mathematicians argue that this relationship is much more important.
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Living on my Moon. Sustainability 4 future

This Learning Scenario concerns future sustainability on the Moon. It is structured for students of middle school (11-13 years old). They will image the future life on the Moon and the right behaviour for the correct use of water, air, food, waste in their hypothetical future homes and their hypothetical future vehicles for mobility. In this way, all students build knowledge on basic features of the Moon, and they are involved in laboratory activity through design thinking. They work in groups in cooperative learning, in fact, they are called to project, to design in group 3d models of their own lunar home on and own car lunar sustainable model with online tools like Tinkercad (https://www.tinkercad.com/), Cospaces (https://cospaces.io/edu/), Minecraft Education Edition. So they can compare their knowledge about the environmental sustainability of Earth and provide alternatives for the Moon on mobility, buildings, waste, air, water, food and cultivation.

In this LS students develop key skills (21st-century skills), improve digital skills concentrating on an awesome topic of aerospace. At the end of the path students in groups will have to produce 3d lunar sustainable models; they will have to produce some presentations, with slides, video, VR/AR tour, printed 3d models. These presentations will have to be in the English language and founded on the basic features learned on the topic of the Moon. In the end, students are involved in a debriefing test for a self-assessment. In the pictures is possible to view some models 3D designed with Tinkercad; all students have worked in the team from their own homes during the pandemic time. In other words, in this Learning Scenario technological tools, environments and devices have allowed (and will allow to all people that want to try building a similar activity based on design thinking) the creation of relationships and communications capable of enriching the experience of simultaneous sharing of physical space.

Young Scientists Working Together

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.

The logo’s YOSWOT project collaboratively created

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

The four international teams

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

Different types of resources have been used

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”:

  1. Read carefully the driving questions for their group-challenge.
  2. Look for some relevant bibliographic material. Don’t worry, we propose some interesting web, videos and documents for you.
  3. Distribute the tasks within your team and share ideas using your team forum
  4. Use some collaborative tool to prepare the infographic poster,
  5. 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:

  1. Chose periodically the leader of their team (it had to be a rotatory role)
  2. 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.
  3. 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. Alejandra Cabaña’s lecture

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. 

Infographics from team Germain and Hypatia
Infographics from team Lamarr and team Mirzakhani

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

AERO-Learning Scenario Habitat on the Moon

This learning scenario aims to teach students some basics about the Moon. By designing, students will experience STEM, learn the Moon subject in the Life Sciences curriculum. Also develop their research and design skills. Airbus Foundation Discovery Space videos were used in the learning scenario.

Keywords
Moon, Atmosphere, Design, Life, Exploration

Integration into the curriculum

Observations of the moon are integrated into the National curriculum. This topic is one of the main topics of the course. The moon aims to provide general information about it. Students are expected to observe the moon and learn its structure.

Aim of the lesson / Learning Objectives
This learning scenario; It aims to teach students to observe the Moon, to teach basic knowledge about the
structure and properties of the Moon. It enables students to design and create a poster about the moon to
establish a living space on the moon.

Results of the lesson
At the end of this course, the students. Will be able to explain the properties of the moon. They will create a living space on the moon.He prepared a poster about the moon.

Trends

STEM: Science, Technology, Engineering, Art and Mathematics will be taught together.
Design Thinking: is a process for creative problem solving.
Poster: Preparing a presentation with student information.
21st century skills and Creativity / Design Thinking / Inquiry-Based Science Education
Depending on which series you are working with, we encourage you to focus on these pedagogical topics:
Creativity: Students use their creativity in living space design.
Critical thinking: Students use critical thinking processes such as reasoning, analysis, evaluation across videos and their research.

Collaboration: Students collaborate while creating posters and making presentations.
Innovation: Students design an innovative material for life on the Moon.
Problem solving: Students solve a problem according to the instructions given to them.
Communication: Students communicate with each other during the poster preparation phase.
Productivity: Students produce by preparing a design and a poster.

Moon, habitat design

All the visuals belong and were provided by the Author – Attribution CC-BY

Teacher’s remarks
The course was applied online. There were no problems during the process. Successfully implemented.

Combating Climate change

Teaching in current times

The new situation caused by the COVID-19 pandemic has brought big changes in the teaching in the virtual classroom compared to the usual teaching. Online teaching has set new requirements for the rapid implementation of ICT and the integration of digital technology without time to learn about the possibilities and principles of using a particular web tool. The question of choice, approach and way of working arises. Teachers quickly set out to select the appropriate technology for teaching activities and certain groups of students while achieving the planned educational outcomes and expectations of cross-curricular topics.

Time to contribute in solving global problems

As part of the school course Socially Responsible Business, students of the 2nd grade of the profession economist with their teacher Nada Ratković, prof. mentor participated in many national, European and international projects solving global problems the world’s most important challenges: climate change. Through the school year students are participating in national projects „E-student for a greener tomorrow“, EU project „Students actions-Fighting climate changes“, eTwinning project „Breathe deeply & Think clearly“, international projects „Climate Action project“ and „SDG goal project“. The projects are significant because they can be presented for any general education and vocational subject. Every age, topic and school requires a different approach and gives students the future they deserve.

eTwinning project “Breathe deeply & Think clearly”
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